1Forces and Motion - Richmond ELT · Unit 1 Forces and Motion 5 Observe and Question 1 Read the...

4 Pathway to Physics

1 Forces❯❯Unit

and Motion

Forces and Motion at an Amusement Park

An amusement park is an exciting place. Peop le s t and in long lines

for the jolt of colliding bumper cars, a ride on their favor i te rol ler coaster, an exhilarating free fall from the top of a tower or the simple pleasure of going around in circles on a carousel. But did you know that amusement parks are also huge physics laboratories?

Look at the photos. Have you ever been on one of these rides? All of them are built with a basic understanding of Isaac Newton’s three laws of motion, and the effects of forces such as friction, inertia and gravity. Some of these forces involve contact, and others act at a distance. Speed, acceleration, energy, mass and moments are all at work in amusement parks and are an important part of what makes the rides so much fun. These concepts will be looked at in depth in this unit.

When objects are in motion, they experience a number of different forces, all of which are simply either pushes or pulls. On a roller coaster, for example, it is a motor that starts the roller coaster moving, but it is not the motor that powers it at high speeds throughout the entire length of the ride. Instead, the motor pulls the roller coaster

up to the top of the fi rst hill; the rest of the trip, including the

loops, is powered by the energy of position that

the cars have gained from their height. Gravity does most of the work as the roller coaster’s energy of position is changed into energy of motion

and back aga in . Inertia—the tendency

of objects to resist changes in their motion—

keeps the riders pressed against their seats as the roller coaster

travels around the loops. And friction is the force that gradually slows the roller coaster down on the tracks. So next time you’re enjoying a ride at an amusement park, think about the various forces at work that make it possible.

Key Wordsforce (n) – a push or pullthat changes an objectin some way, such as itsmotion, the direction of itsmotion or its shape friction (n) – the force that makes it hard for one surface to move over anothergravity (n) – the force that causes objects to be attracted to one another; the force that makes things fall to the groundinertia (n) – the resistanceof an object to a changein motionmotion (n) – the action of movingspeed (n) – how fast something moves

Key Concepts ❯ A force is a push or a pull that may cause a change in an object’s motion. ❯ Some forces, such as friction, act on contact, and others, such as gravity, act at a distance. ❯ Forces can make an object start or stop moving, or they can change its shape. ❯ Motion is a change in position or place and occurs when something moves. ❯ Isaac Newton discovered three laws that relate force, motion, acceleration, mass and inertia.

❯❯Unit

❯ The force of gravity causes a roller coaster to move around a track at high speed.

❯ Amusement parks are huge physics labs!

❯ Bumper cars change speed and direction as they hit each other.

Pathway to Physics unit 1.indd 4Pathway to Physics unit 1.indd 4 11/4/14 4:26 PM11/4/14 4:26 PM

Unit 1 Forces and Motion 5

❯ Observe and Question

1 Read the text, the key words and the key concepts and answer the questions.

a. Draw a picture of your favorite amusement park ride. Label the parts of the ride where you think gravity, inertia and friction are at work.

b. Give examples of the following forces at work in everyday life.

Friction:

Inertia:

Gravity:

c. In what situations is friction useful? When is it not useful?

d. What effect does gravity have on objects on Earth? Give examples.



❯ Topic

ay to Physics

Testing a Homemade Shooter

Key Wordsaction-at-a-distance force (n) – a force that acts on an object without being in contact with itcontact force (n) – a force that exists between two objects that are in contact with each othermass (n) – the amount of matter that something containsnormal force (n) – theforce that the ground (orany other surface) pushesback up withtension (n) – the state created in a rope, cable, chain or similar object when it is pulled tight

All forces are, essentially, either a push or a pull. When you are riding a bicycle, for example, the force from your foot pushes

the pedal down. This push then changes to a pull by the chain on the sprocket of the rear wheel. The wheel then pushes against the ground and makes the bicycle move. An object at rest does not move unless a force is applied to it. As the mass of the object increases, so does its inertia and the force required to start it moving. Once in motion, the object will continue moving until a comparable force makes it stop. Again, an object with a large mass has more inertia than an object with a smaller mass, so a greater force is required to make it stop.

Forces can be defined as interactions between objects, and can be classified either as contact forces or as noncontact forces, commonly known as action-at-a-distance forces.

Contact forces occur when two objects are physically in contact with each other.

Examples include friction (the force exerted by a surface as an object moves across it), tension (the state produced when, for example, a rope is pulled tight from opposite ends) and normal forces (when a cup is on a table, for example, the table exerts an upward force—the normal force— to support the weight of the cup).

Action-at-a-distance forces are forces that occur even though the two interacting objects are not in direct physical contact with each other. Gravitational forces are perhaps the most well known example—the sun and planets apply a gravitational pull on each other despite the fact that they are very far apart. Magnetic forces and electrical forces are two other examples of action-at-a-distance forces. Two magnets for instance, exert a magnetic pull on each other when they are apart (magnetic force), and the protons in the nucleus of an atom and the electrons outside the nucleus similarly experience an electrical pull toward each other (electrical force).

Objective Defi ne a force and describe its effect on an object

Key Concepts ❯ A force is a push or pull. ❯ Forces can make objects start or stop moving. ❯ Forces can also change an object’s shape. ❯ To make an object go faster, the object needs a bigger push. ❯ The mass of an object determines how much force is needed to change its motion.

1

What Is a Force?

pedal

chain

wheel

sprocket

1. Your foot pushes down on the pedal.

2. The chain pulls on the sprocket.

3. The tire pushes against the ground and the bicycle moves.

❯ In a tug of war, each team applies a force—in this case, a pull—on the rope.

clude friction (the force exerted e as an object moves across

n (the state produced when, e, a rope is pulled tight from ds) and normal forces (when

d to change its motion.


Unit 1 Forces and Motion 7Unit 1 Forces and Motion 7


1 Read the text and answer the questions.

a. Look at the photos and answer the questions.

What force moves the needle of the compass?

________________________

What force makes it diffi cult to push the weight?

________________________

What force is exerted between the book and the table?

________________________

b. Write an example of each type of force.

tension:

gravitational force:

electrical force:

c. Describe a situation in which you have felt the effects of force.

❯ Research

Supplies

❯ balloon ❯ plastic cup ❯ scissors ❯ adhesive tape

❯ mini marshmallows ❯ measuring tape ❯ ruler

Procedure

1 Make a marshmallow shooter.

a. Tie a knot in the neck of the balloon and cut about two centimeters off the top of the balloon. Cut the bottom off the cup.

b. Stretch the balloon over the cut end of the cup so that the knot in the balloon is in the center. Secure the balloon to the cup with tape so that it doesn’t come off the cup when you pull on the knot.


Pathway to Physics 8

2 Do tests with your shooter. Try to keep the angle of the shooter the same on each test.

a. Place a marshmallow inside the cup so that it rests on the knot in the balloon. Point the cup away from you and others, pull the knot back and release it so that it shoots the marshmallow out.

b. Repeat the test, this time pulling the knot two centimeters before releasing it. Record the distance the marshmallow travels in the table below. Repeat this two more times and record the results.

c. Repeat the test, this time pulling the knot four centimeters before releasing it.d. Repeat step b using two marshmallows.e. Repeat step b using four marshmallows.

3 Calculate the mean distances: add the three distances for each variable together and divide by three.

Results

1 Record the results in the table.

VariableDistance (cm)

Test 1 Test 2 Test 3 Mean

2-cm pull with 1 marshmallow

4-cm pull with 1 marshmallow

2-cm pull with 2 marshmallows

2-cm pull with 4 marshmallows

❯ Analyze

1 Answer the questions.

a. What force causes the marshmallow to shoot out of the cup?

b. Did the marshmallow fl y farther when the balloon was pulled back two centimeters or four centimeters? Why?

c. Why do the two marshmallows fl y farther than the four marshmallows?

2 Explain the concept of a force and give an example.



❯ Topic 2

Forces operate in conjunction. Balanced forces are equal in size and opposite in direction. They do not cause changes in motion (speed

or direction) or in shape. These forces cancel each other out. A good example of a balanced force is an arm-wrestling contest between two equally strong wrestlers. The force exerted by each wrestler is equal, but because they are pushing in opposite directions, the wrestlers’ arms don’t move.

The same is true in an equally balanced tug of war. Both teams are equally strong, and neither team can move the other. These actions can be illustrated with a force diagram. The arrows indicate both the size of the forces and the direction in which the forces act.

The force diagram for the wrestling match between equal partners looks like this:

Because the force exerted by each arm wrestler is equal but in the opposite direction, the net resultant force is zero.

The force diagram showing the action between two equal teams in a tug of war looks like this:

Here, as with the arm wrestlers, the forces are equal in size and opposite in direction. The net force is also zero, so there is no change in motion.

Another example of a balanced force is an object resting on a table. Its weight (the force exerted on its mass by the downward pull of gravity) is balanced by the upward push of the normal force. Without the normal force, the object would sink through the table, and we would sink into the ground.

Unbalanced forces result when the forces acting on an object do not cancel each other out. Unbalanced forces always result in a change in motion, a change in direction, a change in shape or a combination of these. Forces in opposite directions combine by subtraction, while forces in the same direction combine by addition. A tug of war with different numbers of people on each side is an example of unbalanced forces at work. Another example is a child on one side of a seesaw and an adult on the other. The adult exerts a greater downward force, so the child moves upward.

Balanced and Unbalanced Forces

Balancing ForcesObjective Examine the effects of balanced and unbalanced forces on an object

Key Concepts ❯ When more than one force acts on an object, the forces combine to form a net resultant force. ❯ Net resultant forces can be balanced or unbalanced. ❯ If the combined effect of the forces does not cause an object to move or to change its speed, direction or shape, then the forces are balanced. ❯ If one force is stronger than the others, the forces are unbalanced and will cause a change.

Key Wordsbalanced force (n) – a net resultant force that does not cause a change in motionforce diagram (n) – a diagram showing the forces acting on an objectnet resultant force (n) – the combined effect of all the forces acting on an objectunbalanced force (n) – a net resultant force that causes a change in motion

❯ The forces between these arm wrestlers are balanced, so the arms don’t move.

❯ The forces are balanced between the two dogs in this tug of war.





a. Label the arrows on the diagram: smaller force, larger force. Is this an example of a balanced or an unbalanced force? In what direction will the truck move?

b. Explain the difference between a balanced force and an unbalanced force.

c. Write an example of a balanced force and an unbalanced force that you see every day.

❯ Research

Supplies

❯ 3 balloons ❯ large paper clips ❯ hair dryer

Procedure

1 Prepare the balloons.

a. Infl ate the fi rst balloon one-third full and tie a knot. b. Infl ate the second balloon half full and tie a knot. c. Infl ate the third balloon completely and tie a knot.

2 Work in pairs. Do an experiment to balance the upward force of a hair dryer with the downward force of gravity on a balloon.

a. One student holds the hair dryer facing vertically upward and turns it on.b. The other student tries to balance the fi rst balloon above the airfl ow, adding paper

clips below the knot if necessary. c. Record in the table on the next page how many paper clips you added.

3 Repeat the experiment with the other two balloons.



Results

1 Record the results in the table.

Number of Paper Clips Requiredto Balance Balloon

Small Balloon Medium Balloon Large Balloon

❯ Analyze


a. What force is being produced by the hair dryer?

b. What force(s) are acting on the balloon?

c. Which balloon required the fewest paper clips to balance the forces? Explain.

d. Which balloon required the most paper clips? Explain.

e. Draw and label a diagram of the balloons and the number of paper clips needed to balance the forces.



❯ Topic

Key Wordsclockwise (adj) – in the same direction as the movement of the hands on a clockcounterclockwise (adj) – in the opposite direction to the movement of the hands on a clocknewton (n) – the unit of measurement for forceperpendicular (adj) – at a 90 degree angle to somethingpivot (n) – a fi xed point that something balances or turns on

Balancing Moments

The moment or torque of a force is the turning effect it has around a pivot. A moment, for example, causes a door to turn around its

hinges instead of traveling in a straight line. Now, if you close a door by pushing on its handle, it doesn’t take much force. But if you push it next to the hinges, you need a lot more force.

The ability of a force to make an object turn—the force’s moment or torque—depends on two things: the size of the force and the perpendicular distance from the pivot (the hinge in the door example) to the place where the force is applied (where you push the door). The size of the force is measured in newtons (N), and the perpendicular distance is measured in meters (m). The moment is calculated by multiplying these two numbers together and is expressed in newton-meters (Nm). So, to calculate the moment needed to close the door, you measure the force you apply to move it and the distance between your hand and the hinge.

Like the forces we saw in the previous topic, moments can also be balanced or unbalanced. A seesaw provides good examples of these. When you sit on a seesaw, you apply a downward force, and the seesaw turns around the pivot. If your friend sits on the other end, she also applies a downward force, but the moment of the force is in the opposite direction. If you both weigh the same, the moments are balanced, so the seesaw does not move.

Now, imagine your friend gets off and a

man gets on instead. The man is heavier, so he applies more force. The moments are no longer balanced, so the seesaw moves down at his end. If the man moves closer to the pivot, however, the moments balance again.

Another example of rotation caused by a moment is seen when you tighten or loosen a bolt with a wrench. If you apply force at the end of the wrench, it is much easier to loosen the bolt than it is if you try to move it with just your fi ngers. This is because the wrench allows you to turn the bolt at a greater distance from the pivot, so the moment of force is greater.

Objective Defi ne a moment (torque) and calculate the moment around a pivot

Key Concepts ❯ A moment is the capacity of a force to cause an object to rotate around a fi xed point (called a pivot), such as a door opening or closing around a hinge. ❯ The amount of a moment depends on two factors: how much force is applied and the distance from the force to the pivot. A hinged door, for example, can be opened or closed with less force if pushed farther from the hinge than if pushed closer to the hinge. ❯ A moment is measured in newton-meters (Nm) and is calculated by multiplying the amount of force (in newtons) by the perpendicular distance from the pivot (in meters): moment = force x distance, or M = Fd.

3

1212

Moments and Seesaws

❯

Here the clockwise and counterclockwise moments are unbalanced: the forces are an equal distance from the pivot, but the man applies more force than the girl.

❯

Here the clockwise and counterclockwise moments are balanced again: the man applies more force, but he’s also closer to the pivot.

❯

Here the clockwise and counterclockwise moments are balanced: the forces are the same and at an equal distance from the pivot.





a. Look at the diagram. F is force and d is the distance. Is the seesaw balanced or not? Explain how you could prove your answer.

b. Imagine you spin a bicycle wheel, fi rst from near the axle and then from near the rim, each time with the same force. When does the wheel turn more easily? Explain how the distance to the axle affects the moment of the force.

c. A wrench is used to unscrew a bolt. A force of 30 newtons is applied to the wrench at a distance of 15 centimeters from the center of the bolt. Draw a diagram and calculate the moment in newton-meters.

PivotCounterclockwise

2F F

d 2d

Clockwise



❯ Research1 Watch Video 1 about balancing moments. Then prepare your supplies.

Supplies

❯ 100-gram masses of modeling clay ❯ cardboard tube ❯ scale accurate to 100 grams ❯ meter stick

Procedure

1 Do an experiment to see how moments are affected by force and distance.

a. Set up the equipment as in the diagram below. Place a 100-gram mass of clay at the 40-centimeter mark on the left-hand side of the meter stick.

b. Place another 100-gram mass at the 60-centimeter mark on the right-hand side so they are perfectly balanced.

c. Calculate the moment for each side of the meter stick and complete the fi rst table in the Results section.

d. Add another 100-gram mass on top of the mass on the left. What distance do you need to move the mass on the right to balance the stick?

e. Calculate the moment for each side and complete the second table.

f. Add another 100-gram mass on top of the two masses on the left. What distance do you need to move the mass on the right to balance the stick?

g. Calculate the moment for each side and complete the third table.

❯ You can test the relationship between force, distance and the amount of a moment with a simple seesaw.



Results

1 Complete the table with the moments from the fi rst part of the experiment. Use the graph paper for your calculations.

Left Right

Force (N)

Distance (m)

Moment (Nm)

2 Complete the table with the moments from the second part.

Left Right

Force (N)

Distance (m)

Moment (Nm)

3 Complete the table with the moments from the third part.

Left Right

Force (N)

Distance (m)

Moment (Nm)

❯ Analyze


a. What two factors does the amount of a moment depend on?

b. Based on what you did, explain what a moment is in your own words.

c. Can you think of any other real-life examples of moments?

Force (N) = mass (kg) x 9.8 (m/s2—from gravitational acceleration)100 g mass = 0.1 kg0.1 kg x 9.8 = 1 N (approximately)



❯ Topic

Objective Create a spring scale with an elastic object

Key Concepts ❯ An elastic object resumes its original shape after it has been stretched or deformed. ❯ When a spring is stretched, the increase in length is called its extension. ❯ The extension is directly proportional to the amount of force applied and to the spring constant, which is a measure of how stiff or fl exible the spring is. ❯ The relationship between force, spring constant and extension is expressed by Hooke’s Law: force = spring constant x extension, or F = ke. ❯ Force is measured in newtons (N), the spring constant in newtons per meter(N/m) and the extension in meters (m). ❯ If a spring is stretched too much, it reaches its elastic limit so will not return to its original length.

Key Wordselastic (adj) – (of a material or an object) able to resume its original shape after stretching or compressingelastic limit (n) – the extent to which an object can be stretched without permanently altering its size or shapeextension (n) – the increase in the length of somethingspring constant (n) – a measure of how stiff or strong a spring is

An object is said to be elastic if it springs back to its original shape after it is stretched or compressed. If you stretch a

rubber band and then release it, for example, the rubber band springs back to its original shape or length. If you stretch a paper loop, by contrast, it just breaks. Likewise, if you drop a piece of bread on the fl oor, it does not bounce. This is because bread is not very elastic. But if, instead, you drop a basketball on the fl oor, it bounces back up. As the ball hits the fl oor, the air inside it is compressed; this compressed air forces the ball to spring back into shape, which pushes the ball back up again.

When an elastic object, such as a spring, is stretched, the increased length is called its extension. The extension of a perfectly elastic object is directly proportional to the force applied to it. If you apply a small force to a spring, it will stretch only a small amount. If you apply a large force, however, the spring will stretch more. These observations can be expressed using Hooke’s law, F = ke, where: ❯ F is the force in newtons (N). ❯ k is the spring constant in newtons per meter (N/m). ❯ e is the extension in meters (m).

The spring constant varies for different objects and materials and can be calculated by carrying out an experiment. First, the spring is measured without any mass, or load, on it. Different masses are then added to the spring and its new length measured

each time. The extension is the difference between the unloaded spring length and the loaded spring length. The equation for Hooke’s law works as long as the elastic limit is not exceeded. The elastic limit of a spring is reached when it is stretched too much and does not return to its original length after the force is removed.

Assuming the elastic limit is not exceeded, a graph of force against extension produces a straight line. The slope, or gradient, of the line is the spring constant (k).

Not all elastic objects conform to Hooke’s Law, however. If the extension of an object is not proportional to the force applied to it, the object is not perfectly elastic, and its Force–Extension graph is not a straight line.

Elasticity and Hooke’s Law

Making a Scale4

formed.

o the spring

by Hooke’s

er

ts original

Key Wordselastic (adj) – (of a

n is the oaded spring

ng length. The works as long xceeded. The ached when d does not h after the

mit is not rce against ht line. The

e is the spring

❯ One of these objects is elastic and bounces. Can you guess which one it is?

Extension (meters)

Forc

e (n

ewto

ns)

Gradient (N/m) is the spring constant, k





a. What does the spring constant tell you about a spring?

b. Is a spring with a high spring constant stiff or fl exible?

c. Imagine a force of 16 N is needed to stretch a spring 40 cm from its original length. What force is needed to stretch the same spring by the following extensions?

80 cm 120 cm 20 cm

d. Draw a graph to represent the data above. Plot four points, one for each calculation, and draw a line through them.

e. Using your graph, calculate the spring constant of the spring (remember: k = F/e).

❯ Research

Supplies

❯ 10-gram masses of modeling clay ❯ large rubber band ❯ spring (optional)

❯ scale accurate to 10 grams ❯ large pushpin ❯ ruler or measuring tape

❯ marker pen ❯ string

Procedure

1 Test the elasticity of a rubber band.

a. Measure the rubber band and record its length in the table on the next page.b. Push the pushpin into the side of a wooden table and hang the rubber band from it.c. Tie a length of string to the lowest point of the rubber band. d. Add a 10-gram piece of modeling clay to the string, and record the new length of the

rubber band in the table.e. Add another 10-gram piece of clay and record the new length in the table.f. Add masses of clay three more times until there is a total of 50 grams on the string.

2 Do the same with a spring (if you have one) and record the results in the table.

Extension (meters)

10

20

Forc

e (n

ewto

ns)

0.2 1.0 1.20.4 0.6 0.8

50

40

30



Results

1 Complete the table with the results from the research activity. To calculate the force in newtons, multiply the mass (in kg) by 10 (the approximate gravitational force).

Mass (g)Force (N)

Original Length (cm)

Stretched Length (cm)

Extension (cm)

rubber band

springrubber band

springrubber band

spring

0

10

20

30

40

50

2 Create a graph of your results. Convert the centimeters from the table above to meters. Plot the points and then draw a straight line through them. Use different colors for the rubber band and the spring.

❯ Analyze

1 How could you calculate the mass of an unknown object using your scales? Which scale works better and why?

2 Was the rubber band a perfectly elastic object? Explain.

Extension (meters)

10

30

20

40

50

Forc

e (n

ewto

ns)


❯ Topic

The pronghorn is the fastest land mammal in North America. Although pronghorns are not as fast as cheetahs, they can sustain

a faster speed over a longer period of time than cheetahs. The pronghorn’s top speed is hard to measure accurately and varies between individual animals and according to the distance they are running. Pronghorns can run at a speed of 56 km/h for 6 km, for example, at a speed of 67 km/h for 1.6 km, and at a speed of 88.5 km/h for 0.8 km.

Speed can be defi ned as the rate at which an object changes position. Notice how a pronghorn’s speed changes depending on the distance it has to travel. In order to calculate this speed, you need to know two factors. The first is the distance. Distance tells you how far an object has moved from its starting point and is measured in meters (m). A line showing distance does not have to be a straight line. A distance line simply follows the path from the starting point to the stopping point. The second factor you need to know to calculate speed is the time it takes for an object to travel that distance. Time is usually measured in seconds (s), but it is sometimes measured in minutes (min), hours (h) and even light years (ly—the distance that light travels in one year).

Consider how long it takes for a bus to get from Point A to Point B. The bus does not always travel at the same speed over the entire route. It speeds up and slows down as it travels. But if you know that the bus covers a total distance of 10 kilometers in one hour, you can calculate the average speed of the bus over the route by using

the following formula: average speed equals total distance covered

divided by period of time. In this case, the bus’s

speed is 10 km/h.

Speed, Distance and Time

5

Calculating Speed, Distance and TimeObjective Calculate speed, distance and time during a race

Key Concepts ❯ The speed of an object is a measure of how fast it moves. ❯ Distance is a measure of the space between two objects or of how far an object has moved. ❯ Time refers to how long it takes for an object to move a certain distance. ❯ Speed, distance and time can be calculated using this equation: speed equals distance divided by time, or S = d/t. ❯ Distance is measured in meters (m), time in seconds (s) and speed in meters per second (m/s).

Key Wordsaverage (n) – a number calculated by adding various quantities together and then dividing the total by the number of quantitiesrate (n) – the speed at which something happens within a certain time period

❯ There are approximately 240 Sonoran pronghorn in the wild in Mexico.

1919Unit 1Unit 1 Forces and MotionForces and Motion





a. When is it important to know the speed of something?

b. A car travels at an average speed of 80 kilometers per hour. How long will it take to travel 400 kilometers?

c. A lobster walks 20 meters across the seabed in 10 minutes. Find its average speed in meters per second. (Make sure you convert minutes into seconds.)

❯ Research

Supplies

❯ 100-meter track marked off in 10-meter intervals ❯ measuring tape to mark off track ❯ calculator

❯ 10 timekeepers with stopwatches ❯ 1 starter ❯ 1 runner

Procedure

1 Complete the table below with the interval times and speed for Jamaican sprinter Usain Bolt.

a. First, calculate Bolt’s intervals—how long he took to travel each 10 meters of his world-record-breaking sprint.

b. Use these interval times to calculate his speed over each interval.

2 Make a track and record the time it takes for a runner to cover 100 meters.

a. Choose 10 timekeepers and give each a stopwatch. Choose a runner and a starter. b. Prepare the track using the measuring tape. Have the timekeepers stand at 10-meter

intervals from 10–100 meters.c. On the starter’s signal, the runner should start running from the start of the track and

the timekeepers should start their stopwatches.d. Each timekeeper should stop his or her stopwatch as the runner passes. Record the

times in the student portion of the table.

Results

1 Complete the table with the runners’ intervals and calculate their speed over each one.

Distance (m) 0 10 20 30 40 50 60 70 80 90 100

Stu

den

t Time (s) 0.00

Interval (s) 0.00

Speed (m/s) 0.00

Usa

in

Bolt

Time (s) 0.00 1.89 2.88 3.78 4.64 5.47 6.29 7.10 7.92 8.75 9.58

Interval (s) 0.00 1.89 0.99

Speed (m/s) 0.00



2 Plot a graph with time on the x-axis and distance on the y-axis. Plot one line for the student runner and one for Usain Bolt.

3 Plot another graph with time on the x-axis and speed on the y-axis. Plot one line for the student runner and one for Usain Bolt.

❯ Analyze


a. Why do you think m/s was chosen to express the speed in this activity?

b. Would any other unit of measurement for speed be suitable?

Dis

tan

ce (

met

ers)

10

20

30

40

50

60

70

80

90

100

5 10 15 20

5

5 10 15 20

Time (seconds)

10

15

Spee

d (

met

ers

per

sec

on

d)

Time (seconds)



❯ Topic

Newton’s First Law of Motion

Experimenting with InertiaObjective Understand the relationship between mass and inertia

Key Concepts ❯ Inertia is the tendency of an object to resist a change in motion. ❯ The more mass an object has, the more inertia it has. ❯ An object will stay at rest, or continue in the same direction at the same speed, unless an outside force acts upon it. ❯ To achieve motion or bring about a change in motion, a force must be applied.

6

❯ A Ferris wheel has more rotational inertia than a yo-yo; in other words, it takes more force to start or stop its motion.

Key Wordsrotate (v) – to move or turn in a circle

Born in England in 1 6 4 3 , I s a a c N e w t o n i s c o n s i d e r e d

one of the world’s greatest scientists, mathematic ians and astronomers. He developed the theory of gravity and the three laws of motion, which basically explain w h y o b j e c t s move (or don’t move). He also invented calculus and a reflecting telescope and made several breakthrough discoveries in the study of light.

He began his studies at Cambridge University in 1661, but had to leave in 1665 because of an outbreak of the bubonic plague. While at home, Newton began developing his theories about gravity and the laws of motion. Newton’s First Law—often known as the Law of Inertia—states that an object at rest stays at rest, and an object in motion stays in motion in a straight line and at a constant speed unless acted upon by an unbalanced force. In other words, inertia is the tendency of a body to resist changes to its motion. Galileo is credited with fi rst formulating the idea of inertia, and Newton based his fi rst law on Galileo’s work.

To understand inertia, you need to recall what

you have learned about unbalanced

forces. A ball on the ground will not move unless someone applies an unbalanced force to it by, for example, kicking it. And a ball rolling down a hill will continue rolling unless friction or another force stops

its motion. The iner t i a o f

objects depends on their mass. Objects with

a large mass resist changes in their motion more than

objects with a small mass; for example, it is harder to push a full

shopping cart than an empty one. Likewise, the more mass a moving object has, the less an outside force will affect its motion: a moving bike is far easier to stop than a moving car.

A yo-yo and a Ferris wheel exhibit another type of inertia: rotational or gyroscopic inertia. This is the tendency of a rotating object to keep rotating. Objects with large rotational inertia, such as a Ferris wheel, require a large force to change their rotation, while objects with small rotational inertia, like a yo-yo, require only a small force.

❯ Referring to Galileo, Newton once remarked, “If I have seen further, it is by standing on the shoulders of giants.”




1 Read the text and key concepts and answer the questions.

a. What do you think Newton meant by the quote under his picture?

b. Use the concept of inertia to explain why it is important to wear a seatbelt.

c. Draw an experience you have had with inertia. Write a brief explanation that helps explain how inertia, motion and unbalanced forces were involved in the situation.

❯ Research2 Watch Video 2 about Experiment 1, testing the inertia of a body at rest.

Then prepare all the supplies.

Supplies

Experiment 1 ❯ sheet of paper ❯ book with rough cover

❯ book with glossy cover ❯ several fl at objects with different surfaces and masses

Experiment 2 ❯ sheet of paper ❯ masking tape

❯ tennis ball ❯ chalk

Experiment 3 ❯ three identical jars with lids ❯ fl our or sand

❯ iron fi lings or lead pellets ❯ ramp (e.g., a ring binder)

Experiment 4 ❯ a vinyl LP record or a 30-centimeter diameter circle of cardboard or similar material

❯ pencil ❯ string

Procedure

Form groups of three. Take turns doing the activities with other groups.

1 Do Experiment 1. Test the inertia of a body at rest.

a. Try to remove a sheet of paper from under different objects without moving them. Place the paper on a smooth surface and place the book with a glossy cover on top.

b. In one smooth motion, quickly pull the paper out from under the book. Did the book move? Note the results in the table in the Results section.

c. Repeat with the book with a rough cover and other objects and note what happens.



2 Do Experiment 2. Test the inertia of a body in motion.

a. Mark a target on paper and tape it to the fl oor with 10 meters of space on either side.b. One student is a runner, and the other two are observers. The runner is going to

sprint past the target and drop the tennis ball on it. Predict how far from the target the runner has to drop the ball in order to hit the target and write the predicted distance in the table in the Results section. The observers watch to see exactly at what point the ball is dropped. Mark the point with chalk and measure the distance from this point to the target. Record the distance in the table.

c. Predict what will happen if the runner jogs and then walks by the target. Then repeat the activity and record the distances in the table.

3 Do Experiment 3. Test how the mass of an object affects its inertia.

a. Pack one jar with fl our or sand and secure the lid. Pack the other with iron fi lings or lead pellets and secure the lid. Leave the third jar empty.

b. Place the ramp on a fl at smooth surface, such as a wooden fl oor. Release the empty jar from the top of the ramp. Measure how far it rolls from the bottom of the ramp. Do the same with the other two jars. Record the results in the table on the next page.

c. Repeat the activity on other surfaces, such as a carpet, linoleum, tile, and so on, and record the results.

4 Do Experiment 4. Test the rotational or gyroscopic inertia of a spinning object.

a. Either use the vinyl LP record or punch a small hole in the center of the circle. Tie one end of the string to the middle of the pencil and pull the other end through the hole in the circle (or record). The pencil should be centered under the circle.

b. Swing the circle back and forth like a pendulum. Try to achieve smooth, even movements. Describe what happens in the Results section.

c. Now give the circle a spin so it rotates on top of the pencil (like a CD spins on a CD player). Try to swing the circle again like a pendulum while it is spinning. Describe what happens on the next page.

Results

1 Complete the table with the results from Experiment 1.

Object What happened?

book with glossy cover

book with rough cover


Speed of MovementPredicted Distance from Drop

Point to Target (m)Actual Distance from Drop

Point to Target (m)

Running

Jogging

Walking




SurfaceDistance Traveled

by Empty JarDistance Traveled by

Jar of _______________Distance Traveled by

Jar of _______________

4 Describe what happens in Experiment 4.

a. When you swing the circle from side to side without spinning it:

b. When you spin the circle on the pencil and then swing it from side to side:

❯ Analyze

1 Answer the questions about Experiment 1.

a. What effect did the mass and type of surface of the objects have?

b. How does this experiment relate to Newton’s First Law of Motion?


a. How did the speed of the runner affect the distance of the drop point?

b. How does this experiment relate to Newton’s First Law of Motion?


a. How did the content of the jars and the surface affect the results?

b. What can you conclude about a body’s tendency to maintain its inertia?

4 In Experiment 4, what happens when you spin the circle and why?



❯ Topic

Key Wordsacceleration (n) – a measure of how quickly an object changes velocity air resistance (n) – the forces in opposition to the movement of an object through the air; also called drag

Objective Calculate the velocity, mass and acceleration of balls

Key Concepts ❯ Velocity is the speed of an object in a certain direction. ❯ Two cars traveling at 30 m/s on the same road in opposite directions have the same speed but different velocities. ❯ Acceleration occurs when an object changes speed, direction or both. ❯ Acceleration depends on two factors: the change in velocity (measured in meters per second) and the time this change takes (measured in seconds). ❯ Acceleration is calculated by dividing the change in velocity by the time that this change takes, and is measured in meters per second squared (m/s2). ❯ Newton’s Second Law of Motion states that a force can cause an object to accelerate. The larger the force, the greater the acceleration. The greater an object’s mass, the greater its resistance to change to its motion. ❯ Newton’s Second Law shows this relationship: Force equals mass times acceleration, or F = ma.

Newton’s Second Law of Motion

Investigating Force, Mass and Acceleration

7

Newton’s second law shows how force, mass and acceleration are related. This law is represented by the formula: Force = mass x

acceleration, which shows that both the size of a force and the mass of an object affect its acceleration.

When a soccer player kicks a ball, for example, the ball accelerates. The ball moves in a different direction and at a different speed. Furthermore, the ball accelerates faster when an adult kicks it than when a child kicks it. Why? Because an adult produces a greater force than a child.

In addition to the force, the mass of an object also affects its acceleration. For the same force, a small mass accelerates more than a large mass does. For instance, imagine a boy kicks a cardboard box on the classroom fl oor as hard as he can. If the box is empty, it will fl y across the room. If the box is full of books, however, it won’t move (and the boy will probably hurt his foot!). His two kicks produce forces of about the same size. But the empty box, because it has a small

mass, moves faster and farther than the box of books, which has a larger mass.

When you jump off a diving board into a swimming pool, you fall into water. The higher the diving board, the faster and harder you hit the water. The force of gravity causes the mass of a falling object to increase speed as it falls. Gravity causes

all falling objects to have equal acceleration, provided no air is

present. So, on the moon, where there is no atmosphere, if you drop

a large rock and a pea at the same time, they will fall at the same speed. On Earth, however, air resistance causes objects to fall at different speeds. The amount of air resistance acting on an object depends on its shape. The greater the object’s surface area compared to its mass, the greater the air resistance. For example, a feather and a ping-pong ball have a similar mass. But when you drop them from the same height, the feather will fall more slowly because it has more surface area, so the air will resist its movement more.

❯

The stronger the force, the faster the ball moves.

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❯

The stronger the force, the faster the ball moves.

❯ The force of gravity causes the diver to accelerate until she hits the water.

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❯ The force ofgravity causes the diver to accelerate until she hits the water.




1 Read the text and key concepts and answer the questions.

a. Where have you experienced acceleration? Describe the experience. Draw a picture and label the force, mass and direction of acceleration.

b. Explain how acceleration works in your own words.

c. If an astronaut on the Moon drops a feather and a hammer at the same time, what will happen? Explain.

❯

There is no air on the Moon, and the force of gravity is weaker.



❯ Research

Supplies

❯ 5 different balls (e.g., tennis ball, volleyball, football, baseball, golf ball) ❯ stopwatch

❯ measuring tape ❯ scale (up to 5 kg) ❯ chalk

Procedure

1 Do an experiment to calculate the speed, mass and acceleration of different balls.

a. Mark off a 10-meter track on a fl at surface.b. Measure the mass of the balls and record it in the table.c. Stand at the 0 meter mark with the fi rst ball. Roll your ball to the 10-meter line and

record how long it takes to get there. Write the time in the table.d. Repeat for the other four balls. Try to apply the same force to each ball.

Results

1 Record the mass of the balls and the time it took to travel 10 meters in the table.

Type of BallMass of Ball (kg)

Distance (m)

Time (s)Speed (m/s)

Acceleration (m/s2)

Force (N)

10

10

10

10

10

2 Calculate the speed, acceleration and force for each ball using the following formulas. Write the results in the table.

speed = distance x timechange in speed = fi nal speed – initial speedacceleration = change in speed ÷ timeForce = mass x acceleration

❯ Analyze


a. Which ball rolled the fastest? Which ball rolled the slowest?

b. Is there a relationship between the ball’s mass and how fast it rolled? Describe the relationship and explain how this relates to the inertia of each ball.



❯ Topic

Key Wordsaction (n) – the force that an object applies on anotherinteraction (n) – the way two objects act on each otherreaction (n) – the force that a second object applies on a fi rst object in response to the fi rst object’s action on it

Newton’s Third Law of Motion

Objective Make a balloon rocket in order to explore action-reaction forces

Key Concepts ❯ Newton’s Third Law of Motion states that for every action, there is an equal and opposite reaction. ❯ A force is always exerted by one object on another object—in other words, every force involves the interaction of two objects. ❯ When one object exerts a force (action) on another object, the second object also exerts a force (reaction) on the fi rst object. ❯ Forces always come in these action-reaction pairs. These forces are equal in size and opposite in direction.

Making a Balloon Rocket

8

Objects are subject to many different forces. These forces do not operate in isolation. Forces act as action-reaction pairs.

Newton’s Third Law of Motion explains that for every force (action) in nature, there is an equal but opposite force (reaction). The forces acting on a resting object are in balance. If you are sitting on a chair, for example, you can feel the force of gravity acting on your mass (as weight) as a downward force. The chair exerts an upward force that prevents you from falling. In order to stand up, you have to apply more force on the fl oor with your feet to overcome the force of gravity, but the force that the ground exerts on your feet is also greater, so the action and reaction forces are still equal in size and opposite in direction.

Whenever anything moves, action-reaction forces are at work. When you swim, you use your arms and legs to push (action force) the water backward. The reaction force of this interaction comes from the water pushing back on your body in the opposite direction. That force propels you forward through the water. Another example is a fl ying bird: its wings push the air down (action force), and the air pushes back in the opposite direction (reaction force) allowing the bird to fl y.

Action-reaction pairs also make it possible for you to walk along a path: your feet push down (action) and the ground pushes up (reaction) with equal force but in the opposite direction.

An infl ated balloon models the action of a rocket in space. When rocket fuel burns, it produces gases that expand rapidly

and escape from the end of the rocket. These gases don’t

move the rocket by pushing against

t h e a i r —certainly not in space where there i s no

atmosphere—so how does the rocket

move? In fact, the gases push against the rocket (action)

and the rocket pushes back against the gases (reaction), so they move in opposite directions.

To visualize this another way, imagine you’re standing on a skateboard and holding a heavy object. If you throw the object forward, you and the skateboard will roll backward. You push on the object (action), the object pushes back on you with the same force (reaction), and you and the object move in opposite directions.

In the same way, when you release the infl ated balloon, air pushes against the wall of the balloon and fl ows out of the mouth (action), the balloon pushes back against the air (reaction), and the balloon and the air move in opposite directions.

❯ The owl’s wings push against the air and the air pushes back, allowing the owl to fl y.

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❯ The owl’s wings push against the air and the air pushes back, allowing the owl to fl y.





a. Give an example of action-reaction forces according to the Third Law of Motion.

b. Think back to the Research activity in Topic 2 with the hairdryer and the balloons. The air stream fl owing up from the nozzle of the hairdryer supplies the action force that allows the balloons to fl oat above the hairdryer. What is the reaction force? What is its size and direction? Draw a picture of this interaction using force arrows to show the action-reaction pair.

c. Using the Third Law of Motion, explain how you are able to walk forward.

d. The impact of an insect with the windshield of a car moving at high speed is an example of action-reaction forces at work. Use Newton’s second law to explain why the effect of this interaction is much greater on the insect than on the car window.



❯ Research

Supplies

❯ balloon ❯ clothespin ❯ straw ❯ fi shing line ❯ tape ❯ 10 paper clips ❯ ruler or measuring tape

Procedure

1 Make a balloon rocket and test how far it travels.

a. Thread the fi shing line through the straw, and stretch the fi shing line tightly across the room.

b. Infl ate the balloon and secure the end with the clothespin.

c. Attach the balloon to the straw on the fi shing line with tape.d. Move the balloon to the beginning of the fi shing line.e. Release the clothespin and measure the distance that the balloon travels. Repeat

twice. Record the measurements in the table.f. Repeat the experiment twice, fi rst with 5 paper clips taped to the balloon to increase

its mass, and then with 10 paper clips.

Results

1 Record the distances in the table and calculate the mean distance for each number of paper clips.

Number of Paper Clips

Distance Traveled (cm)

Trial 1 Trial 2 Trial 3 Mean

0

5

10

❯ Analyze


a. How is the experiment related to Newton’s Third Law? Identify the action-reaction forces involved and label them on the illustration above.

b. What would happen if you squeezed the balloon’s side? Would the air go out faster or slower? What would happen to the movement of the balloon rocket?

ow far it ❯ Air escapes from the balloon (action force) and the balloon moves along the fi shing line (reaction force).



❯

1Unit

Progress Check

Forces and Motion1 Which is a contact force?

a. Frictional force.b. Gravitational force.c. Electrical force.d. Magnetic force.

2 Where does a frictional force exist?

a. Between the electrons and the protons in the nucleus of an atom.

b. Between the north pole and south pole of a magnet.

c. Between the ground and your foot as you walk.

d. Between two objects that have mass.

3 How do you know when balanced forces are acting on an object?

a. It moves in a different direction.b. It moves more slowly.c. It doesn’t move.d. It moves more quickly.

4 Which is an example of a pivot?

a. The tire of a bicycle wheel.b. The hinge of a door.c. The end of a seesaw.d. The tension in a cable.

5 A spring has a spring constant of 10 N/m. Which statement is correct?

a. A force of 4 N will stretch it 40 cm.b. A force of 4 N will stretch it 2 m.c. A force of 4 N will stretch it 4 m.d. A force of 4 N will stretch it 4 cm.

6 Which relationship did Isaac Newton not formulate?

a. How the force applied to a spring determines how far it stretches.

b. How the mass of an object affects its inertia.

c. How acceleration depends on mass and force.

d. How every action has an equal and opposite reaction.

7 A horse runs at 30 km/h for 90 minutes. How far does it travel?

a. 90 km.b. 27 km.c. 30 km.d. 45 km.

8 A car travels 10 kilometers in 10 minutes. How fast is it moving?

a. 10 km/h.b. 100 km/h.c. 60 km/h.d. 20 km/h.

9 What causes a bicycle to slow down on fl at ground when you stop pedaling?

a. Inertia.b. Gravity.c. Friction.d. Acceleration.

10 When you throw a ball up, what force causes it to fall back down?

a. Inertia.b. Gravity.c. Friction.d. Tension.

11 What kind of object bounces when you drop it on the fl oor?

a. An elastic object.b. A balanced object.c. A deformed object.d. A rotational object.

12 If you drop a feather and a hammer at the same time on the Moon, which will hit the ground fi rst?

a. The feather.b. The hammer.c. They’ll hit at the same time.d. Neither. They’ll both fl oat in space.

(12 points)

Pathway to Physics unit 1.indd 32Pathway to Physics unit 1.indd 32 11/7/14 9:30 AM11/7/14 9:30 AM


13 Give an example of each type of force. (3 points)

a. friction

b. tension

c. normal force

14 A child sits 3 meters from the pivot of a seesaw and exerts a counterclockwise force of 200 N. To balance the seesaw, how far from the pivot should the child’s mother sit if she exerts a force of 600 N? Draw and label a picture. The equation to calculate a moment is: moment = force x distance (M = Fd). (4 points)

15 Answer the questions about springs (F = ke). (4 points)

a. A spring has a spring constant of 5 N/m. How far will it stretch when these forces are applied to it?

0.5 N: __________________ 2 N: __________________

b. Another spring has a spring constant of 10 N/m. What force is necessary to stretch it to these extensions?

10 cm: __________________ 25 cm: __________________

16 Answer the questions about speed, distance and time (S = d/t). (5 points)

a. A car is traveling at 80 km/h. How far will it travel after:

30 minutes? __________________ 120 minutes? __________________

b. A boy is running at 5 m/s. How long will he take to travel:

20 m: __________________ 100 m: __________________

c. An airplane fl ies 200 km in 15 minutes. How fast is it fl ying?

17 Answer the questions about Newton’s Second Law of Motion (F = ma). (2 points)

a. A 1-kg soccer ball is kicked and accelerates at 20 m/s2. What force was applied to it?

b. A student throws a ball with a mass of 0.5 kg and it hits the catcher’s hand with a force of 20 N. What is the acceleration of the ball?

❯ Total: / 30 points


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