Motion, Acceleration, and ForcesCHAPTER 3

Motion Motion happens all around us.

One – dimensional motion is the simplest form of motion.

The object can only move in one dimension◦ forward and backward◦ left and right◦ up and down

Motion Motion takes place over time and depends on a frame of reference.

Frame of Reference – a coordinate system for specifying the precise location of objects in space

The choice of a reference point is arbitrary, but once chosen, the same point must be used throughout the problem.

Distance and Displacement Distance and displacement are two quantities which may seem to mean the same thing, yet they have distinctly different meanings and definitions.

Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.

Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

Distance and DisplacementTo test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

Distance traveled = Displacement =12 m 0 m

Distance and DisplacementThe diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D. Use the diagram to determine the distance traveled by the skier and the resulting displacement during these three minutes.

Distance traveled = Displacement =420 m 140 m

Seymour Butz views football games from under the bleachers. He frequently paces back and forth to get the best view. The diagram below shows several of Seymour's positions at various times. At each marked position, Seymour makes a "U-turn" and moves in the opposite direction. In other words, Seymour moves from position A to B to C to D. What is Seymour's resulting displacement and distance of travel?

Distance = 95 yards Displacement = 55yards

DisplacementΔX = XF – X I

D I SPLACE M E NT = CHA NG E I N PO S I T I O N

D I SPLACE M E NT = F I NAL PO S I T I O N – I N I T I AL PO S I T I O N

Velocity v. Speed Velocity is like speed in that it describes how much distance is traveled in a given amount of time.

Unlike speed, velocity also has direction.

The velocity of an object can be different even if the speed of the object remains constant.

◦ How?

Calculating Velocity

Velocity can be calculated by the following equation:

V = df – di

tf – ti

Let’s… An ant travels 75 cm in 5 s. What was the ant’s speed?

Again… It took you 6.5 hours to drive 550 km. What was your speed?

Again… An elevator travels a distance of 220m from the first floor to the 60th floor in 27.5 s. What is the elevator’s average speed?

What is the velocity when the elevator travels back down the first floor?

Practice makes perfect…

A bus leaves at 9 a.m. with a group of tourists. They travel 350 km before they stop for lunch. Then they travel an additional 250 km until the end of their trip at 3 p.m. What is the average speed of the bus?

A different look… A motorcyclist travels with an average speed of 20 km/h. If the cyclist is going to a friend’s house 5 km away, how long does it take the cyclist to make the trip?

Graphs of Motion Motion graphs are an

important tool used to show the relationship between position, speed, and time.

Position vs. time data tells you the runner’s position at different points in time.

The runner is at 50 meters after 10 sec., 100 meters after 20 sec. and 150 meters at 30 sec.

Position vs Time Graph To graph data, you

put position on the vertical (y) axis .

Time goes on the horizontal (x) axis.

Data are plotted between x and y axis.

Position vs Time Graph You can use

position vs. time graphs to quickly compare the speeds of different objects.

Position vs Time Graph The “steepness” of

a line is called its slope.

Visualize a triangle with the slope as the hypotenuse.

The rise is equal to the height of the triangle.

The run is equal to the length along the base of the triangle.

Position vs Time Graphs The slope is the ratio

of the “rise” (vertical change) to the “run” (horizontal change).

The slope is therefore a distance divided by a time, which equals speed.

Position vs Time Graphs•So what does it mean if the line on a Position vs Time graph is a horizontal line?•Standing still•Velocity is zero

•What does it mean if there is a negative slope?•The object is moving backwards.

What is happening?

Motion, Acceleration, and ForcesCHAPTER 3

SECTION 2

Acceleration Acceleration is the change in velocity divided by the time for the change to occur.

◦ A vector◦ What can cause acceleration to change?

If the direction of motion doesn’t change, acceleration can be calculated by:

a = (vf – vi)

(tf – ti)

Let’s Try This… A ball is dropped from a cliff and reaches a speed of 29.4 m/s after 3.0 s. What is the ball’s average acceleration?

Another one… It takes a car one minute to go from rest to 30 m/s. What is the acceleration of the car?

Let’s look at it another way…

A sprinter runs with an average acceleration of 4.5 m/s2. What is the sprinter’s speed 2 s after leaving the starter blocks?

Calculating Negative Acceleration

Imagine a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 s. What is the skateboarders acceleration

Velocity-Time GraphsVelocity-time graphs are graphs that represent an object’s velocity versus its time.

Time is marked on the horizontal axis and velocity is on the vertical.

Like position-time graphs, velocity-time graphs are drawn with a line of best fit.

Velocity-time graphs are usually idealized, this means the details of speeding up and slowing down are not important. In the real world the graphs would be more rounded on the corners.

Velocity-Time Graph Horizontal lines show uniform motion (constant speed and direction).

Inclined lines show change in speed or direction, or both: in other words accelerated motion.

Example A: The car was travelling forward at a steady speed of 50 km/h. Then it slowed down to 30km/h as it entered a school zone and continued until the end of the observations.

Example B

Example C

Kinematics in the NFL

Motion and ForcesCHAPTER 3

SECTION 3

Force Force is a push or pull that one object exert on another.

What happens to the motion of an object when you exert a force on it?

Balanced forcesWhen two or more forces act on an object at the same time, the forces combine to form the net force

If the forces are equal in size but opposite in direction they are called balanced forces

The net force is equal to zero

When forces acting on an object are balanced, velocity does not change.

Will the object accelerate?

Unbalanced ForcesWhen two forces are applied in opposite directions, but with unequal strength, the net forces in not zero

The net force that will cause the object to accelerate will be the difference between the two forces. The acceleration with be in the direction of the

greater force

Forces would also be unbalanced if the two forces are being applied in the same direction. Acceleration with be in the direction the two

forces are being applied

Unbalanced forces change _________________

FrictionWhen you push a skateboard with your hand, why does it eventually stop?There must be force acting on the skateboardThe force is known as friction

What Creates More Friction?

Rough Surfaces◦ Rough surfaces have more microscopic hills & valleys.

◦ The rougher the surface, the greater the friction will be.

Greater Force◦ The amount of force exerted increases the amount of friction

Static Friction◦ Type of friction that

prevents two surfaces from slipping past each other

◦ The applied force must be greater then the force of static friction in order for the object to accelerate

Sliding Friction

Force that acts in the opposite direction to the motion of the surface sliding on another surface

The force due to sliding friction is less than the force due to static friction

Less force is necessary to keep an object in motion than to start it in motion

Rolling Friction

As a wheel rolls over a surface, the wheel digs into the surface, causing both the wheel and the surface to be deformed

Static friction acts over the deformed area where the wheel and surface are in contact, producing a frictional force called rolling fiction

Usually much less than sliding friction

Air Resistance

When an object falls to Earth, it is pulled downward by the force due to gravity

Air resistance is a frictional force that opposed the force due to gravity Will cause objects to fall at different speeds and

accelerations What would happen if there was no air resistance?

The amount of air resistance on an object depends on the speed, size, and shape of the object.

Air Resistance

Terminal Velocity

The force of gravity will cause a object to accelerate as it falls until it reaches terminal velocity

Terminal velocity is reached when the force due to air resistance equals the force of gravity

The object will continue to fallThe object will no longer accelerate

Parachutes decrease terminal velocity by making the force of air resistance larger than the force of gravity