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Forces and the Laws of Motion Section 1

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Section 1 Newton's Second

Section 5 Extra questions

Section 2Forces and the Laws of Motion

Net Force - the Sum of the Forces

• This car is moving with a constant velocity.– Fforward = road pushing the tires

– Fresistance = force caused by friction and air

– Forces are balanced

• Velocity is constant because the net force (Fnet) is zero.

Section 2Forces and the Laws of Motion

Equilibrium

• The state in which the net force is zero.– All forces are balanced.– Object is at rest or travels with

constant velocity.

• In the diagram, the bob on the fishing line is in equilibrium.– The forces cancel each other.– If either force changes,

acceleration will occur.


Classroom Practice Problem

• An agricultural student is designing a support system to keep a tree upright. Two wires have been attached to the tree and placed at right angles to each other (parallel to the ground). One wire exerts a force of 30.0 N and the other exerts a force of 40.0 N. Determine where to place a third wire and how much force it should exert so that the net force on the tree is zero.

• Answer: 50.0 N at 143° from the 40.0 N force


Newton’s Second Law

• Increasing the force will increase the acceleration.– Which produces a greater acceleration on a 3-kg model airplane, a force

of 5 N or a force of 7 N?• Answer: the 7 N force

• Increasing the mass will decrease the acceleration.– A force of 5 N is exerted on two model airplanes, one with a mass of 3 kg

and one with a mass of 4 kg. Which has a greater acceleration?• Answer: the 3 kg airplane


Newton’s Second Law (Equation Form)

F represents the vector sum of all forces acting on an object. F = Fnet

– Units for force: mass units (kg) acceleration units (m/s2)– The units kg•m/s2 are also called newtons (N).



• Space-shuttle astronauts experience accelerations of about 35 m/s2 during takeoff. What force does a 75 kg astronaut experience during an acceleration of this magnitude?

• Answer: 2600 kg•m/s2 or 2600 N


What do you think?

• How do the quantities weight and mass differ from each other?

• Which of the following terms is most closely related to the term friction?– Heat, energy, force, velocity

• Explain the relationship.


Weight and Mass

• Mass is the amount of matter in an object.– Kilograms, slugs

• Weight is a measure of the gravitational force on an object.– Newtons, pounds– Depends on the acceleration of gravity

• Weight = mass acceleration of gravity– W = mag where ag = 9.81 m/s2 on Earth

– Depends on location• ag varies slightly with location on Earth.

• ag is different on other planets.


Normal Force

• Force on an object perpendicular to the surface (Fn)

• It may equal the weight (Fg), as it does here.

• It does not always equal the weight (Fg), as in the second example.

• Fn = mg cos


Static Friction• Force that prevents motion• Abbreviated Fs

– How does the applied force (F) compare to the frictional force (Fs)?

– Would Fs change if F was reduced? If so, how?

– If F is increased significantly, will Fs change? If so, how?

– Are there any limits on the value for Fs?


Kinetic Friction

• Using the picture, describe the motion you would observe.– The jug will accelerate.

• How could the person push the jug at a constant speed?– Reduce F so it equals Fk.

• Force between surfaces that opposes movement• Abbreviated Fk

• Does not depend on the speed


Friction

Click below to watch the Visual Concept.

Visual Concept


Calculating the Force of Friction (Ff)

• Ff is directly proportional to Fn (normal force).

• Coefficient of friction ():– Determined by the nature of the two surfaces s is for static friction. k is for kinetic friction. s > k

f nF F f

n

F

F


Typical Coefficients of Friction

• Values for have no units and are approximate.


Click below to watch the Visual Concept.

Visual Concept

Everyday Forces



• A 24 kg crate initially at rest on a horizontal floor requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor.– Draw a free-body diagram and use it to find:

• the weight • the normal force (Fn)• the force of friction (Ff)

– Find the coefficient of friction.

• Answer: s = 0.32


Classroom Practice Problem• A student attaches a rope to a 20.0 kg box of

books. He pulls with a force of 90.0 N at an angle of 30.0˚ with the horizontal. The coefficient of kinetic friction between the box and the sidewalk is 0.500. Find the magnitude of the acceleration of the box.

– Start with a free-body diagram.– Determine the net force.– Find the acceleration.

• Answer: a = 0.12 m/s2


The Four Fundamental Forces

• Electromagnetic– Caused by interactions between protons and electrons– Produces friction

• Gravitational– The weakest force

• Strong nuclear force– The strongest force– Short range

• Weak nuclear force– Short range


Preview

• Multiple Choice

• Short Response

• Extended Response


Multiple Choice

a F

m1

a F

m2

a F

m1 m2

a F

(m1)(m2 )

Use the passage below to answer questions 1–2.

Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1.

1. What is the acceleration of the two blocks?

A. C.

B. D.


Multiple Choice, continued


Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1.

2. What is the horizontal force acting on m2?

F. m1a

G. m2a

H. (m1 + m2)a

J. m1m2a



3. A crate is pulled to the right with a force of 82.0 N, to the left with a force of 115 N, upward with a force of 565 N, and downward with a force of 236 N. Find the magnitude and direction of the net force on the crate.

A. 3.30 N at 96° counterclockwise from the positive x-axisB. 3.30 N at 6° counterclockwise from the positive x-axisC. 3.30 x 102 at 96° counterclockwise from the positive x-axisD. 3.30 x 102 at 6° counterclockwise from the positive x-axis



5. A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 N, how long would it take to increase the speed of the train from rest to 85 km/h? (Disregard friction.)

A. 4.7 x 102sB. 4.7sC. 5.0 x 10-2sD. 5.0 x 104s




A truck driver slams on the brakes and skids to a stop through a displacement x.6.

A. x/4B. xC. 2xD. 4x

If the truck’s mass doubles, find the truck’s skidding distance in terms of x. (Hint: Increasing the mass increases the normal force.)


Short Response

Base your answers to questions 10–12 on theinformation below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball.

10. How long does the ball take to hit the ground?


Short Response


10. How long does the ball take to hit the ground?Answer: 6.00 s


Short Response, continued


11. How far from the building does the ball hit the ground?



11. How far from the building does the ball hit the ground?Answer: 72.0 m




12. When the ball hits the ground, what is its speed?




12. When the ball hits the ground, what is its speed?Answer: 63.6 m/s



16. A student pulls a rope attached to a 10.0 kg woodensled and moves the sled across dry snow. The student pulls with a force of 15.0 N at an angle of 45.0º.

If k between the sled and the snow is 0.040, whatis the sled’s acceleration? Show your work.

Extended Response


16. A student pulls a rope attached to a 10.0 kg woodensled and moves the sled across dry snow. The student pulls with a force of 15.0 N at an angle of 45.0º.

If k between the sled and the snow is 0.040, whatis the sled’s acceleration? Show your work.

Answer: 0.71 m/s2

Extended Response


Extended Response, continued

17. You can keep a 3 kg book from dropping by pushingit horizontally against a wall. Draw force diagrams,and identify all the forces involved. How do they combine to result in a zero net force? Will the force you must supply to hold the book up be different for different types of walls? Design a series of experiments to test your answer. Identify exactlywhich measurements will be necessary and whatequipment you will need.


17. You can keep a 3 kg book from dropping by pushingit horizontally against a wall. Draw force diagrams,and identify all the forces involved. How do they combine to result in a zero net force? Will the force you must supply to hold the book up be different for different types of walls? Design a series of experiments to test your answer. Identify exactlywhich measurements will be necessary and whatequipment you will need.

Answer: Plans should involve measuring forces such as weight, applied force, normal force, and friction.

Extended Response, continued

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