Chapter 4

• Forces and Newton’s Laws of Motion

Slide 4-2

4 Forces and Newton’s Laws of Motion

Slide 4-3

Slide 4-4

Slide 4-5

Slide 4-6

What Causes Motion?

In the absence of any forces acting on it, an object will continue moving forever. Motion needs no “cause.”

Slide 4-15

What causes motion?

Newton’s First Law: An object in uniform motion will not accelerate unless there is an external interaction

What causes motion?

Force from the ground on Usain

Seat Belts: An Application of Newton’s First Law

Slide 4-16

What Is a Force?

A force...

... is a push or a pull. ... acts on an object.

... requires an agent.

... is a vector. ... is a contact force or a long-range force. Slide 4-17

Force VectorsThe magnitude of a force is measured in Newtons

Newtons

angle

What about multiple forces acting on one mass?

Force Vectors

Slide 4-18

Force is

A. something Yoda told Han Solo to use

B. a scalar quantityC. a vector quantityD. a unit of power

someth

ing Yoda to

ld Han

Sol...

a sca

lar quantity

a vec

tor q

uantity

a unit o

f power

7% 4%

89%

0%

Force Vectors add tooA hanging street sign with more than one force acting on it

Worst Buy

+ =0

�⃗� 1

�⃗� 3

�⃗� 2

Force types

• Weight• Spring• Tension• Normal• Friction• Drag• Thrust• Electromagnetic

A Short Catalog of Forces: Weight w

Slide 4-19

Weight

Gravity pulling down

�⃗�❑�⃗�=𝑚�⃗�

Is your weight the same on the moon?

Spring Force Fsp

Slide 4-20

�⃗� sp=−𝑘 �⃗�

SpringWhen a coiled spring is displaced from equilibrium it wants to return

�⃗� sp=−𝑘 �⃗�

Tension

Found in ropes, chains, cloth

𝑇 r=𝑚�⃗�

Tension ForceT

Slide 4-21

NormalPerpendicular to the surface of interacting objects

NormalPerpendicular to the surface of interacting objects

|⃗𝑁|=𝑚|𝑔|cos𝜃

𝜃

𝜃𝑚𝑔 cos𝜃

𝑚𝑔

𝑥

𝑦

Friction• Resistance to motion from interactions with other surfaces

𝜃

𝜃

𝑚𝑔sin 𝜃𝑚𝑔

𝑥

𝑦�⃗� f

Normal Force n

Slide 4-22

Friction fk and fs

Slide 4-23

Drag• Resistance to motion through a fluid

Fenway Park (Red Sox) 420 feet dead center 32 feet high

PARABOLA

Drag D and Thrust Fthrust

Slide 4-24

Thrust

• Exerted when mass is released

mm

m

m

�⃗� t𝑣1

𝑣2

𝑣3

𝑣4

Identifying Forces

Slide 4-25

The force on an object at an interface is called the

A. natural force.B. nurturing forceC. normal forceD. negligible force

natural

force

.

nurturin

g force

normal

force

negligib

le force

4% 0%

96%

0%

Example ProblemA block is dragged uphill by a rope. Identify all forces acting on the block.

Slide 4-26

�⃗� 𝑔

�⃗�𝑁

𝑇 𝑅

�⃗� 𝑓

Example ProblemBlock A hangs from the ceiling by a rope. Another block B hangs from A. Identify the forces acting on A.

Slide 4-27

�⃗� 𝑔1

𝑇 1

𝑇 2

A ball, hanging from the ceiling by a string, is pulled back and released. Identify the forces acting on it just after its release.

Example Problem

Slide 4-28

�⃗� 𝑔

𝑇 𝑠

Newton’s Second Law• An object’s acceleration is directly

proportional to Force and inversely proportional to mass

mF

𝑎=𝐹𝑚

Newton’s Second law• Force is a vector, so acceleration is

too

m �⃗�=�⃗�𝑚

�⃗�

How many masses are seen here?… 1 VERY IMPORTANT

Newton’s Second Law

Slide 4-29

Newton’s second law states:

A. The force on a weight is equal to its velocity times gravity.

B. The force of an object equals its acceleration divided by its mass.

C. The force on an object is equal to its mass multiplied by the rate of change of its velocity.

D. The force on a mass is equal to the distance pushed times work done on the mass.

The f

orce on a w

eight is equ..

The f

orce of a

n object e

quals...

The f

orce on an object

is equ..

The f

orce on a m

ass is

equal ..

0% 2%

85%

13%

An elevator, lifted by a cable, is going up at a steady speed. • Identify the forces acting on the elevator. • Is T greater than, equal to, or less than w? Or is there not

enough information to tell?

Example Problem

Slide 4-30

�⃗� 𝑔

𝑇 𝑐

Free Body Diagrams

• Draw all forces acting on the mass in question

m

�⃗�N

�⃗�

Σ �⃗�=0

Free Body Diagrams• If the object is accelerating draw an

acceleration vector away from the object

m

�⃗�N

�⃗�

�⃗� s

�⃗�

Σ �⃗�=𝑚�⃗�

Free-Body Diagrams

Slide 4-31

Newton’s Third Law• Every force occurs as one member

of an action/reaction pair of forces

m

�⃗�N

�⃗�

Newton’s Third Law

Slide 4-32

Checking UnderstandingAn object, when pushed with a net force F, has an acceleration of 2 m/s2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be

A. ½ m/s2.B. 1 m/s2.C. 2 m/s2.D. 4 m/s2.

Slide 4-33

AnswerAn object, when pushed with a net force F, has an acceleration of 2 m/s2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be

A. ½ m/s2.B. 1 m/s2.C. 2 m/s2.D. 4 m/s2.

Slide 4-34

A 40-car train travels along a straight track at 40 mph. A skier speeds up as she skis downhill. On which is the net force greater?

A. The train.B. The skier.C. The net force is the same on both.D. There’s not enough information to tell.

Checking Understanding

Slide 4-35

AnswerA 40-car train travels along a straight track at 40 mph. A skier speeds up as she skis downhill. On which is the net force greater?

A. The train.B. The skier.C. The net force is the same on both.D. There’s not enough information to tell.

Slide 4-36

Checking Understanding10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is

A. greater than the force of Sarah on Jack.B. equal to than the force of Sarah on Jack.C. less than the force of Sarah on Jack.

Slide 4-37

Answer10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is

A. greater than the force of Sarah on Jack.B. equal to than the force of Sarah on Jack.C. less than the force of Sarah on Jack.

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Summary

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Summary

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Summary

Slide 4-41

Reading Quiz1. A “net force” is

A. the sum of the magnitudes of all the forces acting on an object.

B. the difference between two forces that are acting on an object.

C. the vector sum of all the forces acting on an object.D. the force with the largest magnitude acting on an object.

Slide 4-7

Answer1. A “net force” is

A. the sum of the magnitudes of all the forces acting on an object.

B. the difference between two forces that are acting on an object.

C. the vector sum of all the forces acting on an object.D. the force with the largest magnitude acting on an object.

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Reading Quiz2. Which of the following is NOT one of the steps used to identify

the forces acting on an object?

A. Name and label each force the object exerts on the environment.

B. Name and label each contact force acting on the object.C. Draw a picture of the situation.D. Identify “the system” and “the environment.”E. Name and label each long-range force acting on the

object.

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Answer2. Which of the following is NOT on of the steps used to identify

the forces acting on an object?

A. Name and label each force the object exerts on the environment.

B. Name and label each contact force acting on the object.C. Draw a picture of the situation.D. Identify “the system” and “the environment.”E. Name and label each long-range force acting on the

object.

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Reading Quiz3. Which of these is not a force discussed in this chapter?

A. The tension force.B. The normal force. C. The orthogonal force.D. The thrust force.

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Answer3. Which of these is not a force discussed in this chapter?

A. The tension force.B. The normal force. C. The orthogonal force.D. The thrust force.

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Reading Quiz4. An action/reaction pair of forces

A. point in the same direction.B. act on the same object.C. are always long-range forces.D. act on two different objects.

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Answer4. An action/reaction pair of forces

A. point in the same direction.B. act on the same object.C. are always long-range forces.D. act on two different objects.

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MCAT style question

• The sum of the three forces acting on the center point of the rope is assumed to be zero because…A. This point has a very small massB. Tension forces in a rope always cancelC. The point is not acceleratingD. The angle of deflection is very small

MCAT style question

• When you are pulling on the rope as shown, what is the approximate direction of the tension force on the tree?A. NorthB. SouthC. EastD. West

MCAT style question

• Assume that you are pulling on the rope, but the car is not moving. What is the approximate direction of the force from the mud on the car?A. NorthB. SouthC. EastD. West

MCAT style question

• Suppose your efforts work and the car begins to move forward out of the mud. As it does so, the force of the car on the rope is…A. zeroB. Less than the force of the rope on the carC. Equal to the force of the rope on the carD. Greater than the force of the rope on the car