• In this chapter we will learn about the relationship between the forces exerted on an object and the acceleration of the object.

• Forces

• Newton’s three laws.

• Free body diagrams!

• Friction.

Chapter 5: The laws of motion

Reading assignment: Chapter 5; up next Chapter 6 and Chapter 4.4 and 4.5

Homework 5: (due Monday, Sept. 24):

AE1, AE4, AF16, 1, 5, 8, 14, 21, 22, 25, 28, 36, 37, 41, 43(AE – active example, AF – active figure, boxed – student solution manual), long HW set, because chapter combines many concepts.)

Remember: Homework 4 is due Monday, Sept. 17

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Contact forces- Involve physical contact between objects.

Field forces:

-No physical contact between objects

- Forces act through empty space

gravity

electricmagnetic

Measuring forces

- Forces are often measured by determining the elongation of a calibrated spring.

- Forces are vectors!! Remember vector addition.

- To calculate net force on an object you must use vector addition.

Newton’s first law:

In the absence of external forces:

• an object at rest remains at rest

• an object in motion continues in motion with constant velocity (constant speed, straight line)

(assume no friction).

Or: When no force acts on an object, the acceleration of the object is zero.

Inertia: Object resists any attempt to change is velocity

Inertial frame of reference:

-A frame (system) that is not accelerating.

- Newton’s laws hold only true in non-accelerating (inertial) frames of reference!

Are the following inertial frames of reference:

- A cruising car?

- A braking car?

- The earth?

- Accelerating car?

Mass

- Mass of an object specifies how much inertia the object has.

- Unit of mass is kg.

- The greater the mass of an object, the less it accelerates under the action of an applied force.

- Don’t confuse mass and weight (see: bit later).

Newton’s second law(very important)

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

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Unit of force:

• The unit of force is the Newton (1N)

• One Newton: The force required to accelerate a 1 kg mass to 1m/s2.

• 1N = 1kg·m/s2

Two forces act on a hockey puck (mass m = 0.3 kg) as shown in the figure.

(a) Determine the magnitude and direction of the net force acting on the puck

(b) Determine the magnitude and the direction of the pucks acceleration.

Black board example 5.1(related to HW problem) F2 = 8.0 N

2 = 60°

F1 = 5.0 N

1 = 20°

The force of gravity and weight

• Objects are attracted to the Earth.

• This attractive force is the force of gravity Fg.

• The magnitude of this force is called the weight of the object.

• The weight of an object is, thus m·g.

gmFg

The weight of an object can very with location (less weight on the moon than on earth, since g is smaller).

The mass of an object does not vary.

Newton’s third law

If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2 on object 1:

“For every action there is an equal and opposite reaction.”

2112 FF

Action and reaction forces always act on different objects.

Where is the action and reaction force?

Conceptual example:

A large man and a small boy stand facing each other on frictionless ice. They put their hands together and push against each other so that they move apart.

(a) Who experiences the larger force?

(b) Who experiences the larger acceleration?

(c) Who moves away with the higher speed?

(d) Who moves farther while their hands are in contact?

• Analyzing forces

• Free body diagram

• Tension in a rope = magnitude of the force that the rope exerts on object.

Black board: Free body diagram

Applying Newton’s laws

1. Make a diagram (conceptualize)

2. Categorize: no acceleration:

accelerating object:

3. Isolate each object and draw a free body diagram for each object. Draw in all forces that act on the object.

4. Establish a convenient coordinate system.

5. Write Newton’s law for each body and each coordinate component. set of equations.

6. Finalize by checking answers.

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A traffic light weighing 125 N hangs from a cable tied to two other cables fastened to a support as shown in the figure.

Find the tension in the three cables.

Black board example 5.2 (on HW)

Black board example 5.3 (on HW)

A crate of mass m is placed on a frictionless plane of incline = 30.

(a) Determine the acceleration of the crate.

(b) Starting from rest, the crate travels a distance d = 10.2 m to the bottom of the incline. How long does it take to reach the bottom, and what is its speed at the bottom?

Black board example 5.4(on HW)

Attwood’s machine.

Two objects of mass m1 = 2.00 kg and m2 = 4.00 kg are hung over a pulley.

(a) Determine the magnitude of the acceleration of the two objects and the tension in the cord.

Forces of Friction

• Static friction, fs

• Kinetic friction, fk

Friction is due to the surfaces interacting with each other on the microscopic level.

• sliding over bumps

• chemical bonds

time

The following empirical laws hold true about friction:

- Friction force, f, is proportional to normal force, n.

- s and k: coefficients of static and kinetic friction, respectively

- Direction of frictional force is opposite to direction of relative motion

- Values of s and k depend on nature of surface.

- s and k don’t depend on the area of contact.

- s and k don’t depend on speed.

- s, max is usually a bit larger than k.

- Range from about 0.003 (k for synovial joints in humans) to 1 (s for rubber on concrete). See table 5.2 in book.

nf ss nf kk

Black board example 5.5(related to HW)

Measuring the coefficient of static friction

A brick is placed on an inclined board as shown in the figure. The angle of incline is increased until the block starts to move.

Determine the static friction coefficient from the critical angle, c, at which the block starts to move. Calculate for c = 26.5°.

Approximate friction coefficients

s k

Rubber on concrete

1.0 0.8

Wood on wood 0.25-0.5 0.2

Waxed wood on wet snow

0.14 0.1

Synovial joints in humans

0.01 0.003

Black board example 5.6 (on HW)

A car is traveling at 50.0 mi/h on a horizontal highway.

(a) If the coefficient of kinetic friction and static friction between road and tires on an icy day are 0.080 and 0.1, respectively, what is the minimum distance in which the car can stop?

(b) What are the advantages of antilock brakes?