Chapter 7. Kinetic Energy and Work 7.1. What is Physics? 7.2. What Is Energy? 7.3. Kinetic Energy 7.4. Work 7.5. Work and Kinetic Energy 7.6. Work Done.

Chapter 7. Kinetic Energy and Work

7.1. What is Physics?      7.2. What Is Energy?      7.3. Kinetic Energy      7.4. Work      7.5. Work and Kinetic Energy      7.6. Work Done by the Gravitational Force      7.7. Work Done by a Spring Force      7.8. Work Done by a General Variable Force      7.9. Power

What is Physics?  

Kinetic Energy

Kinetic energy K is energy associated with the state of motion of an object.

For an object of mass m whose speed v is well below the speed of light, Kinetic energy K is:

Unit for Kinetic energy is:

Kinetic energy is a scalar quantity.

Work

Work W is energy transferred to or from an object by means of a force acting on the object.

• Energy transferred to the object is positive work,• Energy transferred from the object is negative

work.

Finding an Expression for Work

Properties of Work

• Only the force component along the object’s displacement will contribute to work.

• The force component perpendicular to the displacement does zero work.

• A force does positive work when it has a vector component in the same direction displacement,

• A force does negative work when it has a vector component in the opposite direction.

• Work is a scalar quantity.

Conceptual Example

The figure shows four situations in which a force acts on a box while the box slides rightward a distance across a frictionless floor. The magnitudes of the forces are identical; their orientations are as shown. Rank the situations according to the work done on the box by the force during the displacement, from most positive to most negative.

Question

A shopping bag is hanging straight down from your hand as you walk across a horizontal floor at a constant velocity.

(a) Does the force that your hand exerts on the bag’s handle do any work? Explain.

(b) Does this force do any work while you are riding up an escalator at a constant velocity? Give a reason for your answer.

Example During a storm, a crate of crepe is sliding across a

slick, oily parking lot through a displacement while a steady wind pushes against the

crate with a force . The situation and coordinate axes are shown in Fig. 7-5. How much work does this force do on the crate during the displacement?                            .

Work Done by Variable Forces

2

1

( )x

xxW F x dx

Work Done by a Three-Dimensional Variable Force

The infinitesimal amount of work dW done on the particle by the force is ( )dW F r dr

The work W done by while the particle moves from an initial position with coordinates (x1, y1, z1) to a final position with coordinates (x2, y2, z2) is then 2

1

( )r

rW F r dr

Net Work–Kinetic Energy Theorem

When a net external force does work Wnet on an object, the change of kinetic energy of the object equals to the net work:

netf iW KE KE

Units of work and energy are: 1 joule = 1 J =1 kg∙m2/s2 = 1 N∙m

2

1

( )rnet net

rW F r dr

Where

Conceptual Example   Work and Kinetic Energy

Figure illustrates a satellite moving about the earth in a circular orbit and in an elliptical orbit. The only external force that acts on the satellite is the gravitational force. For these two orbits, determine whether the kinetic energy of the satellite changes during the motion.

EXAMPLE A 2.0 kg stone moves along an x axis on a horizontal

frictionless surface, acted on by only a force Fx(x) that varies with the stone's position as shown in Fig.

• (a) How much work is done on the stone by the force as the stone moves from its initial point at x1 = 0 to x2 = 5 m?

• (b) The stone starts from rest at x1 = 0 m. What is its speed at x = 8 m?

Checkpoint 1

A particle moves along an x axis. Does the kinetic energy of the particle increase, decrease, or remain the same if the particle’s velocity changes

(a) from −3 m/s to −2 m/s and

(b) from −2 m/s to 2 m/s?

(c) In each situation, is the work done on the particle positive, negative, or zero?

EXAMPLE During a storm, a crate of crepe is sliding across a slick,

oily parking lot through a displacement while a steady wind pushes against the crate with a force The situation and coordinate axes are shown in Fig.

netF F

(a)How much work does this force from the wind do on the crate during the displacement?

(b)If the crate has a kinetic energy of 10 J at the beginning of displacement , what is its kinetic energy at the end of assuming ?

Example:   Deep Space • The space probe Deep Space 1 was launched October

24, 1998. Its mass was 474 kg. The goal of the mission was to test a new kind of engine called an ion propulsion drive, which generates only a weak thrust, but can do so for long periods of time using only small amounts of fuel. The mission has been spectacularly successful. Consider the probe traveling at an initial speed of v0=275 m/s. No forces act on it except the 56.0-mN thrust of its engine. This external force F is directed parallel to the displacement s of magnitude . Determine the final speed of the probe, assuming that the mass remains nearly constant.

Example Three Forces Figure shows three forces applied

to a trunk that moves leftward by 3.00 m over a frictionless floor. The force magnitudes are FA = 5.00 N, FB = 9.00 N, and FC = 3.00 N. During the displacement, (a) what is the net work done on the trunk by the three forces and (b) does the kinetic energy of the trunk increase or decrease?

Example The skateboarder in Figure a is coasting down a ramp,

and there are three forces acting on her: her weight W (magnitude=675 N), a frictional force f (magnitude=125 N) that opposes her motion, and a normal force FN (magnitude=612 N). (a) Determine the net work done by the three forces when she coasts for a distance of 9.2 m. (b) If the skateboard’s initial speed is zero, what will be her final kinetic energy?

Work Done by the Gravitational Force

gravity ( ) ( ) ( )y f i f i f iW F h h mg h h mgh mgh

gravity 0W

gravity 0W

Work done on the ball by the gravity is:

If an object is moving down,

•If an object is moving up,

Work done by the gravity only depends on the change of height, not depends on the path.

Work Done by a Spring ForceThe spring force given by

Hooke’s Law:springxF k x

The work done by spring force:

2 22 1

1 1( )2 2

springW kx kx

Example•  In Fig., a horizontal force Fa of magnitude 20.0 N is applied to a

3.00 kg psychology book as the book slides a distance d=0.500m up a frictionless ramp at angle θ=30 degrees. (a) During the displacement, what is the net work done on the book by Fa , the gravitational force on the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement?

Example

The only force acting on a 2.0 kg body as it moves along a positive x axis has an x component , with x in meters. The velocity at is 8.0 m/s. (a) What is the velocity of the body at ? (b) At what positive value of x will the body have a velocity of 5.0 m/s?

Power The rate at which work is done by a force

is called the power.

• The average power due to the work done by a force during that time interval as

• We define the instantaneous power P as the instantaneous rate of doing work, so that

The units of power

Sample Problem • Figure 7-16 shows constant forces F1 and F2 acting on

a box as the box slides rightward across a frictionless floor. Force F1 is horizontal, with magnitude 2.0 N; force F2 is angled upward by 60° to the floor and has magnitude 4.0 N. The speed v of the box at a certain instant is 3.0 m/s. What is the power due to each force acting on the box at that instant, and what is the net power? Is the net power changing at that instant?