Chapter 5

Work and Energy

J joule 1 mN 1

Force, displacement WORK

Units of work

1180cos

090cos

10cos

Work is a scalar, but it can be negative!!!

Example 1 Pulling a Suitcase-on-Wheels

Find the work done if the force is 45.0-N, the angle is 50.0 degrees, and the displacement is 75.0 m.

Just holding the weight = 0 J of work

The truck is accelerating ata rate of +1.50 m/s2. The massof the crate is 120-kg and itdoes not slip. The magnitude ofthe displacement is 65 m.

What is the total work done on the crate by all of the forces acting on it?

Consider a constant net external force acting on an object.

The object is displaced a distance s, in the same direction asthe net force.

The work is simply

F

DEFINITION OF KINETIC ENERGY

The kinetic energy KE of and object with mass mand speed v is given by

221KE mv

Energy and work have the same unit: [J]

THE WORK-ENERGY THEOREM

When a net external force does work on and object, the kineticenergy of the object changes according to

2212

f21

of KEKE omvmvW

Example 4 Deep Space 1

The mass of the space probe is 474-kg and its initial velocityis 275 m/s. If the 56.0-mN force acts on the probe through adisplacement of 2.42×109m, what is its final speed?

sm805fv

Answer:

A 58-kg skier is coasting down a 25o slope.Near the top of the slope, her speed is 3.6 m/s. She accelerates down the slope because of the gravitational force, even though a kinetic friction force is acting on her. The coefficient of kinetic friction = 0.137. Determine the speed at a point that is displaced 57 m downhill.

Determine acceleration:

Mass of the skier will not matter in this problem.

Energy

Mechanical

Nonmechanical

Gravitational

Kinetic Potential

Elastic

Kinetic Energy

Practice – in your head

A 6.0 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy?

The 0.100 kg mouse runs as fast as the cat. What is the mouse’s kinetic energy?

A 24 kg dog joins the race with the same kinetic energy as the cat. What is the dog’s speed?

Potential Energy

• Potential energy – the energy of the body due to its position (state)

• Gravitational potential energy – the energy of an object due to its position relative to the Earth or some other gravitational source (it is relative!!!)

Potential energy – ‘stored’ energy

Compare potential energy of these balls.

Elastic Potential EnergyElastic potential energy – energy in a

stretched or compressed elastic object

k – spring constant

x – distance of deformation21

2ePE kx

Elastic Potential Energy

When a 2.0 kg object is attached to a vertical spring, the spring is stretched 10.0 cm so that the mass is 50.0 cm above the table.a) What is the gravitational potential energy

associated with the mass relative to the table?b) What is the spring’s elastic potential energy if the

spring constant is 400.0 N/m?c) What is the total potential energy of this system?

Work-Energy Theorem

On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

Conservation of ME

IN IDEAL SYSTEMS(no friction!)

Example 1

Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg.

Friction is present!• Mechanical Energy

is not conserved in the presence of friction.

• As a sanding block slides on a piece of wood, energy (in the form of heat) is dissipated into the block and surface.

But idealizing helps…

Example 2• A small 10.0 g ball is held to a slingshot that

is stretched 6.0 cm. The spring constant is 2.0·102N/m

• a) what is the elastic potential energy of the slingshot before it is released?

• b) what is the kinetic energy of the ball just after the slingshot is released?

• c) What is the ball’s speed at that instant?• d) how high would the ball rise if it was shot

directly upward?

Example 2

Power

Power

Many mountain roads are built so that they zigzag up the mountain rather than go straight up toward the peak. What is the advantage of such a design from the viewpoint of energy conservation is power?

A light bulb is described as having 60 watts. What’s wrong with this phrase?

Example 1

• Two horses pull a cart. Each exerts a 250.0 N force at a 2.0 m/s speed for 10 min.

• a) Calculate the power delivered by the horses.

• b) How much work is done by the two horses?

Example 1

Example 2

• A 1000kg elevator carries a maximum load of 800.0 kg. A constant frictional force of 4kN retards the elevator’s motion upward. What minimum power, in kilowatts, must the motor deliver to lift the fully loaded elevator at a constant speed of 3.00 m/s?

Example 2