10.2 work 10.3 energy and conservation of energy · measurable change in a system, caused by a...

Chapter 10: Work and Energy

10.2 Work

10.3 Energy and Conservation of Energy

10.2 Work

In physics, work

has a very specific

meaning.

In physics, work

represents a

measurable change

in a system, caused

by a force.

10.2 Work

If you push a box with a force of one

newton for a distance of one meter, you

have done exactly one joule of work.

10.2 Work (force is parallel to distance)

W = F x dDistance (m)

Force (N)

Work (joules)

10.2 Work (force at angle to distance)

W = Fd cos (q)

Distance (m)

Force (N)

Work (joules) Angle

10.2 Work done against gravity

W = mghHeight object raised (m)

Gravity (m/sec2)

Work (joules)

Mass (g)

1. You are asked for the work and time it takes to do work.

2. You are given mass, height, and work done per second.

3. Use: W = mgh.

4. Solve: W = (1,500 kg) ( 9.8 N/kg) (50 m) = 735,000 J

5. At a rate of 10,000 J/s, it takes 73.5 s to lift the beam.

Calculate work done against gravity

A crane lifts a steel beam with a mass of 1,500

kg. Calculate how much work is done against

gravity if the beam is lifted 50 meters in the air.

How much time does it take to lift the beam if

the motor of the crane can do 10,000 joules of

work per second?

10.2 Work done by a machine

Work is usually done when a force is applied to

a simple machine.

All machines can be described in terms of input

work and output work.

In any machine, some of the input work goes to

overcoming friction.

The output work is always less than the input

work because of the energy lost to friction.

Chapter 10 Work and Energy

10.2 Work

10.3 Energy and Conservation of Energy

Inv 10.3 Energy and Conservation of

Energy

Investigation Key Question:

How is motion on a track

related to energy?

10.3 Energy and Conservation of Energy

Energy describes a system’s ability to cause

change.

A system that has energy has the ability to do

work.

Energy is measured in the same units as work

because energy is transferred during the

action of work.

10.3 Different forms of energy

Mechanical energy is the energy possessed by

an object due to its motion or its position.

Radiant energy includes light, microwaves,

radio waves, x-rays, and other forms of

electromagnetic waves.

Nuclear energy is released when heavy atoms

in matter are split up or light atoms are put

together.

The electrical energy we use is derived from

other sources of energy.

The workings of the universe can be

viewed as energy flowing from one

place to another and changing back

and forth from one form to another.

10.3 Potential Energy

Objects that have potential energy do not use

the energy until they move.

An object’s potential energy comes from the

gravity of Earth.

Technically, energy from height is called

gravitational potential energy.

Other forms of potential energy also exist, such

as potential energy stored in springs.

10.3 Potential Energy

Ep = mgh Height (m)

Mass (kg)

Potential Energy

(joules)

Acceleration

of gravity (m/sec2)

1. You are asked for potential energy and time.

2. You are given mass, height and work done per second.

3. Use: Ep = mgh.

4. Solve for Ep = (102 kg) (9.8 N/kg) (4 m) = 3,998 J.

5. At a rate fof 50 J/s, it takes 80 s to push the cart up the

ramp.

Calculating potential energy

A cart with a mass of 102 kg is pushed up a ramp.

The top of the ramp is 4 meters higher than the

bottom. How much potential energy is gained by

the cart? If an average student can do 50 joules of

work each second, how much time does it take to

get up the ramp?

10.3 Kinetic Energy

Energy of motion is called kinetic energy.

The kinetic energy of a moving object

depends on two things: mass and speed.

Kinetic energy is proportional to mass.

10.3 Kinetic Energy

Mathematically, kinetic energy increases as the square of speed.

If the speed of an object doubles, its kinetic energy increases four times (mass is constant).

10.3 Kinetic Energy

Ek = 1 mv2

2

Speed (m/sec)

Mass (kg)

Kinetic Energy

(joules)

10.3 Kinetic Energy

Kinetic energy becomes important in

calculating braking distance.

10.3 The formula for kinetic energy

A force (F) is applied to mass (m) and

creates acceleration (a).

After a distance (d), the ball has reached speed (v),

therefore the work done is its mass times acceleration

time distance: W= fd = (ma) x d = mad

Also: d = ½ at2

Replace d in the equation for work, combine similar

terms: W= ma (½ at2) = ½ ma2t2

Also: v = at, so v2 = a2t2

Replace a2t2 by v2 shows that the resulting work is the

formula for kinetic energy: W = ½ mv2

1. You are asked for kinetic energy and stopping distance

2. You are given mass, speed and force of brakes.

3. Use Ek = 1/2mv2 and W= fd

4. Solve for Ek = ½ (1,300 kg) ( 30 m/s)2 = 585,000 J

To stop the car, work done by brakes = Ek of car, so W = Ek

Solve for distance = W ÷ f = 585,000J ÷ 9,500 N = 62 m

Calculating kinetic energy

A car with a mass of 1,300 kg is going straight ahead at a speed

of 30 m/s (67 mph). The brakes can supply a force of 9,500 N.

Calculate:

a) The kinetic energy of the car.

b) The distance it takes to stop.

10.3 Law of Conservation of Energy

As energy takes different forms and changes

things by doing work, nature keeps perfect

track of the total.

No new energy is created and no existing

energy is destroyed.

10.3 Energy in a closed system

The conservation of energy is most useful when

it is applied to a closed system.

Because of the conservation of energy, the total

amount of matter and energy in your system

stays the same forever.

10.3 Energy in a closed system

The total energy in the system is the potential

energy of the ball at the start.

Later, the ball is at a lower height (h) moving

with speed (v) and has both potential and kinetic

energy.

Every day in the United States the average person uses

about 90 million joules of electrical energy.

This energy comes from many sources, including burning

coal, gas and oil, nuclear power, and hydroelectric power.

Hydroelectric Power

In hydroelectric power, the potential

energy of falling water is converted

to electricity.

No air pollution is produced, nor

hazardous wastes created.

Practice Problem #1.

A 50-kilogram boy and his 100-kilogram father went jogging. Both ran at a

rate of 5 m/sec. Who had more kinetic energy? Show your work and

explain.

Practice Problem #2.

What is the potential energy of a 10-newton book sitting on a shelf 2.5

meters high?