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Work, Energy, and Power

- Samar Hathout
- KDTH 101

Work

Work is the transfer of energy through motion.

In order for work to take place, a force must be

exerted through a distance. The amount of work

done depends on two things the amount of force

exerted and the distance over which the force is

applied. There are two factors to keep in mind

when deciding when work is being done something

has to move and the motion must be in the

direction of the applied force. Work can be

calculated by using the following formula

Workforce x distance

Work

Work is done on the books when they are being

lifted, but no work is done on them when they are

being held or carried horizontally.

Work can be positive or negative

- Man does positive work lifting box
- Man does negative work lowering box
- Gravity does positive work when box lowers
- Gravity does negative work when box is raised

Work done by a constant Force

- W F s F s cos ? Fs s
- F magnitude of force
- s s magnitude of displacement
- Fs magnitude of force in
- direction of displacement
- Fs F cos ?
- angle between displacement and force
- vectors
- Kinetic energy Ekin 1/2 m v2
- Work-Kinetic Energy Theorem

F

s

?Ekin Wnet

Work Done by Gravity

- Example 1 Drop ball

Wg (mg)(S) S h0-hf Wg mg(h0-hf)

mg(h0-hf) Epot,initial Epot,final

S

S

mg

mg

y

y

x

x

Work Done by Gravity

- Example 2 Toss ball up

Wg (mg)(S) S h0-hf Wg -mg(h0-hf)

Epot,initial Epot,final

S

mg

y

x

Work Done by Gravity

- Example 3 Slide block down incline

h0

Wg (mg)(S)cos? S h/cos? Wg

mg(h/cos?)cos? Wg mgh with h h0-hf

?

h

S

mg

hf

- Work done by gravity is independent of path
- taken between h0 and hf
- The gravitational force is a conservative

force.

Work done by a Variable Force

- The magnitude of the force now depends on the
- displacement Fs(s)
- Then the work done by this force is equal to the
- area under the graph of Fs versus s, which can be

- approximated as follows
- W S DWi S Fs(si) Ds

(Fs(s1)Fs(s2)) Ds

Concept Question

- Imagine that you are comparing three different

ways of having a ball move down through the same

height. In which case does the ball reach the

bottom with the highest speed? - 1. Dropping2. Slide on ramp (no friction)3.

Swinging down4. All the same

In all three experiments, the balls fall from the

same height and therefore the same amount of

their gravitational potential energy is converted

to kinetic energy. If their kinetic energies are

all the same, and their masses are the same, the

balls must all have the same speed at the end.

Types of Energy

Kinetic Energy

Potential Energy

Forms of Energy

Chemical

Sound

Radiant

Electrical

Mechanical

Magnetic

Thermal

Nuclear

Mechanical Energy

Mechanical energy is the movement of machine

parts. Mechanical energy is also the total

amount of kinetic and potential energy in a

system. Wind-up toys, grandfather clocks, and

pogo sticks are examples of mechanical energy.

Wind power uses mechanical energy to help create

electricity.

Potential energy Kinetic energy Mechanical

energy

Mechanical Energy

Potential energy Kinetic energy Mechanical

energy

Example of energy changes in a swing or pendulum.

Conservation of Mechanical Energy

- Total mechanical energy of an object remains

constant - provided the net work done by

non-conservative forces - is zero
- Etot Ekin Epot constant
- or
- Ekin,fEpot,f Ekin,0Epot,0
- Otherwise, in the presence of net work done by
- non-conservative forces (e.g. friction)
- Wnc Ekin,f Ekin,0 Epot,f-Epot,i

Example Problem

- Suppose the initial kinetic and potential

energies of a system are 75J and 250J

respectively, and that the final kinetic and

potential energies of the same system are 300J

and -25J respectively. How much work was done on

the system by non-conservative forces? - 1. 0J 2. 50J 3. -50J 4. 225J 5.

-225J

Work done by non-conservative forces equals the

difference between final and initial kinetic

energies plus the difference between the final

and initial gravitational potential energies. W

(300-75) ((-25) - 250) 225 - 275 -50J.

Samar Hathout

Samar Hathout

Kinetic Energy

Same units as work

Remember the Eq. of motion

Multiply both sides by m,

Samar Hathout

Example

Samar Hathout

Potential Energy

- Potential energy exists whenever an object which

has mass has a position within a force field

(gravitational, magnetic, electrical). - We will focus primarily on gravitational

potential energy (energy an object has because of

its height above the Earth)

Potential Energy

If force depends on distance,

For gravity (near Earths surface)

Samar Hathout

Conservation of Energy

- Conservative forces
- Gravity, electrical, QCD
- Non-conservative forces
- Friction, air resistance
- Non-conservative forces still conserve

energy!Energy just transfers to thermal energy

Samar Hathout

Example

A diver of mass m drops from a board 10.0 m above

the water surface, as in the Figure. Find his

speed 5.00 m above the water surface. Neglect air

resistance.

9.9 m/s

Example

A skier slides down the frictionless slope as

shown. What is the skiers speed at the bottom?

start

H40 m

finish

L250 m

28.0 m/s

Example

Three identical balls are thrown from the top of

a building with the same initial speed.

Initially, Ball 1 moves horizontally. Ball 2

moves upward. Ball 3 moves downward.Neglecting

air resistance, which ball has the fastest speed

when it hits the ground?

A) Ball 1 B) Ball 2 C) Ball 3 D) All have the

same speed.

Springs (Hookes Law)

Proportional to displacement from equilibrium

Potential Energy of Spring

Example

A 0.50-kg block rests on a horizontal,

frictionless surface as in the figure it is

pressed against a light spring having a spring

constant of k 800 N/m, with an initial

compression of 2.0 cm.

b) To what height h does the block rise when

moving up the incline?

3.2 cm

Power

- Average power is the average rate at which a net

force - does work
- Pav Wnet / t
- SI unit P J/s watt (W)
- Or Pav Fnet s /t Fnet vav

Example

A 1967 Corvette has a weight of 3020 lbs. The 427

cu-in engine was rated at 435 hp at 5400 rpm.

a) If the engine used all 435 hp at 100

efficiency during acceleration, what speed would

the car attain after 6 seconds? b) What is the

average acceleration? (in gs)

a) 120 mph b) 0.91g

Example

Consider the Corvette (w3020 lbs) having

constantacceleration of a0.91g

a) What is the power when v10 mph? b) What is

the power output when v100 mph?

a) 73.1 hp b) 732 hp (in real world a is

larger at low v)

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