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Physics 121 6. Work and Energy 6.1 Work 6.3 Kinetic Energy 6.4 Potential Energy 6.5 Conservative and Non-conservative forces 6.6 Mechanical Energy / Problem Solving 6.8 Conservation of Energy 6.9 Dissipative Forces / Problem Solving 6.10 Power Work

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6 work and energy
6.Work and Energy

6.1 Work

6.3 Kinetic Energy

6.4 Potential Energy

6.5 Conservative and Non-conservative forces

6.6 Mechanical Energy / Problem Solving

6.8 Conservation of Energy

6.9 Dissipative Forces / Problem Solving

6.10 Power

slide3
Work

Work = Force x Distance

W = F . d

example 6 1 work for slackers

200 N

Example 6.1 . . . Work for Slackers!

You push a car with a force of 200 N over a distance of 3 m. How much work did you do?

solution 6 1 work for slackers
Solution 6.1 . . . Work for Slackers!

W = F.d

W = 200x3

W = 600 Nm

W = 600 J

Note: A Joule (J) is just another term for newton . meter (N m)

energy
Energy

Energy is the capacity to do work

Kinetic Energy

(motion)

Potential Energy

(position)

kinetic energy
Kinetic Energy

K.E. = 1/2mv2

example 6 2 kinetic energy
Example 6.2 . . . Kinetic Energy

The K.E. of a car is 600 J and its mass is 1000 kg. What is its speed?

solution 6 2 kinetic energy
Solution 6.2 . . . Kinetic Energy

K.E. = 1/2 m v2

600 = 1/2(1000)(v2)

v = 1.1 m/s

example 6 3 save your work
Example 6.3 . . . Save your work!

You lift a 2 kg book and put it on a shelf 3 meters high.

(a) How much work did you do?

(b) Was the work “lost”?

solution 6 3 save your work
Solution 6.3 . . . Save your work!

(a)

W = F.d

W = mgh

W = 2x10x3

W = 60 J

(b)

Work was stored as Potential Energy (hidden). So gravitational P.E. = mgh

example 6 4 downhill

15 m

30 m

Example 6.4 . . . Downhill

A 65 kg bobsled slides down a smooth (no friction) snow-laden hill. What is its speed at the bottom?

solution 6 4 downhill

15 m

30 m

Solution 6.4 . . . Downhill

P.E. = K.E.

mgh = 1/2 mv2

9,555 = (1/2)(65) v2

v = 17.1 m/s

example 6 5 sticky bobsled
Example 6.5 . . . Sticky bobsled

Suppose the speed of the bobsled was actually measured to be 14.8 m/s instead of 17.1 m/s

(a) What could have caused that?

(b) What was the work done by the bobsled against friction?

solution 6 5 sticky bobsled
Solution 6.5 . . . Sticky bobsled

(a) Not all the P.E. was converted to K.E. because some work was lost (heat energy) in doing work against friction: P.E. = K.E. + Wf

(b) mgh = 1/2 mv2 + Wf

9,555 = 1/2(65) (14.8)2 + Wf

Wf = 2,436 J

stretching springs

Lab Experiment

Slope = “k”

F

x

Stretching Springs

Hooke’s Law: The amount of stretch is directly proportional to the force applied.

F = k x

example 6 6 springy spring
Example 6.6 . . . Springy Spring

The spring constant (k) of a spring is 20 N/m. If you hang a 50 g mass, how much will it stretch?

solution 6 6 springy spring

Lab Experiment

Solution 6.6 . . . Springy Spring

F = k x

mg = kx

(50 /1000)(9.8) = (20)(x)

x = 2.5 cm

example 6 7 body building
Example 6.7 . . . Body building

How much work would you have to do to stretch a stiff spring 30 cm (k = 120 N/m)?

solution 6 7 body building
“Solution” 6.7 . . . Body building

W = F . d

W = (kx)(x)

W = kx2

W = (120)(0.3)2

W = 10.8 J

X

correct solution 6 7 body building
Correct Solution 6.7 . . . Body building

W = F . d

We must use the AVERAGE Force!

W = (1/2)(kx)(x)

W =1/2 kx2

W = (1/2)(120)(0.3)2

W = 5 .4 J

P.E. of a Spring = 1/2kx2

example 6 8 lugging the luggage

40 N

600

10 kg

Hawaii or

Bust!

Example 6.8 . . . Lugging the Luggage

What is the speed when the distance is 3 m?

solution 6 8 lugging the luggage

40 N

600

10 kg

Hawaii or

Bust!

Solution 6.8 . . . Lugging the Luggage

What is the speed when the distance is 3 m?

F.d = 1/2 m v2

(40 cos 600)(3) = (1/2)(10)(v2)

v = 3.5 m/s

Moral of the story

W = (F)(d)(cos)

conservative forces
Conservative Forces

If the work done against a force does not depend on the path taken then that force is called a conservative force. Examples are gravity and spring force. The total mechanical energy (P.E. + K.E.) will remain constant in this case.

If the work done against a force depends on the path taken then that force is called a non-conservative force. Example is friction. The total mechanical energy (P.E. + K.E.) will not remain constant in this case.

Vote Democrat . . . Just kidding!

example 6 9 playing with power
Example 6.9 . . . Playing with Power

Power is the rate of doing work

P = W / t

A pump can lift at most 5 kg of water to a height of 4 m every minute. What is the power rating of this pump?

solution 6 9 playing with power
Solution 6.9 . . . Playing with Power

W = mgh

W = (5)(10)(4)

W = 200 J

P = W / t

P = 200 J / 60 s

P = 3.3 J / s

P = 3.3 W

Note: Watt (W) is just another term for Joules / second (J / s)