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

Work = Force x Distance

W = F . d

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?

200 N

Solution 6.1 . . . Work for Slackers!

W = F.dW = 200x3W = 600 NmW = 600 J

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

Energy

Energy is the capacity to do work

Kinetic Energy

(motion)

Potential Energy

(position)

Kinetic Energy

K.E. = 1/2 mv2

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

K.E. = 1/2 m v2

600 = 1/2(1000)(v2)v = 1.1 m/s

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!

(a) W = F.dW = mghW = 2x10x3W = 60 J

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

Example 6.4 . . . Downhill

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

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

15 m

30 m

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

(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

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

F = k x

F

x

Slope = “k”Lab Experiment

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

F = k xmg = kx(50 /1000)(9.8) = (20)(x)x = 2.5 cm

Lab Experiment

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

W = F . dW = (kx)(x)W = kx2

W = (120)(0.3)2

W = 10.8 J

X

Correct Solution 6.7 . . . Body building

W = F . dWe 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 = 1/2 kx2

Example 6.8 . . . Lugging the Luggage

What is the speed when the distance is 3 m?

600

40 N

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 storyW = (F)(d)(cos)

600

40 N

10 kg

Hawaii or

Bust!

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

Power is the rate of doing workP = 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

W = mghW = (5)(10)(4)W = 200 JP = W / tP = 200 J / 60 sP = 3.3 J / sP = 3.3 W

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

That’s all folks!