Download Inv 6

Name________________KEY___________________________________ Date_____10/2/15_____________
Investigation 6
Work, Power, and Energy
In physics, the definition of work is very different from its use in everyday conversation. Specifically,
work equals the force acting on an object multiplied by the distance the object moves in the direction of
the force. Or in equation form: work = force x distance.
1.
Write your mass in kilograms, mass = _____80__________ kg. (If you know your weight in pounds,
you can get an approximate value of your mass by dividing your weight in Pounds by 2.2).
2.
When you climb stairs, you are doing work lifting your body upward against the earth’s downward
gravitational pull. The force you need to exert to lift yourself vertically at a constant velocity is equal
to your weight (remember w = m x g, where g = 10 m/s2).
Calculate your weight in Newtons, weight = ___80 x 10 = 800_____ Newtons.
Now calculate the work you do in climbing stairs. Remember that the work done is the force (your
weight) times the distance you move the object (height of the stairs).
Work = Force x (distance moved in the direction of the force)
The approximate height of the staircase outside our lab is ___2.4___ m.
The work done by you climbing the stairs is
Work = (800 N) x (2.4 m) = 1920
_____1920____ Joules
3.
Time yourself climbing the stairs. You can do it rapidly, slowly, or at any speed you choose. But no
matter how you do it, hold onto the railing. The time is
____5.2______ seconds
4.
Now find your power output while you were climbing the stairs.
Power output 
work done in Joules
time in seconds
My power output = (1920 Joules)/(5.2 sec) = 369
____369____
Joules
or Watts
sec
How does your power output compare to a 100 Watt lightbulb? (rhetorical question)
5.
This value can also be expressed in horsepower. In order to do so, divide the power output
expressed in Watts by 746 to get your horsepower.
369/746 = 0.49
_____0.49_____ hp
How does your power output compare to a horse’s power output? (rhetorical question)
Kinetic Energy represents the ability or capacity of an object to do work because of its motion (the energy
an object has because of it is moving). The units for kinetic energy are the same as the units for work. In
order to determine the kinetic energy of an object, the following expression can be used:
kinetic energy = (1/2) x mass x (velocity)2
6.
Calculate the kinetic energy of your physics book (mass = 2 kg) when thrown with a velocity of 3
m/s toward a wall.
KE = (1/2) x (2 kg) x (3 m/s)2 = 9
____9_______ Joules
7.
If you threw the book with a velocity that was twice as great, would the damage to the wall by twice
as much? Explain.
The damage would be four times greater. Note that the kinetic energy in this case is four times
greater.
KE = (1/2) x (2 kg) x (6 m/s)2 = 36 Joules, 4 times greater than 9 Joules
Potential energy represents the ability or capacity of an object to do work because of its position (the
energy an object has because of where it is located). The units for potential energy are the same as the
units for work. In order to determine the potential energy of an object (specifically, gravitational
potential energy), the following expression can be used:
potential energy = (mass) x g x (height) = (weight) x (height)
8.
Calculate the potential energy of your 2 kg physics book when held 3 meters above the floor.
PE = (2 kg) x (10 m/s2) x (3 m) = 60
_____60____ Joules
9.
You let the book drop. When the book is 1 meter above the floor, calculate its potential energy.
PE = (2 kg) x (10 m/s2) x (1 m) = 20
_____20_____ Joules
10. Instead of dropping the book, suppose you threw the book downward with a velocity of 10 m/s
from a height of 3 m. Calculate the potential energy of the book when it is 1 meter above the floor.
PE = (2 kg) x (10 m/s2) x (1 m) = 20
_____20_____ Joules
11. The answers to questions 9 and 10 above should be the same. But why should the answers be the
same since the book in question 10 is traveling faster than the book in question 9?
The potential energy of a object only depends on its height. The speed of the object has no effect
on the potential energy.
Conservation of Energy
We know that energy cannot be created or destroyed, but can only be converted from one form to another
(e.g., kinetic energy to potential energy and vice versa). So, we say that since it cannot be created or
destroyed, the total mechanical energy must remain the same value at all times. It is “conserved”
(conservation of energy), i.e., the value of the total mechanical energy stays the same.
Suppose a 1 kg ball is at the top of a 40 meter high cliff. In the first case, at position A, we drop the ball
and in the second case we throw the ball downward so that it leaves our hand at 10 m/s. Position D is
just before the ball hits the ground. Take the acceleration due to gravity to be 10 m/s 2.
Complete the table below. Make as few calculations as possible. If you keep in mind the idea of
conservation of energy, you will not need to make only a few calculations.
Notice that the gravitational potential energy is zero at position D, that is, the potential energy is
measured from the ground. (Notice that the heights are given, so potential energies can be easily found.)
A
position
ball dropped
10 m
gravitational
potential
energy
(Joules)
kinetic
energy
(Joules)*
total
mechanical
energy
(Joules)
gravitational
potential
energy
(Joules)
kinetic
energy
(Joules)*
total
mechanical
energy
(Joules)
A
1 x 10 x 40 =
400
(1/2) x 1 x
02 = 0
400 + 0 =
400
1 x 10 x 40
=
400
(1/2)x1x102
= 50
400 + 50 =
450
B
1 x 10 x 30
= 300
400 – 300
= 100
400,
energy
conserved
1 x 10 x 30
= 300
450 – 300
= 150
450,
energy
conserved
C
1 x 10 x 20
= 200
400 – 200
= 200
400,
energy
conserved
1 x 10 x 20
= 200
450 – 200
= 250
450,
energy
conserved
D
0
400 – 0
400
400,
energy
conserved
0
450 – 0
450
450,
energy
conserved
B
10 m
C
20 m
D
ground
ball thrown downward at 10 m/s
*In this case, the kinetic energy can only be calculated directly (using
1
2
2
mv ) at
position A.
After the ball hits the ground and stops, its gravitational potential energy is zero, its kinetic energy is zero,
and therefore its total mechanical energy appears to be zero. So what happened to all the energy?
The energy was converted into other forms of energy, namely heat energy and sound (kinetic energies).