Download Work, Power, Energy

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Investigation 4
Work, Power, Energy
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 = ____60___________ 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 = (60 kg) x (10 m/s2) = 600_________ 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_______ m.
The work done climbing the stairs is
____1200_______ Joules
(600 N) x (2 m) = 1200 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_______ seconds
4.
Now find your power output while you were climbing the stairs.
Power output 
work done in Joules
time in seconds
Power = (1200 Joules)/(5 sec) = 600 Watts
_____600_____
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.
Power = (600 Joules)/(746 Jouels/hp) = 0.8 hp
`
_____0.8______ 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
(Joules). 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)x(3 m/s) = 9 Joules
_____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 will be four times greater. At a speed of 6 m/s the kinetic energy will be
(1/2)x(2)x(6)x(6) = 36 Joules.
Potential energy represents the ability or capacity of an object to do work be cause 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 physics book when held 3 meters above the floor.
PE = (2 kg)x(10 m/s2)x(3 m) = 60 Joules
____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 Joules
_____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.
Potential energy does not depend on the speed, only on its height. So, potential energy is still
(2 kg)x(10 m/s2)x(1 m) = 20 Joules.
_____20_____ Joules
11. If you were to double the height from which you dropped the book, would it hit the floor twice as
hard? Explain.
Yes. The potential energy is now (2 kg)x(10 m/s2)x(2 m) = 40 Joules – twice as much as before.
Conservation of Energy
We know that energy cannot be created or destroyed, and we also know that it can be converted from one
form to another (e.g., kinetic energy to potential energy and vice versa). So, we say that the total
mechanical energy 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, not the time.)
A
ground
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)(10)(40) =
400
0
400 + 0 =
400
400
(1/2)(1)(10)2
=50
400 + 50 =
450
B
(1)(10)(30) =
300
400 – 300
= 100
400
300
450 – 300 =
150
450
C
(1)(10)(20) =
200
400 – 200
= 200
400
200
450 – 200 =
250
450
D
0
400
400
0
450
450
B
10 m
C
20 m
ball thrown downward at 10 m/s
position
ball dropped
D
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, e.g., heat, sound, and deforming the ground.