Name________________________________________________________ Date__________________________
Investigation 3
Work, Power, Energy, Impulse, Momentum
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/s2.
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
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
ball thrown downward at 10 m/s
position
10 m
ball dropped
20 m
D
ground
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.
Impulse and Momentum
The Impulse-Momentum relationship says: Impulse = Force x time of impact = change in momentum
1.
An unfortunate bug splatters on the windshield of a car traveling at 100 km/hr on the freeway.
a.
Compare the force of the car on the bug to the force of the bug on the car. Which one is greater?
Forces are the same – Newton’s Third Law (car on bug, bug on car)
b.
The time of impact is the same for both the bug and the car. Compare the impulse on the bug to
the impulse on the car. Which one is greater?
Impulses are the same. Same force and same time give the same impulse.
c.
Compare the change in momentum of the bug to the change in momentum of the car. Which
one is greater?
Impulse equals change in momentum. So, if the impulses are the same, then the changes in
momentum are the same.
d.
Does the bug or the car undergo the greater acceleration? Explain briefly.
The bug undergoes the greater acceleration. It has less mass. For the same force (which they
are), the smaller the mass, the greater the acceleration and the greater the mass, the smaller
the acceleration – Newton’s Second Law.
2.
Block A is 8 kg and is sliding on a horizontal, frictionless surface at 4 m/s. It collides with and sticks
to a 2 kg block that is at rest.
a.
What is the value of the total momentum of the system before the collision?
Before: (8 kg)x(4 m/s) + (2 kg)x(0 m/s) = 32 kg m/s
b.
What should the value of the total momentum of the system be after the collision?
The same as before: 32 kg m/s
c.
What are the speeds of the blocks after the collision?
Momentum before = Momentum after.
Momentum after = (8 kg + 2 kg)x(unknown speed) = 32 kg m/s
Unknown speed = (32 kg m/s)/(8 kg + 2 kg) = (32 k m/s)/(10 kg) = 3.2 m/s
A 50 kg bungee jumper jumps off a bridge. She is in free fall for 3 sec. At 3 sec the bungee cord begins to
stretch, slows her down, and brings her to a stop 2 sec later. Take the acceleration due to gravity to be 10
m/s2.
Fill in the blanks in the following table.
type of
motion
time (sec)
velocity
(m/s)
momentum
(kg m/s)
0
0
(50)x(0) = 0
1
10
(50)x(10) =
500
2
20
(50)x(20) =
1000
3
30
(50)x(30) =
1500
0
0
1 sec
2 sec
free
fall
3 sec
slowed by
bungee
v=0
4
5
5 sec
By how much did her momentum change from time t = 3 sec to time t = 5 sec?
___-1500__________ kg m/s
Change in momentum = 0 – 1500 kg m/s = -1500 kg m/s
What is the value of the impulse on her from 3 sec to 5 sec?
Impulse = change in momentum = -1500 kg m/s
_____-1500__________ Newton sec
What is the average force that acted on her by the bungee cord from 3 sec to 5 sec?
Average force = Impulse/Time = (-1500 N sec)/(2 sec) = -750 N
______-750___ Newtons
Would there be a problem if the bungee cord stopped her in 1/10 sec instead of 2 sec? Explain.
The average force acting on the jumper will be (-1500)/(1/10) = -15000 N. This is a very large force and
will hurt a lot!!!!
Momentum – Recoil
A steel ball (A = 4 kg) and a wooden ball (B = 1 kg) are at rest and separated by a compressed
spring.
1.
What is the value of the total momentum of the system before the spring is released?
Zero. There is no motion.
The spring is now released causing the balls to recoil in opposite directions. In this case,
2.
what is the value of the total momentum of the system? Still zero – Momentum is
conserved.
3.
does the spring exert a greater force on ball A or ball B? Same force – Newton’s 3rd Law.
4.
which ball has a higher recoil speed? Why? Explain.
A
B
spring
With the same force, the lighter ball will experience a greater acceleration and thus have a
greater speed – Newton’s 2nd Law.
5.
If you were to jump straight upward from the earth’s surface, will the earth recoil? Explain.
Yes! But since the earth’s mass is so-o-o-o-o-o-o large compared to your mass, it will have an
infinitesimally small acceleration.
Two-dimensinal Elastic Collision
3.
The diagram shows the top view of the corner of a pool table with the cue ball and the eight ball.
Carefully draw the position of the cue ball when it makes contact with the eight ball so that it causes
the eight ball rolls into the corner pocket. Show also the path of the cue ball takes after the collision.
cue ball
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