Download Investigation 3

Name_____________________KEY________________________________ Date_______3/11/11____________
Investigation 3
Impulse, Momentum, Work, Power, Energy
The Impulse-Momentum relationship says: Impulse = Force x time of impact
1.
An unfortunate bug splatters on the windshield of a car traveling at 60 mi/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?
The force is the same. Newton’s Third Law.
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?
Impulse equals force times time. The forces and times are the same so the impulses are the
same.
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. If the impulses are the same, then the change in
momentums are the same.
d.
Does the bug or the car undergo the greater acceleration? Explain briefly.
The acceleration depends on the mass. The greater the mass is the smaller the acceleration
and vice versa. The car is much more massive than the bug, so the car has a much smaller
acceleration.
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?
Momentum before = (8 kg)x(4 m/s) + (2 kg)x(0 m/s) = 32 + 0 = 32 kg m/s
b.
What should the value of the total momentum of the system be after the collision?
Momentum before the collision = momentum after the collision = 32 kg m/s
c.
What are the speeds of the blocks after the collision?
After the collision, the blocks stick together so the new mass is (8 + 2) = 10 kg. The momentum
after is 32 kg m/s = (10 kg) x V, where V is the velocity after the collision. Solving for V, we get
V = 3.2 m/s.
Impulse and Momentum
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 and slows her down. It then 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 m/s
50 x 10 = 500
2
20 m/s
50 x 20 =
1000
3
30 m/s
50 x 30 =
1500
0
50 x 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 is momentum = (0 – 1500) = -1500 kg m/s
What is the value of the impulse on her from 3 sec to 5 sec?
Impulse = change in momentum
_______-1500_________ Newton sec
What is the average force that acted on her by the bungee cord from 3 sec to 5 sec?
Force x time = Impulse, so Force = Impulse/time = -1500/2
_____-750__________ Newtons
Would there be a problem if the bungee cord stopped her in 1/10 sec instead of 2 sec? Explain.
Force = Impulse/time. The smaller the time, the greater the force.
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 – no motion.
The spring is now released causing the balls to recoil in opposite directions.
2.
A
What is the value of the total momentum of the system?
Zero – momentum is conserved.
3.
B
spring
Does the spring exert a greater force on ball A or ball B?
Forces are the same. Newton’s Third Law.
4.
Which ball has a higher recoil speed? Why? Explain.
The smaller the mass is, the greater the acceleration for the same force. B is smaller.
5.
If you were to jump straight upward from the earth’s surface, will the earth recoil? Explain.
From question 4 above, the greater the mass the smaller the acceleration. The earth is much more
massive than you, so the earth will have a much smaller acceleration than you.
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 after the collision.
cue ball direction after hitting 8 ball
direction to aim
cue ball
cue ball
8
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 ______70_________ 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).
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 __2.5____ m.
The work done climbing the stairs is
____1750______ Joules
(70)x(10)x(2.5) =
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 = 1750/5 = 350
____350______
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.
350/746 = 0.47
___0.47_________ 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.
Kinetic energy = (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 is four times greater because when you double the velocity, you quadruple the kinetic
energy.
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 - Joules. 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)
8.
Calculate the potential energy of your physics book when held 3 meters above the floor.
Potential energy = (2 kg) x (10 m/s^2) 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.
Potential energy = (2 kg) x I(10 m/s^2) 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 = (2 kg) x (10 m/s^2) x (1 m) = 20 Joules. Potential energy only depends on its
position.
____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.
The potential energy varies directly with height. So, if the height doubles, the potential energy also
doubldes.
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).
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. Keep in mind the idea of conservation
of energy. Notice that the gravitational potential energy is zero at position D, that is, the potential energy
is measured from the ground. (Notice that heights are given, not time.)
10 m
B
ball dropped
ball thrown downward at 10 m/s
position
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 x 10 x 40
= 400 J
0
400 + 0 =
400 J
1 x 10 x 40
= 400 J
(1/2) x 1 x
10 x 10 =
50 J
400 + 50 =
450 J
B
1 x 10 x 30
= 300 J
400 – 300
= 100 J
400 J
1 x 10 x 30
= 300 J
450 – 300
= 150 J
450 J
C
1 x 10 x 20
= 200 J
400 – 200
= 200 J
400 J
1 x 10 x 20
= 200 J
450 – 200
= 250 J
450 J
D
0
400 – 0 =
400 J
400 J
0
450 – 0 =
450 J
450 J
10 m
C
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 is zero. So what happened to all the energy?
Energy cannot be destroyed. It was converted into other forms such as sound, heat, and work needed to
deform the ground.