Download Impulse / Momentum Problem Set

Physics
Momentum
Name:
Impulse / Momentum Problem Set
A. Conceptual Questions
1)
2)
3)
4)
5)
6)
7)
8)
9)
Explain two ways a heavy truck and a person on a skateboard can have the same momentum.
In stopping an object, how does the time of impact effect the magnitude of the force used to stop the object?
What is the relationship between an impulse of a force on an object and the change in momentum of that object?
For a constant force, if the time the force is applied to an object doubles, the impulse will __________.
For a constant force, if the time the force is applied to an object doubles, the change in momentum will be _________.
In a car crash, what is the advantage of an air bag in terms of impulse/change in momentum?
Why is the impulse greater on a falling object that bounces instead of an equally massive object that doesn’t bounce?
Explain why a tossed egg can be caught with a sagging sheet but not a piece of plywood?
A bug and the windshield of a moving car collide. Indicate which of the following statements are TRUE.
a. The impact force on the bug and the car are the same magnitude.
b. The impulse on the bug and the car are the same magnitude.
c. The change in momentum of the bug and the car are the same magnitude.
d. The change in velocity of the bug and the car are the same.
1) Both could be at rest; or, the truck
could be moving really slow and the
skateboard could be moving really fast.
4) double
2) The smaller the time, the larger the
force that must be exerted, and vice
versa.
5) twice as great
7) The bouncing object has twice the
change in momentum (since it must
come to a stop and start moving back
up) as the object that doesn’t bounce.
8) The change in momentum takes
longer, therefore the force is smaller
(and does not crack the egg).
3) The impulse is equal to the change
in momentum.
6) The change in momentum takes
place over a longer time period (so the
force can be less).
9) a. True
b. True
c. True
d. False
B. Problems
1) (I) A force of 6.0 N acts on a 3.0 kg object for 10.0 s.
a) What is the object's change in momentum?
b) What is the new velocity of the object if it started at rest?
2) (I) An 1100 kg car moves at 22.0 m/s. Neglecting friction, what braking force is needed to stop the car in 20.0 s?
3) (I) A net force of 2000 N acts on a rocket of mass 1000 kg. How long must the force be applied in order to increase the
rocket's velocity from 10.0 m/s to 200.0 m/s?
4) (II) A snow scooter has a mass of 250 kg. A constant force acts upon the scooter for 1.0 minute. The scooter's velocity
changes from 6.0 m/s to 28 m/s.
a) What change in momentum occurs?
b) What is the magnitude of the force acting on the scooter?
5) (II) A 58.0 g tennis ball flies across the net with a velocity of 15.6 m/s and is returned with a velocity of −18.4 m/s. If the
racket exerts an average force of 172 N on the ball, determine the contact time between the ball and the racket.
6) (II) A constant force of 300 N acts on a 600 kg mass for 68 s. The initial velocity of the mass is 10.0 m/s. The direction of
the force and the velocity is the same. What is the final velocity of the mass?
1) a) 60. kg m/s
b) 20. m/s
2) −1210 N
5) 0.0115 s
3) 95 s
6) 44 m/s
4) a) 5500 kg m/s
b) 92 N
C. Conservation of Momentum:
7) (II) A 95 kg fullback, running at 8.2 m/s, collides in midair with a 128 kg defensive tackle moving in the opposite direction.
Both players end up with zero speed.
(a) What was the fullback’s momentum before the collision?
(b) What was the change in the fullback’s momentum?
(c) What was the change in the tackle’s momentum?
(d) What was the tackle’s original momentum?
(e) How fast was the tackle moving originally?
8) (II) Marble A, mass 5.0 g, moves at a speed of 20.0 cm/s. It collides with a second marble, B, mass 10.0 g, moving at
10.0 cm/s in the same direction. After the collision, marble A continues with a speed of 8.0 cm/s in the same direction.
(a) Calculate the total momentum of the system before the collision.
(b) Calculate the momentum of marble A after the collision.
(c) Calculate the momentum of marble B after the collision.
(d) What is the speed of marble B after the collision?
9) (II) A 0.105 kg puck moving at 48 m/s is caught by a stationary 75 kg goalie, causing him to slide backward on the ice.
With what speed does the goalie slide after catching the puck?
10) (II) A 35.0 g bullet strikes a 5.0 kg stationary wooden block and embeds itself in the block. The block and bullet fly off
together at 8.6 m/s. What was the original velocity of the bullet?
11) (II) A 0.50 kg ball traveling at 6.0 m/s collides head on with a 1.00 kg ball moving in the opposite direction at 12.0 m/s. The
0.50 kg ball bounces back with a velocity of 14.0 m/s after the collision. What is the velocity (magnitude & direction) of the
1.00 kg ball after the collision?
12) (II) A green ball (m = 10.0 g) moving with a velocity of 20.0 cm/s catches up to and collides with a red ball (m = 20.0 g)
moving along the same line with a velocity of 10.0 cm/s. After the collision, the green ball is still moving in its original
direction with a velocity of only 8.0 cm/s. Determine the final velocity of the red ball.
13) (II) A 700 kg car traveling at 20.0 m/s collides with a stationary 1400 kg truck. The two vehicles interlock and travel
together. What is the final velocity of the car?
14) (II) A 40.0 kg projectile leaves a 2000 kg launcher with a velocity of 800 m/s. What is the recoil velocity of the launcher?
15) (II) Upon launching, a model rocket expels 50.0 g of fuel from its exhaust at an average velocity of 600 m/s. If the rocket
moves upward at 7.5 m/s, what is the mass of the rocket?
16) (III) Two campers dock a canoe. One camper (80.0 kg) steps onto the dock moving at 4.0 m/s. The canoe and other
camper move backwards at 2.9 m/s. If the second camper’s mass is 75.0 kg, what is the mass of the canoe?
17) (II) Two students (90.0 kg and 60.0 kg) on roller skates face-to-face push against each other. The 90.0 kg student moves
at 5.0 m/s just after their hands lose contact.
(a) What is the velocity of the other student?
(b) What average force was exerted on each student if they were in contact for 0.003 s?
7)
8)
9)
12)
16)
(a) 779 kg m/s (b) −779 kg m/s (c) +779 kg m/s (d) −779 kg m/s (e) −6.1 m/s
(a) 200 g cm/s (b) 40 g cm/s (c) 160 g cm/s (d) 16 cm/s
0.0671 m/s (not 0.0672 m/s)
10) 1200 m/s
11) 2.0 m/s in its original direction of motion
16 cm/s (same direction)
13) 6.67 m/s
14) 16 m/s backwards
15) 4.0 kg
35 kg
17) (a) 7.5 m/s backwards (b) 1.5 x 105 N
D. Force vs. Time Graphs
Determine the total impulse delivered by the force represented by each of the following force versus time graphs. In each
case, determine the final velocity of a 5-kg object initially at rest after being acted on by the force indicated in the graph.
18)
19)
20)
18) 2000 N∙s; 400 m/s
21)
19) 8 N∙s; 1.6 m/s
20) 12 N∙s; 2.4 m/s
21) 115 N∙s; 23 m/s
E. Elastic & Inelastic Collisions:
22) In an inelastic collision, ______________________________ is/are conserved.
23) In an elastic collision, ______________________________ is/are conserved.
24) (II) A 0.015 kg marble moving to the right at 22.5 cm/s collides with a 0.015 kg marble moving to the left at 18.0 cm/s.
After the collision, the first marble moves to the left at 18.0 cm/s.
(a) What is the final velocity of the second marble after the collision?
(b) Is the collision elastic or inelastic?
25) (III) A 0.25 kg arrow with a velocity of 12 m/s to the west strikes and pierces the center of a 6.8 kg target.
a) What is the final velocity of the combined mass?
b) What is the decrease in kinetic energy?
22) momentum
24) (a) 22.5 cm/s to the right (b) elastic
23) momentum and kinetic energy
25) (a) 0.43 m/s (b) 17.35 J
Physics Examples: Conservation of Momentum
1. A 1.0 kg dodgeball moving to the right at 11.0 m/s collides with a 5.0 kg bowling ball
moving to the left at 2.0 m/s. The bowling ball rebounds with a velocity of 1.0 m/s to the
right. What is the velocity of the dodgeball after the collision?
2. A 1200 kg freight car (A) is moving along a set of train tracks at 15 m/s when it collides
with an 800 kg freight car (B) that is stationary. The cars lock together and continue to
move along the tracks. What is the velocity of each car after the collision?
3. A 75 kg ice skater is holding 3 kg package while motionless on a frictionless frozen pond.
If the skater throws the package to the right with a speed of 5 m/s, what will be the
velocity of the skater after throwing the package?