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Sierzega: Momentum 2
Impulse to the Rescue
2.1 Derive Your hand pushes horizontally on a cart of mass m, exerting a force F H on C for a
time interval (tf – ti). The forces exerted downward on the cart by the Earth and upward on the
cart by the track are balanced. The track is very smooth, so we assume that F H on C is the only
force exerted in the horizontal direction on the cart. The cart is initially moving at velocity vC i
at the clock reading ti and, after the pushing, is moving at velocity vC f at the clock reading tf .
a. Use Newton’s second law and the definition of acceleration to derive an expression
relating forces and momentum change.
b. Why do we approximate a varying force as the average force exerted during a time
interval? Represent a variable force graphically and approximate the area.
c. What physical quantity does this area represent?
d. Suppose that friction is not negligible. How would you modify the expression for the
impulse on the cart to include both the effect of the hand and of friction?
e. Suppose the cart’s forward velocity decreased due to the force of a hand pushing lightly
back on it. How would you write the expression for the impulse due to that force?
2.2 Test An Idea You have two identical mass and size
bouncy balls that behave very differently. When you drop the
so-called “sad” ball it thuds on the floor and does not bounce
at all. When you drop the so-called “happy” ball from the
same height, it bounces back to almost the same height from
which it was dropped.
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Next, you place a wood board at the end of a metal ramp. When you release each ball from the same
height on the same ramp, you see that their motions are exactly the same, each moving at the same speed
with respect to the ground at each moment
Use conservation of momentum to predict which ball is more likely to cause the plank to fall over.
Include sketches, bar charts, force diagrams, motions diagrams, and equations in your prediction.
Once you have made your prediction, use the QR code at the right or the link below to
observe the outcome of the experiment.
http://paer.rutgers.edu/pt3/experiment.php?topicid=3&exptid=129.
Questions
1. Choose a different system for analysis (if you chose the ball as the system in your original
analysis, now choose the ball and the plank as the system; and vice versa). Are your predictions
the same or different based on the system you chose? Explain.
2. What judgment can you make about the conservation momentum?
Sierzega: Momentum 2
2.2 You drop a ball from a window. After falling 2.0 m, the ball acquires considerable speed.
a) Explain why the ball speeds up as it falls using the knowledge of impulse and momentum
(System 1: ball and Earth; System 2: ball).
b) Explain why the ball speeds up as it falls using your knowledge of Newton’s laws.
c) Discuss whether the explanations based on impulse-momentum and Newton’s laws are
consistent with each other.
2.3 A 60-kg person is traveling in a car that is moving at a speed of 16 m/s with respect to the
ground when the car hits a barrier. The person is stopped by an air bag in a time interval of 0.20
s. Determine the average force that the air bag exerts on the person while stopping him.
2.4 The train tracks for a train exert a 2.4 x 105 N friction force on the train, causing it to stop in
40 s. Determine the average force needed to stop the train in 25 s. Determine the stopping time
interval if the tracks exert a 1.0 x 105 N friction force on the train.
2.5 Use the concept of impulse to explain why a slingshot should be pulled back as far as
possible to get the longest shot.
2.6 A van carrying three passengers collides with a concrete support for an overpass. The
stopping time interval for the collision is 0.20 s, and the impulse exerted by the support on the
van is 10.0 x 103 N•s. Determine everything you can about the collision using this information.
2.7 A 70-kg astronaut pushes against the inside back wall of a 2500-kg spaceship and moves
toward the front. Her speed increases from zero to 1.5 m/s. (a) If her push lasts 0.30 s, what is the
average force that the astronaut exerts on the wall of the spaceship? (b) If the spaceship was
initially at rest, with what speed does it recoil? (c) What is the system for your analysis?
2.8 According to a report on traumatic brain injury, the force that a professional boxer’s fist
exerts on his opponent’s head is equivalent to being hit with a 13-pound bowling ball traveling at
20 mph if the ball stops in 0.018 s. Determine the average force that the ball (and the fist) exerts
on the head.
2.9 Regular problem A 1120-kg Ford Escort hits a 1420-kg Chrysler Sebring at rest. The two
cars lock together and skid 12.0 m on a level surface before stopping. Police determine that the
coefficient of kinetic friction between the tires and road is 0.70. Was the first car exceeding the
45 mph speed limit?
2.10 Regular problem A 0.10-kg ball moving at speed 6.0-m/s hits a 0.20-kg box that is at rest.
The ball stops and the box slides 1.80 m before stopping. Determine the coefficient of kinetic
friction between the box and the horizontal tabletop on which it slides.
2.11 Challenge problem A 3000-kg spaceship travels toward the moon at a speed of 1.5 x 104
m/s. The captain of the ship wishes to change direction by 5o. Rockets eject a fuel at a speed of
3.0 x 106 m/s perpendicular to the ship's initial direction. Determine the mass of fuel that must be
ejected to change course as the captain wishes. What assumptions did you make?