Studio Physics I
Impulse and Translational Momentum
Calculate the total momentum of the following systems. Use the conventional
coordinate system with right positive, left negative, up positive and down negative.
1. A 0.5 kg cart moving to the left at 3 m/s and a 0.5 kg cart moving to the left at 2
m/s.
2. A 0.3 kg cart moving to the right at 3 m/s and a 0.5 kg cart moving to the left at 2
m/s.
3. A 0.5 kg cart moving to the left at 4 m/s and 0.5 kg cart moving to the right at 4
m/s
4. A 0.3 kg cart that is slowing down and has a positive acceleration (at a moment it
has a speed of 2 m/s) AND a 0.3 kg cart that is slowing down and has an
acceleration that points right (at a moment it has a speed of 3 m/s.)
5. A 0.3 kg cart that is speeding up and has an acceleration to the right (at the
moment it has a speed of 2 m/s ) and a 0.3 kg cart that is slowing down and has a
positive acceleration (at the moment it has a speed of 2 m/s).
6. The figure below shows an approximate plot of force versus time during the
collision of a 58 gram tennis ball with a wall. The initial velocity of the ball is 34 m/s
perpendicular to the wall, and it rebounds with the same speed, also perpendicular to
the wall. What is Fmax, the maximum value of the contact force during the collision?
Fmax
Force (N)
Time (sec)
2
6
9
7. A pitched 140-gram baseball, in horizontal flight with a speed 39 m/s, is struck by a
batter. After leaving the bat, the ball travels in the opposite direction with speed 39 m/s.
a) What impulse J acts on the ball while it is in contact with the bat?
b) If the impact time for the baseball –bat collision is 1.2 ms, What average force acts on
the baseball?
c) What is the average acceleration of the baseball?
d) How many times “g” is this?
8. You have taken a summer internship working as a design engineer in car
manufacturing company. You current job is to check the specifications of the air
bags installed in the new model. You are to report to your supervisor as to whether
they are satisfactory, over-designed, or under-designed. You check around and find
that human beings can endure accelerations around 5g for periods of time up to about
3 seconds. They can endure accelerations of around 80g for periods of about 0.05
seconds. In a collision between a car (originally moving at 60 mph) and a tree, the
force exerted on the car (and its occupants) starts at a maximum value and decreases
linearly to 0 N over the course of 0.002 seconds. The average car has a mass of 1000
kgs. The current air bag deploys over 0.75 seconds. How likely is a human to
survive the collision without the airbag? Assuming the force of impact still decreases
linearly with time, what is your recommendation to your supervisor about the current
airbag? Make your arguments in terms of the maximum accelerations (in terms of g)
experienced by the driver. (1m/s=2.24 mi/hr)
9. (A return to forces and projectile motion)
You are watching a ski jump contest on television when you wonder how high the
skier is when she leaves the starting gate. In the ski jump, the skier glides down a
long ramp. At the end of the ramp, the skier glides along a short horizontal section
which ends abruptly as that the skier goes into the air. You measured that the skier
was in the air for 2.3 seconds and landed 87 meters away, in the horizontal direction,
from the point she went into the air. Make the best estimate you can of the height of
the starting gate at the top of the ramp (measured from the horizontal section from
which the skier takes off into the air). Make clear on what assumptions your answer
depends (why this is an estimate).