Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1190004     Change in momentum of a rebounding tennis ball     1190004
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A 57-gram tennis ball with a velocity of m/s rebounds from a wall with a velocity of m/s. What is the tennis ball's change in momentum in kg m/s?

 

1190001     Change in momentum of a golf ball (as it rims out)     1190001
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A 0.045-kg golf ball is rolling toward the hole with a velocity m/s. A s, it hits the edge of the hole; it then travels around the hole ("rimming out") and continues rolling. It leaves the hole at s with a velocity m/s. A picture of the ball at 0.1 s intervals is shown in the figure below.


Figure: The path of a golf ball as it travels around the rim of the hole on a putting green.

(View a simulation at

http://linus.highpoint.edu/~atitus/mandi/physlets/1190001/1190001.html

to visualize the motion.)

  1. Sketch the golf ball's initial momentum and final momentum vectors for the time interval that the ball and hole interact.
  2. Sketch the golf ball's change in momentum during the time interval that it interacts with the hole.
  3. What is the change in momentum of the golf ball as a result of interacting with the hole?
  4. What is the magnitude and direction of the change in momentum of the golf ball?

 

1190005     Change in momentum of the Huygens spaceprobe upon impact with Titan     1190005
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The following quote is from http://spaceflightnow.com/cassini/050115science.html

Huygens entered Titan's thick nitrogen atmosphere around 5:13 a.m. Friday. John Zarnecki, principal investigator of the surface science package, said it took the spacecraft two hours 27 minutes and 50 seconds to complete its parachute descent to the surface. It hit that surface at a velocity of 10.1 mph and experienced a very brief impact deceleration of 15 Gs. The jolt knocked one sensor off line, but it came back to life on its own a few minutes later.

A "penetrometer" on the bottom of the probe extended six inches into the frigid soil. That data, coupled with the deceleration experienced by Huygens as it hit the ground, provided new insights into the nature of the surface material at the landing site.

"What we're seeing is, we think, a material which might have a thin crust followed by a region of relatively uniform consistency," said Zarnecki. "In terms of this (impact) force, the closest analog that I can give you - and remember, this is not suggesting these are the materials we hit, but that the mechanical consistency is similar - then I would say wet sand or clay are materials which give a similar sort of trace."

The mass of the Huygens spacecraft is 192 kg.

  1. What was the momentum of the Huygens just before impact with the surface of Titan?
  2. What was Huygens' change in momentum as a result of the impact?

 

1190006     Sketch the change in momentum of a roller coaster     1190006
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Consider the roller coaster shown below.


Figure: Momentum vectors for a roller coaster.

The car's momentum just before the dip and just after the dip are shown in the picture. Sketch the change in the momentum of the roller coaster as it travels around the dip.

 

1190007     Change in momentum of a colliding cart on a track     1190007
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A cart of mass 0.50 kg (labeled Cart A) is rolling on a track in the physics lab in the –x direction at a speed of 2.0 m/s when it collides with another, more massive cart (labeled Cart B) which is at rest. After the collision, cart A rebounds and moves in the +x direction with a speed of 0.67 m/s, and Cart B moves in the –x direction. What is the change in momentum of Cart A as a result of the collision?

 

1190002     Change in momentum of a bouncing ball     1190002
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Suppose that you use video analysis to measure the velocity of a 0.01-kg superball just before it hits the floor and you find that its velocity is downward with a magnitude of 4.5 m/s. You also measure its velocity just after it hits the floor and find that it is upward with a magnitude of 3.9 m/s. The time interval that it is contact with the floor is approximately 1/30 of a second.

  1. Sketch the superball's initial momentum vector (just before hitting the floor), the final momentum vector (just after hitting the floor), and the change in momentum during the time interval that it interacts with the floor.
  2. What is the change in momentum of the superball during the time interval that it interacts with the floor?
  3. Write the change in momentum vector in the form: magnitude direction (i.e. ).

 

1190003     Relativistic momentum update and speed of a proton     1190003
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A proton of mass kg has an initial speed 0.9c, in the +x direction. During a certain time interval, its change in momentum is kg m/s.

  1. What is the proton's initial momentum?
  2. What is the proton's final momentum (i.e. at the end of this time interval)?
  3. What is the proton's final speed?

 

1130001     Linear interaction(s); three different hockey pucks     1130001
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You view the motion of a hockey puck in a video and mark its location every 0.2 s. The resulting motion map for three different hockey pucks is shown below. The hockey puck in each case is moving to the right.


Figure: A hockey puck travels to the right in three different cases.

In which case (A, B, or C) is there no interaction between the hockey puck and its surroundings? (Or rather, no net interaction.) If there is no interaction in all or none of the cases, then state so. Explain your reasoning.

 

1170005     Average velocity and position (update) for three hockey pucks     1170005
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You view the motion of a hockey puck in a video and mark its location every 0.2 s. The resulting image for three different hockey pucks is shown below. The hockey puck in each case is moving to the right. The gridlines in the images are 1 cm apart.


Figure: A hockey puck travels to the right in three different cases.

  1. In which case (A, B, or C) is there no interaction between the hockey puck and its surroundings? (Or rather, no net interaction.)
  2. What is the (approximate) velocity of the puck in each case at t=0? (Note: this is when the puck is at the location of the first image shown in the motion map. In each case, it is moving to the right.)
  3. Why is your answer to the previous question an approximation and what could be done (in the experiment that produced the image) to make a better measurement of the velocity of the object at t=0?
  4. In Case (A), what do you predict will be the position of the puck at t=2.0 s?
  5. Is your prediction for the position of the puck at t=2.0 s in Case (A) exactly correct or approximately correct? Explain.

 

1170004     Position (update) of a fish     1170004
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A graduate student in biology is analyzing video of a school of fish and measures a certain fish to be at the position m moving with a velocity m/s at some instant. Approximately where will the fish be 0.100 s later?

 


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