Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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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?

 

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.

 

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?

 

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?

 

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.

 

1820001     Center of mass of a car and truck.     1820001
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A car of mass 500 kg and a truck of mass 1200 kg are moving directly toward each other at the same speed of 20 m/s. Define the +x direction to the direction of the car.

  1. What is the velocity of the center of mass of the system, defined to be the car and truck?
  2. At the moment when the vehicles are 100 m apart, what is the location of the center of mass of the system? Treat the vehicles as point particles.

 

1820002     2-D collision of pucks.     1820002
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While playing around with identical hockey pucks on an air hockey table, you push one puck so that it collides with another stationary puck. Before the collision, puck B is at rest and puck A is moving with a speed of 0.500 m/s. After the collision, puck A's velocity is at an angle of 20 (below the horizontal) and puck B has a velocity at 65 (above the horizontal). What are the speeds of puck B and puck A after the collision?

 

1850001     Applying the energy principle to an accelerating box of fluid     1850001
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Using a string, you pull a box along a low-friction table with a constant force of 100 N, starting from rest. The box is full of fluid and is a cube of dimensions 1m x 1m x 1m with a total mass of 2.0 kg. When the box was at rest, the center of mass of the system was located at relative to the left, lower corner of the box. At some time later, your hand has pulled through a distance of 0.5 m, and the center of mass has shifted to relative to the left, lower corner of the box.


Figure: A box with fluid being pulled by a constant force.

The box is thermally insulated and the table is nearly frictionless, so assume that there is no energy transferred thermally between the box and its surroundings.

  1. Define the box and fluid to be the system. What is of the system?
  2. What is of the system?
  3. What is the speed of the system (after your hand has moved through a distance of 0.5 m)?
  4. What is the change in the thermal energy of the system?

 

14h0001     Tension holding a buoy that is chained to the ocean floor.     14h0001
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An underwater buoy of total mass 5.0 kg and volume contains instruments to measure temperature and current at the bottom of a coral reef in the ocean. The buoy is completely submerged and tied by a chain to an anchor on the ocean floor. It's at a depth of 10 m below the surface of the ocean. The density of seawater is . What is the tension in the chain?

 


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