Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1150003     Adding position and displacement vectors     1150003
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The initial position of a mouse in a maze is . Its displacement (i.e. change in position) during a time interval of 1 minute is . What is its new position?

 

1180001     Momentum of a toy airplane     1180001
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A 0.020-kg toy airplane is tied to a string which is hung from a ceiling. With the engine turned on, the airplane flies in a horizontal circle. Let's assume that the airplane travels clockwise along the path shown in the figure.


Figure: A toy airplane flying in a circle.

Suppose that the plane's position at s is m, relative to the center of the circle. (A dot is placed at this location in the figure.) A small time interval later, at , the plane's position is m.

  1. Sketch a vector for the initial position (i.e. at s) of the airplane.
  2. Sketch a vector for the final position (i.e. at s) of the airplane.
  3. Sketch a vector for the average velocity of the airplane during this time interval.
  4. What is the average velocity of the airplane during this time interval?
  5. What is the average momentum of the airplane during this time interval?

 

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?

 

1170003     Position (update) of a near-Earth asteroid     1170003
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Near-Earth asteroids are carefully tracked by NASA so that Earthlings will have some notice in the case of a catastrophic collision. You can following the tracking of near-Earth asteroids at

http://neat.jpl.nasa.gov/

Suppose that in a simulation of Asteroid 2007 TU24, it is at the location km relative to the center of Earth with a velocity km/s at some clock reading. What will be its (approximate) position 1 hour later?

Note: Asteroid TU24 made its closest approach to Earth on January 29, 2008. You can read more about it at:

http://www.jpl.nasa.gov/news/news.cfm?release=2008-014a


Figure: According to JPL, "This radar image of 2007 TU24 was obtained on January 28, 2008, about 12 hours before the asteroid's 1.4-lunar-distance pass by the Earth. The Arecibo Observatory in Puerto Rico and the Greenbank Telescope in West Virginia were used to take this image."

 

1170006     Position (update) of Earth     1170006
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At some instant in time, Earth is located at the position m relative to Sun. Its velocity at this instant is m/s in the +y direction.

  1. Where will it be 1 day later?
  2. What assumption did you make in doing this calculation, and is your calculation exact or approximate?

 

1170002     Average velocity of a putted golf ball     1170002
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A golf ball rolls across the green toward the hole as shown below. Due to the grass and the slope of the green, it breaks toward the hole.


Figure: A golf ball rolling towards the hole.

View Simulation

The positions of the golf ball at each second as it rolls toward the hole are given below.

 

t (s) (m)
0.0
1.00
2.00
3.00
4.00

Table: Positions and clock readings for the golf ball

 

  1. What is the average velocity of the golf ball from to s?
  2. What is the magnitude of its average velocity and what is its direction from to s?
  3. If the golf ball continues with the same average velocity, what position would it be located at the clock reading s?
  4. How does the predicted position at s compare to the actual position? Why is the predicted and actual position different?

 

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.

 

1170001     Average velocity of an elephant (from GPS data)     1170001
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A GPS collar is used to track the movement of elephants in Timbuktu. (See the article at

http://animal.discovery.com/fansites/wildkingdom/elephant/science/science.html

for more information about the use of GPS to learn about migration patterns of animals.) The position of a single elephant can be downloaded every 30 minutes. At 8:00 AM, data shows that the elephant is at the position km (relative to some origin). At noon, the elephant is at km.

  1. What is the average velocity of the elephant during this time interval?
  2. What is the magnitude of its average velocity and what is its direction?
  3. To know more about the path the elephant traveled or to know its (approximate) velocity at exactly 9:00AM, what data is needed?

 

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?

 

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?

 


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