Matter & Interactions 3rd ed. Practice Problems
Aaron Titus | High Point University
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1     Linear interaction(s); three different hockey pucks     1
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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.

 

2     Vector sum, magnitude, direction, and angle     2
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The following forces act on an object at some instant of time.



  1. What is the sum of the forces (called the net force) on the object at this instant?

  2. What is the magnitude of the net force?

  3. What is the direction of the net force?

  4. What angle does the net force make with the axis?

  5. What angle does the net force make with the axis?

  6. What angle does the net force make with the axis?

 

3     Magnitude and direction of a velocity vector     3
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At some instant, you are traveling in your car and your velocity is . What is your speed and what is your direction (unit vector)?

 

4     Adding position and displacement vectors     4
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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?

 

5     Displacement; direction cosines     5
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A girl walks from the position to the position .

  1. How far is the girl from the origin when she's at ?
  2. What is her displacement?
  3. What is the magnitude and direction of her displacement?
  4. What angle does her displacement make with the x-axis?
  5. What angle does her displacement make with the y-axis?
  6. What angle does her displacement make with the z-axis?

 

6     Sketch position and displacement vectors     6
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The picture shows a 0.4-kg football after it is thrown. The ball is traveling from left to right in the picture. On the picture, sketch the initial position vector , the final position vector and the displacement vector for the football.


Figure: A football travels left to right.

 

7     Directon cosines in three dimensions     7
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The longest edge of a sail on a sailboat extends from the top of the mast (the origin) to a location . A picture is shown below.


Figure: A sail on a sailboat.

  1. What is the length of the longest edge of the sail (i.e. the length of the hypotenuse of the sail)?
  2. What is the length of the bottom edge of the sail?
  3. What angle does the longest edge of the sail make with the x-axis?
  4. What angle does the longest edge of the sail make with the y-axis?
  5. What angle does the longest edge of the sail make with the z-axis?

 

8     Average velocity of an elephant (from GPS data)     8
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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?

 

9     Average velocity of a putted golf ball     9
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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?

 

10     Position (update) of a near-Earth asteroid     10
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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."

 


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