Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1220003     Impulse and average net force on a model rocket by the engine     1220003
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The thrust of a certain model rocket engine as a function of time is shown below. Here, the word "thrust" refers to the force by the exhaust on the rocket as the rocket engine is firing.


Figure: The thrust curve of a certain model rocket engine.

The total area under the curve is 1.84 N s. The total burn time of the rocket engine is 1.24 s. The peak thrust has a magnitude 8.60 N. Since force is a vector, assume that the thrust is in the +y direction.

  1. Calculate the average thrust on the rocket due to the rocket engine.
  2. Compare the average thrust to the peak thrust. Explain why the average thrust is so much smaller than the peak thrust.
  3. If the thrust by the rocket engine on the rocket is the only force acting on the rocket, then what will be the change in the rocket's momentum during the time interval from t=0 to t=1.24 s?

 

1220004     Change in momentum of Earth in 1 day during its orbit around Sun     1220004
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Earth orbits Sun in a nearly circular orbit with a speed m/s. Suppose that at a certain instant, Earth's velocity is in the –x direction. At this instant, the force by Sun on Earth is . What will be Earth's momentum 1 day later? During this time interval, the only significant force acting on Earth is the gravitational force by Sun on Earth.


Figure: The gravitational force by Sun on Earth.

 

1220002     Impulse on an alpha particle by a gold nucleus (Rutherford scattering)     1220002
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An alpha particle has a speed of m/s in the +x direction when it collides with a gold nucleus. and deflects at an angle above the +x axis. Its speed after the collision nearly the same as its speed before the collision because the gold nucleus is so massive compared to the alpha particle. What is the impulse on the alpha particle due to the collision with the gold nucleus?

 

1220001     Net force on an air hockey puck     1220001
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While playing air hockey, the puck comes toward you with a speed of 0.8 m/s at an angle of above the –x axis. You strike it with your paddle, and after the collision, the puck travels in the +x direction with a speed of 2 m/s toward the opponent's goal. The mass of the puck is 0.020 kg.


Figure: An air hockey puck before being struck by the air hockey paddle.

  1. What was the impulse on the puck?
  2. What is the direction of the net force on the puck during the collision?
  3. What must be measured if you want to calculate the net force on the puck during the collision?

 

1220005     Impulse on a proton at relativistic speeds in the LHC     1220005
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What impulse is required to accelerate a proton of mass from 0.95c to 0.99999999c (which is the maximum speed achieved with the Large Hadron Collider)? Assume that the proton travels along a straight line in the +x direction.

 

1150002     Magnitude and direction of a velocity vector     1150002
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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)?

 

1150005     Sketch position and displacement vectors     1150005
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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.

 

1150004     Displacement; direction cosines     1150004
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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?

 

1150006     Directon cosines in three dimensions     1150006
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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?

 

1150001     Vector sum, magnitude, direction, and angle     1150001
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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 +x axis?
  5. What angle does the net force make with the +y axis?
  6. What angle does the net force make with the +z axis?

 


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