Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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View records 1-10 | 11-18

1230001     Force by a merry-go-round on a child     1230001
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A 20-kg girl rides on a merry-go-round. She is sitting near the edge of the merry-go-round and is rotating counterclockwise. The +z axis is defined to be perpendicular to the merry-go-round, and the +x and +y axes are in the plane of the merry-go-round. (See figures below.)


Figure: A merry-go-round.

At , the velocity of the girl is m/s, and 0.15 s later, her velocity is m/s.

  1. Sketch the location of the girl on the merry-go-round, her initial momentum, her final momentum, and her change in momentum.
  2. What is the net force on the girl during this time interval? Calculate and sketch this vector.
  3. What is the force by the merry-go-round on the girl during this time interval?

 

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.

 

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?

 

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?

 

1240001     Momentum and position of a proton accelerated across charged plates     1240001
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In a mass spectrometer (an instrument used in chemistry to measure the mass and therefore identity of unknown atoms) positively charged ions are accelerated between two charged plates. Suppose that a proton is nearly at rest at the positively charged plate on the left. It is accelerated toward a negatively charged plate on the right, as shown below. The plates are 5 cm apart.


Figure: A proton accelerated between charged plates.

The electric force by the charged plates on the proton is in the +x direction. This is the only significant force acting on the proton.

  1. If the initial velocity of the proton is zero, what is the velocity of the proton after a time interval of ?
  2. If you define the origin to be at the initial location of the proton, what is the position of the proton at ?

 

1240002     Momentum and position of a nerf basketball moving through the air     1240002
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You toss a nerf basketball of mass 0.002 kg into the air. At t = 0, the ball leaves your hand. At t = 0.11 s, the net force on the ball is , its velocity is , and its position is . What is its position at t = 0.13 s?

 


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