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

12a0001     Conservation of momentum for colliding cars on a track.     12a0001
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You do an experiment with colliding cars on a low-friction track. Car 1 of mass 0.5 kg is moving in the direction at a speed of 2 m/s when it collides with Car 2 of mass 1.0 kg which is at rest. After the collision, Car 1 rebounds and moves to the right with a speed of 0.67 m/s. Define the system as Car 1.

  1. What is the change in the momentum of the system as a result of the collision?
  2. What objects in the surroundings interact with the system during the collision and what is the change in the momentum of the surroundings?
  3. What is the velocity of Car 2 after the collision?

 

12a0002     Conservation of momentum for colliding cars on a track.     12a0002
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A hockey puck (A) on a level air hockey table has mass = 0.100 kg and initial velocity m/s just before it collides with another hockey puck (B), which has mass kg. Just before the collision, puck B has a velocity m/s. The pucks stick together (because they are wrapped in velcro) upon colliding. What is the velocity of the system after the collision? Define the system as both hockey pucks, and assume that there is no net external force on the system.

 

1210001     Different systems for colliding carts on a track     1210001
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Cart A has a speed of 1.5 m/s in the +x direction and Cart B is at rest when they collide. After the collision, Cart A rebounds in the –x direction with a speed of 0.75 m/s, and Cart B travels in the +x direction with a speed of 0.75 m/s. The mass of Cart A is 0.50 kg, and the mass of Cart B is 1.5 kg.

  1. Define Cart A to be the system. What is the change in momentum of the system due to the collision?
  2. Define Cart B to be the system. What is the change in momentum of the system due to the collision?
  3. Define Cart A and Cart B, together, to be the system. What is the change in momentum of the system due to the collision?

 

1260001     Force by the road on a truck as it slows down.     1260001
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A 1200-kg truck travels in a straight line and has a speed 25 m/s in the +x direction when the driver hits the brakes. The truck slows down to 5 m/s in 10 s. Assume that the net force on the truck is constant.

  1. What is the force by the road and air on the truck as it slows down?
  2. What is the displacement of the truck during this time interval?

 

1260002     Forces on a Moon lander as it is landing.     1260002
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A 500-kg Moon lander has a velocity of 10 m/s downward when it is a certain height above the ground. 1 minute later, it is 1 m from the ground and its speed is 0.5 m/s downward. Assume that the thruster on the lander fires upward with a constant force. Moon's gravitational field strength near its surface is 1.6 N/kg.

  1. What is the force by the exhaust on the lander (i.e. thrust)?
  2. What was its initial height, when its speed was 5 m/s downward?

 

1250001     Projectile motion with no air resistance     1250001
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A 0.4-kg soccer ball is kicked from a location m (on the ground) with initial velocity m/s. The ball's speed is low enough that air resistance is negligible. Therefore, you can assume that the net force is constant. (Note: the +y direction is defined to be perpendicular to the ground and upward, and the x-z plane is the soccer field. t = 0 is defined to be the instant the ball leaves the foot.)

  1. What is the velocity and position of the ball at t = 0.3 s after being kicked?
  2. What is the maximum height reached by the ball?

 

1250002     Momentum and position for an electron moving between charged plates with a constant electric force on the electron.     1250002
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An electron of mass and initial speed in the –y direction enters a region between charged plates in which the force on the electron is constant, in the –x direction with a magnitude . After the electron travels 5 cm in the -y direction, it exits the region between the plates. At this instant when it exits, what is its momentum and how far has it deflected to the left from where it started?


Figure: An electron travels between two charged plates.

 

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?

 

1230003     Net force on a model rocket; momentum update.     1230003
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Ad a certain instant, the velocity of a 0.050-kg model rocket is , and all significant forces on the rocket are:

  1. What is the net force on the rocket?
  2. Assuming a constant net force during a small time interval, what will be the rocket's momentum 0.02 s later?

 

1230002     Force on a box that is pushed in equilbirum across a floor.     1230002
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You push a 15-kg box across a somewhat smooth concrete floor as shown below.


Figure: A box being pushed across the floor.

You push with a force of 20 N at an angle, with respect to the horizontal, of . If the box moves in the +x direction with a constant speed, what is the force by the floor on the box? (Note: the gravitational force of Earth on the box is .)

 


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