Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1450001     Approximate length of an atomic bond for solid aluminum.     1450001
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Spring A of stiffness 10 N/m is hung vertically from a ringstand. From the lower end of this spring, a different spring (Spring B) of stiffness 20 N/m is hung. And from the lower end of this spring, a 0.25-kg block is hung in equilibrium. When springs are connected in this orientation, they are said to be in series. Neglect the mass of the springs.

  1. How far is Spring A stretched from its relaxed length?
  2. How far is Spring B stretched from its relaxed length?
  3. If you were to replace the set of springs with a single spring that would stretch the same amount when the block is hung from it, what is the stiffness of the single spring?

 

1450003     Bond stiffness of solid tin.     1450003
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A certain tin wire (white tin, as opposed to gray tin) has a length of 1.5 m and a square rectangular cross section that is (1 mm x 1 mm). With a tension of 200 N applied to the wire, it stretches 6 mm. Use a simple ball-and-spring model of a solid, and assume that tin's crystal lattice is simple cubic, with atoms essentially stacked next to and on top of one another, like inflated basketballs stacked in a box. From these measurements, approximate the bond stiffness of tin. The density of white tin is . Its atomic weight is 118.7 g/mol.


Figure: A 3-D ball-and-spring model of the tin wire.


Figure: The top view and side view of a simple cubic lattice.

 

1450002     A 2-D lattice of balls and springs.     1450002
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Suppose that in the lab, you build a set of identical balls connected by identical springs, as shown below.


Figure: A 2-D ball-and-spring model.

The masses of the balls and springs are negligible compared to the block that you hang from the apparatus. If you hang a 0.25-kg block in equilibrium, the apparatus stretches 0.050 m from its relaxed length.

  1. What is the stiffness of each spring?
  2. How much did each spring stretch?

 

1360001     A comet orbiting Sun     1360001
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A comet of mass orbits Sun which has a mass . Use the following constants and initial conditions for the comet in your calculations.

Assume that Sun remains stationary during the orbit (i.e. it does not "wobble").

  1. What is the position and momentum of the comet at t = 30 days.
  2. What is the period of the comet's orbit?
  3. What is the position of the comet at aphelion (the point in its orbit when it is furthest from Sun.

 

1320001     The net force on a dart in a spring-loaded dart gun.     1320001
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A spring-loaded dart gun is used to shoot a 5-gram dart straight upward. Its spring has a stiffness 50 N/m, and its relaxed length is 5.0 cm. The spring is compressed 4.0 cm from its relaxed length. What is the velocity of the dart when it leaves the spring (i.e. at the instant the spring returns to its relaxed length)? Apply the Momentum Principle iteratively in order to answer the question.

 

1310003     A block hanging vertically from a spring in equilibrium.     1310003
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In the lab, you connect one end of a 15 N/m spring to a ringstand, and you hang a 0.25-kg block from the other end of the spring. It hangs vertically in equilibrium.

  1. How far is the spring stretched from its relaxed length?
  2. Suppose that you put your hand beneath the block and lift up on the block in order to partially support it. It is still in equilibrium with the spring stretched 5 cm from its relaxed length. What is the force of your hand on the block?

 

1310002     The spring force of parallel springs in an exercise apparatus.     1310002
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The piece of exercise equipment shown below includes two handles that are on each end of two parallel springs, each with a stiffness 500 N/m. To build strength, a person holds the two handles and pulls them apart with equal magnitude forces applied in opposite directions to the handles, thus stretching the springs. Neglect the mass of the springs and assume that they are pulled horizontally.


Figure: Two parallel springs between two handles that can be pulled apart.

  1. If a person stretches the springs 5 cm from their relaxed lengths and holds it at rest, what is the net force applied to the system and what magnitude force must he apply to each handle?
  2. What magnitude force must he apply to each handle to stretch it twice as far (10 cm) and hold it at rest?
  3. If the two parallel springs were replaced with a single spring such that the same force would be required to stretch it 10 cm as for the two parallel springs, what would be the stiffness of the single spring?

 

1310001     The net force on a dart in a spring-loaded dart gun.     1310001
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A spring-loaded dart gun is used to shoot a 5-gram dart straight upward. Its spring has a stiffness 50 N/m, and its relaxed length is 5.0 cm. The spring is compressed 4.0 cm from its relaxed length.

  1. What is the net force on the dart at the instant the spring is released?
  2. What is the net force on the dart at the instant the dart leaves the spring? At this instant, the spring has returned to its relaxed length.

 

1340001     The gravitational force by a star on a planet.     1340001
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A planet of mass kg is at a location m. A star of mass kg is at a location m. What is the gravitational force by the star on the planet?

 

1350001     Gravitational field and the weight of an astronaut in the International Space Station.     1350001
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The International Space Station orbits Earth at an altitude of about 350 km (from Earth's surface).

  1. What is the magnitude of Earth's gravitational field g at the altitude of the space station?
  2. What is the weight of a 90-kg astronaut who is in the space station? (Note weight in this case is defined as the gravitational force by Earth on the astronaut.)

 


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