Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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14i0001     Forces on a banked airplane that travels in uniform circular motion.     14i0001
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A propeller-driven airplane of mass 680 kg is turning in a horizontal circle with a constant speed of 280 km/h. Its bank angle remains during the turn. A head-on view of the airplane and a top view are shown below.


Figure: An airplane speeds up along a circular path.

The forces on the airplane are due to Earth (gravitational force) and air. The force by the air on the airplane can be written as three components: lift (perpendicular to the wings), thrust (in the direction of the velocity), and drag (opposite to the velocity). Neglect wind.

  1. What is the magnitude of the force of lift on the airplane?
  2. Which force on the airplane is larger in magnitude, the thrust or the drag?
  3. What is the net force on the airplane?
  4. If it flies at a constant speed, what will be the radius of its path?

 

14a0001     Forces on a parasail.     14a0001
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Parasailing is a recreational activity where a person with a parachute (or rather, a parasail) is pulled by a boat, as shown below.


Figure: A parasailor being pulled by a boat.

The boat and parasail (including the person) are traveling at a constant speed of 15 m/s in the +x direction. The person and parasail together have a mass of 120 kg. The tension in the rope is .

  1. What is the force by air on the person and parasail?
  2. What is the drag force on the person and parasail? (Note: drag is the component of the force by air on the system that is opposite the velocity of the system.
  3. What is the lift force on the person and parasail? (Note: lift is the component of the force by air on the system that acts opposite the gravitational force on the system.)

 

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?

 

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.

 

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?

 

1440001     Approximate length of an atomic bond for solid aluminum.     1440001
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What is the approximate length of an interatomic bond between adjacent atoms in solid aluminum?

 

14d0001     Forces on a sample in a centrifuge that is in uniform circular motion.     14d0001
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A centrifuge is used to separate white blood cells, red blood cells, and blood plasma by rotating the sample at a high angular speed. Suppose that a sample of blood is placed in a test tube and is swung in a circle of radius 0.0375 m at an angular speed of 360 rad/s. A picture of the test tube at a certain instant is shown below. The mass of the blood and tube (combined) is 0.0069 kg.


Figure: A sample in a centrifuge.

There are only two forces acting on the tube, the gravitational force on the tube and the force by the holder on the tube. Define the system to be the tube and blood sample together. What is the force by the holder on the tube at the instant shown.

 

14d0003     A bobber accelerometer     14d0003
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A bobber is attached to a string and submerged in a jar of water. The jar travels around a circle of radius at a constant speed . What is the angle of the string with respect to the vertical?


Figure: A bobber attached to string and submerged in a jar of water. The device is on a car's dashboard as the car drives at constant speed around a curve.

 

14d0002     Perpendicular and tangential forces on a comet in an elliptical orbit.     14d0002
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A comet orbits a star counterclockwise as shown below.


Figure: A comet orbiting a star.

For each point shown (A, B, C, and D), answer the following questions.

  1. Sketch a vector showing the momentum of the comet.
  2. Sketch a vector showing the net force on the comet.
  3. Sketch the perpendicular component of the net force on the comet.
  4. Sketch the tangential component of the net force on the comet.
  5. At this instant, is the comet speeding up or slowing down?

 

1430001     Variable tension in a steel rod.     1430001
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Suppose that in a theatre, a steel rod of length 1.2 m and cross-sectional radius 1 cm hangs vertically from the ceiling and supports a 10-kg spotlight that hangs in equilibrium from the end of the rod. Steel has a density of 7860 kg/m .

  1. What is the tension at the bottom of the rod?
  2. What is the tension at the top of the rod?

 


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