Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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14h0001     Tension holding a buoy that is chained to the ocean floor.     14h0001
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An underwater buoy of total mass 5.0 kg and volume contains instruments to measure temperature and current at the bottom of a coral reef in the ocean. The buoy is completely submerged and tied by a chain to an anchor on the ocean floor. It's at a depth of 10 m below the surface of the ocean. The density of seawater is . What is the tension in the chain?

 

14h0002     A helium balloon in air.     14h0002
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You hold a string that is tied to a helium balloon that is approximately spherical with a radius of 10 cm. The balloon is in equilibrium. At atmospheric pressure and a temperature of , helium has a density of and air has a density of . (Note: the volume of a sphere is .) Assume that the densities of helium and air at room temperature are close to their densities at . The mass of the latex balloon before being inflated is 2 g.

  1. What is the buoyant force of air on the balloon?
  2. What is the tension in the string?
  3. Suppose that you cut the string from the balloon and watch the balloon rise vertically. As it speeds up, it eventually reaches a terminal velocity as it is rising. Assume constant density for helium and air as the balloon rises at its terminal velocity. What is the force of air resistance on the balloon as it rises at terminal velocity?

 

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?

 

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?

 

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?

 

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.)

 

1470001     Normal force on a girl sliding down a waterslide     1470001
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Wet 'n Wild has a waterslide called Daredevil Drop. At the steepest part of the slide, the angle is about . A girl goes down the slide. Her mass is 40 kg and the frictional force of the slide on her at its steepest angle at is 20 N.

  1. What is the normal (compression) component of the force by the slide on the girl?
  2. What is the girl's acceleration?
  3. What is the fundamental cause of the normal force by the slide on the girl?

 

14f0001     Analyze a position vs. time graph of a simple harmonic oscillator.     14f0001
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An cart on a very low-friction track has a mass 0.4 kg and is attached to a compressible, horizontal spring. It is pulled back and released from rest. A graph of its position with respect to time is shown below. (Note that the x-axis is oriented along the direction of oscillation.)


Figure: A harmonic oscillator.

  1. What is the period of oscillation?
  2. What is the amplitude of oscillation?
  3. What is the angular frequency?
  4. What is the spring's stiffness?
  5. What is the x-position as a function of time for the cart?
  6. What is the x-velocity as a function of time for the cart?
  7. What is the x-acceleration as a function of time for the cart?
  8. What is the x-component of the net force on the cart as a function of time?

 

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.

 

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.

 


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