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Opus in profectus

Conservation of Momentum

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Problems

practice

  1. In the action-adventure movie Eraser, (1996) Arnold Schwarzenegger plays a US Marshall working for the Witness Relocation Program. He obtains a high-tech weapon that launches projectiles at "nearly the speed of light". Arnold wields the weapon like a shotgun, firing it several times from an unbraced, standing position. Bad guys are then seen flying through the air (for several meters) after being hit. Explain the physical impossibility of operating such a weapon in the manner described above.

  2. If a significant portion of the population of China (say one billion people) simultaneously jumped up at 1 m/s, how fast would the Earth recoil? Assume an average mass of 60 kg per person. (Do not use a calculator to compute your answer. This is meant to be an order of magnitude calculation.)
  3. Write something different.
  4. Write a conveyor belt problem and make it interesting.

numerical

  1. An eight year old boy (26 kg) sits on a wheeled office chair (16 kg) holding a fire extinguisher (18 kg empty). He points the discharge horn to the right and ejects 9 kg of carbon dioxide at 20 m/s. What is his speed and direction after the fire extinguisher is emptied (assuming friction is negligible)?
  2. A group of students are performing an experiment in class using collision carts on a track. An 8.0 kg cart moving to the right at 4.0 m/s hits a 4.0 kg cart moving to the left at 6.0 m/s. Immediately after the collision, the 4.0 kg cart moves to the right at 3.0 m/s. What are the speed and direction of the 8.0 kg cart after the collision?
  3. A 2,600 kg SUV traveling west at 15 m/s collides head on with a 1,300 kg four door sedan traveling east at 20 m/s. Determine the speed and direction of the two cars immediately after impact if they lock together.
  4. A 136 kg offensive lineman is about to tackle a 100 kg quarterback. Right before impact, the lineman is moving north at 6.0 m/s and the the quarterback is moving north at 1.0 m/s. Determine the speed and direction of the two players immediately after the tackle.
  5. A 125,000 kg locomotive is traveling south at 1.0 m/s through a switching yard. A connected set of parked gondola cars weighing 1,750,000 kg are directly ahead. Determine the speed and direction of the completed train after the locomotive has been coupled to the cars.
  6. Two adjacent students stand on stationary skateboards, face each other, and push apart. The skateboarder on the left weighs 65 kg, the one on the right is 85 kg. If the lighter skateboarder moves at 3.2 m/s, determine the speed and direction of the heavier skateboarder.
  7. A nucleus of uranium 238 (3.95292599 × 10−25 kg) ejects an alpha particle (6.64465675 × 10−27 kg) transmuting into a nucleus of thorium 234 (3.88638509 × 10−25 kg). If the alpha particle is ejected to the right at 1.421 × 107 m/s, determine the speed and direction of the recoiling nucleus.
  8. A baseball sits on a tee-ball stand. A child hits it with a bat moving east at 6.0 m/s and the ball flies off at 15 m/s. Determine the speed and direction of the bat immediately after impact. Tee-ball equipment is smaller than regular baseball equipment. The ball weighs 125 g and the bat 500 g.
  9. The Walther P38 is an 800 g semiautomatic pistol that fires 7.45 g bullets. If a Walther P38 fires a single bullet south at 390 m/s, determine its recoil speed and direction.
  10. A 3.0 kg fish is swimming at 1.5 m/s to the right. It swallows a 0.25 kg fish swimming to the left at 4.0 m/s. What is the velocity of the larger fish immediately after lunch?
  11. At what speed does a 650 g cue need to strike a 160 g cue ball if the the ball is to be given a forward velocity of 1.5 m/s and the speed of the cue is to decrease by 90%.
  12. A 60 kg woman rides a 25 kg canoe until she is 30 cm away from a dock. She takes a 50 cm stride forward. Does her foot land on the dock or in the water?

statistical

  1. student-data.txt
    The picture below shows an experiment performed by a group of students. Two lab carts are placed end to end in the center of an aluminum track. The cart on the left has a trigger that will release a spring-loaded piston when pressed. This pushes the two carts in opposite directions across the track. The plastic cards on top of each cart then passed through the photogates on opposite ends and a computer computed the speeds of the carts.

    The students placed various combinations of iron weights on the carts and repeated the experiment several times. The mass (in kg) of each cart plus the weights and the recoil speeds (in cm/s) were recorded in the accompanying tab delimited text file.
    1. Compute the recoil momentums of each cart.
    2. Construct a graph with the momentum of the first cart on the horizontal axis and the momentum of the second cart on the vertical axis.
    3. Add a best fit straight line to this graph and determine its slope and y-intercept. (Include the uncertainty, coefficient of correlation or determination, and the root mean square error if you have the ability to do so.)
    4. Does this analysis show that momentum was conserved when the lab carts recoiled?

investigative

  1. Determine "delta vee" for a typical Space Shuttle from SRB separation to MECO. Begin by finding the following information…
    1. mass of the orbiter
    2. mass of the external fuel tank…
      1. full
      2. empty
    3. time after liftoff of…
      1. solid rocket booster (SRB) separation
      2. main engine cutoff (MECO)
    4. exhaust velocity of the main engines
    5. type of fuel used in the main engines
    6. the Space Shuttle's "destination" in space
  2. Determine "delta vee" for either the Deep Space 1 or Dawn space probes after leaving the Earth's gravitational field. Begin by finding the following information…
    1. mass of the probe when…
      1. full of propellant
      2. empty
    2. exhaust velocity
    3. type of propellant used
    4. engine burn time
    5. where the probe was sent

calculus

  1. A rocket or some other kind of space travel problem.
  2. A conveyor belt problem.