Problems

practice

1. Which would you rather be hit by: the fastest pitched baseball or the fastest served tennis ball? To answer this question determine the following quantities …
   1. the momentum of each ball
   2. the impulse delivered if the baseball stops dead on impact but the tennis ball rebounds at nearly the same speed.
   Write your answers in the table below.

   quantity	baseball	tennis ball
   mass	145 g	57 g
   speed	45 m/s	75 m/s
   momentum
   impulse

2. A problem for Americans — because Americans still think non-metric units are fine. Analyze this …

   Now, the bears I live with average, the males, eight to twelve hundred pounds. They're the largest bears in the world …. They've been clocked at 41 [mph] and they've run a hundred meter dash in 5.85 seconds, which a human on steroids doesn't even approach.
   Timothy Treadwell author of Among Grizzlies. The Late Show with David Letterman. NBC. 20 February 2001.

   1. Mr. Treadwell states two different top speeds for the grizzly bear — one directly and one indirectly. Are they effectively the same?
   2. Pick whichever speed you wish and compute the momentum of a Grizzly bear (in SI units) using the average mass quoted by Mr. Treadwell.
   3. How fast would a 200 lb man have to run to have the same momentum you calculated in part b? (Do not use a calculator to compute your answer.)
   4. How fast would a 2000 lb car have to drive to have the same momentum you calculated in part b? (Do not use a calculator to compute your answer.)
3. Read this passage about one of the difficulties of interstellar travel.
   

   After all, the faster we go, the more difficult it is to avoid collisions with small objects and the more damage such a collision will wreak. Even if we are fortunate enough to miss all sizable objects, we can scarcely expect to miss the dust and individual atoms that are scattered throughout space. At two-tenths of the speed of light, dust and atoms might not do significant damage even in a voyage of 40 years, but the faster you go, the worse it is — space begins to become abrasive. When you begin to approach the speed of light, each hydrogen atom becomes a cosmic ray particle and will fry the crew. (A hydrogen atom or its nucleus striking the ship at nearly the speed of light is a cosmic ray particle, and there is no difference if the ship strikes the hydrogen atom or nucleus at nearly the speed of light. As Sancho Panza: "Whether the stone strikes the pitcher, or the pitcher strikes the stone, it is bad for the pitcher.") So 60,000 kilometers per second may be the practical speed limit for space travel.
   Isaac Asimov. "Sail On! Sail On!" The Magazine of Fantasy & Science Fiction, Vol. 72 (February 1987): 141.

   The density of the interstellar medium is about one hydrogen atom per cubic centimeter. Imagine a 1000 tonne, 4 by 6 meter, classroom-sized interstellar spacecraft traveling at 60,000 km/s on its way to Proxima Centauri (the nearest solar system to our own).
   1. preliminaries
      1. How long would it take our hypothetical spacecraft to complete its hypothetical journey?
   2. impulse–momentum
      1. Determine the momentum of our spacecraft.
      2. What mass of interstellar medium is swept up during the journey?
      3. What impulse does the interstellar medium deliver to the spacecraft?
      4. How does this impulse compare to the momentum of the spacecraft?
   3. work–energy
      1. Determine the kinetic energy of our spacecraft.
      2. What is the effective drag force of the interstellar medium during the journey?
      3. How much work does the interstellar medium do on the spacecraft?
      4. How does this work compare to the kinetic energy of the spacecraft?
4. Write something completely different.

conceptual

1. In older passenger cars, body panels were attached to a single frame around the perimeter, making them very rigid. This is known as body-over-frame construction. In newer cars, different body parts have stress-bearing elements within them and these parts are then welded to each other. This is known as unitized body construction. Repairing "unibody" cars after collision is comparatively difficult as stress (and thus damage) are distributed throughout the different parts. Why then are cars now built this way
2. To escape from a horrible fire, two people are forced to jump from the third story of a burning building on to solid concrete. Which person is more likely to sustain serious injuries: the jumper who comes to an abrupt halt when he lands or the jumper who bounces after impact?

numerical

1. When hit, the velocity of a 0.145 kg baseball changes from +20 m/s to −20 m/s. What is the magnitude of the impulse delivered by the bat to the ball?
2. A rubber ball of mass 0.025 kg traveling at 4.0 m/s down strikes the floor and bounces straight up at 2.0 m/s. Find the magnitude of the impulse that the floor gave to the ball.
3. A model rocket has mass of 1.5 kg. The engine exerts an effective upward thrust of 120 N for 3.2 seconds. (Assume a negligible amount of air resistance while the rocket is ascending.) Determine …
   1. the net force on the rocket
   2. the net impulse on the rocket
   3. the speed of the rocket when the engine stopped
   4. the height of the rocket above the ground when the engine stopped
   After the engine shuts down, the rocket is still moving upward.
   5. What maximum height above the ground did the rocket reach?

statistical

1. The National Association of Rocketry has a web page with links to data sheets for certified model rocket motors. Pick any one of these data sheets and find the following …
   • the thrust–time data used to generate the graph on the data sheet
   • the propellant mass
   • the mass after firing (i.e., the mass of the empty rocket)
   Calculate the following quantities as functions of time and make a time series graph of the …
   1. impulse provided by the motor
   2. fractional propellant mass loss (You need to determine the initial and final mass of the rocket. Assume that the loss of mass is directly proportional to the cumulative impulse. When the impulse is zero at the beginning, the mass loss is zero. When the impulse reaches its final value, the mass loss is 100%.)
   3. mass of the rocket
   4. speed of the rocket (Don't forget to include the force of gravity in your calculations.)
   5. acceleration of the rocket
   6. altitude of the rocket
   Please note: because aerodynamic drag cannot easily be included into the calculations, you will wind up with final speeds that are too fast (but still within an order of magnitude of being "correct").

investigative

1. Which requires the bigger punch: stopping the fastest pitched baseball completely or returning the fastest served tennis ball in the opposite direction with the same speed. To answer this question, complete a table like the one below. Provide the source of your info as well as its value. Use whatever units you find for mass and speed, but please report the impulses in Ns.

   	mass	(source)	speed	(source)	impulse
   baseball
   tennis ball

2. Plate
   Antarctic
   African
   Arabian
   Caribbean
   Cocos
   Eurasian
   Indian
   Nazca
   North American
   Pacific
   Philippine
   South American

   Determine the momentum of one of earth's tectonic plates (sometimes referred to as continental plates). A list of the most popular plates is shown on the right.
   1. Answer these three related questions first.
      1. Which plate have you chosen to work with?
      2. What is the speed of this plate?
      3. What is the area of this plate?
   2. Now answer these three related questions.
      1. Is the plate you've chosen continental or oceanic?
      2. What is a typical density of this kind of crust?
      3. What is a typical thickness of this type of crust?
   3. Compute the momentum of the tectonic plate you've chosen from the data you've found. State your answer to the nearest order of magnitude (the nearest power of ten). Don't forget the unit.