## Activity Based Physics Thinking Problems in Mechanics: Momentum and Energy |

1) The mass of the earth is about 6x10 2) According to some recent highly accurate measurements made from satellites, the continent of North America is drifting at a rate of about 1 cm per year. Assuming a continent is about 50 km thick, estimate the kinetic energy the continental US has a a result of this motion.
3) Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the positive x direction and cart 2 moves in the negative x direction. They bounce off each other elastically. The graphs below describe some of the variables associated with the motion as a function of time. For the experiment described and for each item in the list below, identify which graph is a possible display of that variable as a function of time. If none apply, write N (for none). (a) the momentum of cart 1
4) An electron collides elastically with a hydrogen atom which is initially at rest. The initial and final motions are along the same straight line. What fraction of the electron's initial kinetic energy is transferred to the hydrogen atom? The mass of the hydrogen atom is 1840 times the mass of the electron.
Based on a problem from the book of Arnold Arons. 5) The conservation of momentum is useful in some situations and not in others. Describe how you obtain the impulse-momentum theorem from Newton's second law and what situations lead to momentum conservation. How would you decide if conservation of momentum could be used in a particular problem? 6) Energy conservation is sometimes a useful principle in helping us solve problems concerning the motion of objects. Suppose a single object is moving subject to a number of forces. Describe how you would know whether energy conservation would hold for the given example and in what kinds of problems you might find it appropriate to use it. 7) A professor of physics is going ice skating for the first time. He has gotten himself into the middle of an ice rink and cannot figure out how to make the skates work. Every motion he makes simply slips on the ice and leaves him in the same place he started. He decides that he can get off the ice by throwing his gloves in the opposite direction. (a) Suppose he has a mass M and his gloves have a mass m. If he throws
them as hard as he can away from him, and they leave his hand with a velocity
8) A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. By compressing the spring, the child can launch the ball up the ramp.
The spring has a spring constant (a) Assuming that friction and air resistance can be ignored for the
purposes of this problem, describe the changes in the forms of energy in
the system from the time the spring is compressed until the ball first
hits the ground. 9) Two identical carts of mass m are sliding on an air track. Cart 1
approaches cart 2 with velocity V (a) You want to find the velocities of the two carts after the collision,
V 10) Construct the Newton drag law for air resistance by filling in the
equations that go with the following arguments. Assume a sphere of radius
R is moving with velocity v through a dense crowd of tiny particles, of
number density n per cm (a) Assume in a small time Dt that the sphere's
velocity doesn't change. What volume of air does it move through and how
many particles get swept away in the time Dt?
11) When objects are too small to be seen by a microscope, physicists often probe them by shooting microscopic particles from the objects and observing how the particles scatter. (R. P. Feynman once described this process as "trying to find out the shape of a wineglass by shooting buckshot at it"!) The M.U.P.P.E.T. program SCATTER * simulates a simple model for this process. The program models shooting a beam of classical particles at a force
field in two dimensions. (The best way to think about this is to imagine
rolling a bunch of marbles or ball bearings along the ground and trying
to use their paths as seen from above to determine the shape of hills and
valleys in the ground they move over. The height of the ground corresponds
to the potential energy of the force field.) A typical screen is shown
below. The particles start at the bottom of the graph and move upward.
The picture shown has a beam of 5 particles all travelling parallel toward
the top of the graph at a speed of 2 m/s. You can change the number of
particles, the width of the beam (by changing y The trajectory of each particle is laid down as dots, one place every 0.15 second. (You can change this by changing dt.) When the dots are close together the particle is moving slowly. When they are far apart, the particle is moving fast. There are 7 different force fields that you may probe. Choose one, find out all you can about it and write up your results. You may give information about the force as a function of position or about the potential energy as a function of position. You may use energy conservation, momentum conservation, or whatever else you like. You may print out the screen and measure the change in spacing of the dots to get the acceleration. 12) An electron at rest has an angular momentum equal to h/4p,
where h = Planck's constant (6.63 x 10 (a) Find the value of w required to get the
necessary angular momentum. 13) An oxygen molecule of mass M is sitting at rest minding its own business. Suddenly, a cosmic ray photon passes by and adds an energy D to the molecule. The molecule sits and wiggles for a while, and the breaks up into two equal mass oxygen atoms traveling in opposite directions. (a) How fast is each oxygen atom traveling? 14) (a) Describe how a solid ball can move so that (i) its total kinetic
energy is just the energy of motion of its center of mass, and (ii) its
total kinetic energy is the energy of its motion relative to its center
of mass.
In the graphs below are shown a number of possible plots for the various physical parameters associated with the two carts. Each graph has two curves, one for each cart and labeled with the cart's letter. For each property (a)-(e) select the letter of the graph that could be a plot of the property. (a) The force
16) Can a system whose momentum is conserved be made up of smaller systems whose individual momenta are not conserved? Explain why or why not and give an example. 17) In the figure below are shown two carts on an air track. The carts have equal masses. At the time shown, cart B is moving in the negative x direction and the center of mass of cart A is at the origin and at rest. When the carts collide, they stick together. Friction with the track is small and may be neglected In the graphs below are shown a number of possible plots for the various physical parameters associated with one of the two carts. For each property (a)-(e) select the number of the graph that could be a plot of the property as a function of time. (a) the momentum of cart A
18) Energy conservation is sometimes a useful principle in helping us solve problems concerning the motion of objects. Suppose a single object is moving subject to a number of forces. Describing how you would know whether energy conservation would hold for the given example and in what kinds of problems you might find it appropriate to use it. 19) Is it possible for a system of interacting objects to conserve momentum but not mechanical energy (kinetic + potential)? Discuss and defend your answer, then given an example that illustrates the case you are trying to make.
22) Kinetic energy and momentum are both quantities that tell something about an object's motion. Define what each one is and discuss the similarities and differences between them. 23) Two blocks collide on a frictionless surface. After the collision
the two blocks stick together. Block A has a mass M and is initially
at rest. System C is composed of both blocks. a) Draw a free body diagram for each block at an instant b) Rank the magnitudes of the horizontal forces in your diagram. Explain your reasoning. c) Calculate the change in momentum of block A, block B, and system C. Show all work. d) Is kinetic energy conserved in this collision? Explain your reasoning. |

* To download an executable of the program SCATTER, click on the program name. This program is a DOS program. (It can be run from Windows, but you will probably need to create a PIF file to do so.) To run it you must also have a "Borland Graphics Interface" (BGI) file appropriate for your graphics screen in the same directory as the program. For most computers today, the appropriate file is "EGAVGA.BGI". Both the program and the BGI file are contained in a "zip" file. Unzip them into the same directory using PKUNZIP or WINUNZIP.

These problems written and collected by E. F. Redish. Photos and figures
by E. F. Redish. These problems may be freely used in classrooms. They
may be copied and cited in published work if the *Activity Based Physics
Thinking Problems in Physics site* is mentioned and the URL given. Web
page edited by K. A. Vick.

To contribute problems to this site, send them to redish@physics.umd.edu.

Go back to the Thinking Problems page

Go back to the Thinking Problems in Mechanics page

Maintained by
University of Maryland PERG

Comments and questions may be directed to
E. F. Redish

Last modified June 21, 2002