AP Physics

Simulating Inelastic Collisions

Introduction:

The Interactive Physics™ program makes it easy to simulate inelastic collisions between objects of various masses with various velocities. In addition, the software makes it possible to switch reference frames quickly and easily.

In particular, collisions turn out to be very interesting (and simple!) when viewed from the center of mass, or as a physicist would say, in the center of mass frame of reference. When you finish this simulation you should be able to tell:

• How does the center of mass of a system move during an inelastic collision? Why does it do that?
• How do the colliding objects move relative to the center of mass during a one-dimensional inelastic collision?
• How do the colliding objects move relative to the center of mass during a two-dimensional inelastic collision?

---

Part 1 - The Earth Frame of Reference:

Setup:

1. Open the Interactive Physics program.
2. Create 2 circle (or square) objects, one toward the left of the window, the other toward the right side of the window (as shown).
3. Set Gravity to "None" (World menu).
4. Open the properties window (Window menu), and:
   1. give each object a mass of 1.0 kg,
   2. give each object an elasticity of 0.00
   3. give one object a velocity (v_x) of 2.0 m/s toward the other. Leave the second object at rest.
5. Attach a "meter" to each object to measure the x-component of its velocity (v_x).
   1. Select "X Graph" from the Velocity sub menu in the Measure menu.
   2. Select "Digital" from the pop up menu on the upper-left corner of the meter.

Run the Simulation:

Run the simulation for various values of the masses, and various initial velocities. Do the results correspond to your theoretical predictions?

---

Part 2 - The Center of Mass

Setup:

1. Select "System Center of Mass" from the View menu.

Run the Simulation:

When you run the simulation, the center of mass of the system will appear as a bold "X" in the window. Study the motion of the center of mass of the system for several collisions. What can you conclude about the motion of the center of mass before and after the collision? Turn on "Tracking." Discuss the reasonableness of your findings.

---

Part 3 - The Center of Mass Frame of Reference

Setup:

1. Select the center of mass with the mouse, and choose "New Reference Frame" from the View menu to establish a "System Center of Mass" reference frame.
2. Be sure that the center of mass reference frame is selected as the current reference frame (at the bottom of the View menu).

Run the Simulation:

Run the simulation using several different masses and initial velocities. Viewed from the center of mass of the system, how do these motions appear? Why?

---

Part 4 - Two-Dimensional Inelastic Collisions

Setup:

1. Delete your velocity meters, and replace them with meters to measure the two-dimensional velocity (All).
2. A difficulty with two-dimensional collisions is that the objects can easily miss each other. To avoid this, turn on "GridLines" in the Workspace sub menu of the View menu. This will allow you to align your objects for a collision. For instance, since the objects at right have equal speeds, they are positioned at equal distances from the collision point. If one object had twice the speed of the other, position it twice as far from the collision point.

Run the Simulation:

Run the simulation using different masses and velocities. Be sure to view each collision from both reference frames (Earth and center of mass). What can you conclude?

---

[Lab Index]

---