M-D3: Acceleration of a body does not depend upon the source of the forces

PIRA: 1H10.10

Equipment: 2 rolling tables or skateboards, a long rope. Set 9, Cabinet 3, Shelf 3 contains the skateboards, while the rope is in Set 7, Cabinet 2, Shelf 3. Note: WD-40 can be used to reduce the friction evident with the rolling tables or skateboards.

Procedure: "If using tables place them 15 to 20 feet apart and so aligned that they will roll directly toward each other. Seat a student on the near end of each table and place the rope in their hands. Have one student act merely as a clamp, holding the rope tightly in their hands. Have the other student pull in the rope with sufficient force that each table accelerates. (The force must exceed the greater rolling friction of the two tables if both are to move. This condition is not necessary to prove the point of the experiment, but students, I have found, accept the results more readily when both do move). Separate the tables, keeping each student in place on his table, align the tables as before, and repeat the experiment reversing the active and passive role of the students. Both tables will accelerate much as before.

"The point is that it makes no difference whether the motor for the operation is associated with one table or the other; the resulting motions are the same. Since the mass of the rope is negligible, it is impossible for the rope to exert a force on one table without exerting an equal force on the other. In either case each table will move according to this force and the mass and friction of that table.

"Discussion of this experiment often helps clarify the misconception that if two people at opposite ends of a rope pull on the rope with a force of [magnitude] T, the tension in the rope is 2T; while if one man pulls with a force of [magnitude] T on a rope the other end of which is attached to a solid wall, the tension in the rope will be just T.

"You may desire to perform the experiment a third time, allowing both students to pull in rope simultaneously. However, my experience has been that they tend to pull in rope at the same speed as when they pulled alone rather than with the same force. Nevertheless, this can lead to worthwhile discussion if you care to pursue it.

"I like to point out that it is only a matter of convenience that an automobile for transporting people has the motor in the vehicle. People can be transported cable car or traveling sidewalk where the motor is based in the ground. The only condition is that a force pair must be set up between vehicle and ground." — Percy Carr (1970)