Question

A force $F=kt$ is applied to a block $A$ as shown in figure, where $t$ is time in second. The force is applied at $t=0$, when the system was at rest. Which of the following graphs correctly gives the frictional force on block A as a function of time?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Tension is an elastic force. That means that tension arises due to the deformation of the string. Unless the string does not get deformed, tension will not act. Initially, the string is straight without any tension. As the force F increases, immediately frictional force acts to resist relative motion. Therefore, as long as F is less than maximum friction, the string remains unstretched and there is no tension in the string. However, once F becomes greater than maximum friction, friction alone will not be able to stop relative motion. The string begins to get stretched, and tension starts to act. Now, tension begins to act on block B as well. In order to resist relative motion, friction begins to act on block B. As tension increases, even friction increases until maximum static friction is reached. After that it cannot resist motion any longer and the blocks begin to move. At this point, maximum kinetic friction begins to act.