Question

A block of mass 1 kg lying on the floor is subjected to a horizontal force given by $F=2\sin \omega t$ newtons. The coefficient of friction between the block and the floor is 0.25. The acceleration of the block will be:

• A. positive and uniform
• B. positive and nonuniform
• C. zero
• D. depending on the value of $\omega$

Answer 1

The correct option is C zero

For a sinusoidal force given by $F=2\sin \omega t$, the maximum force that can be applied is its amplitude which is $2N$.
The frictional force that can occur between the block and the floor is $f=\mu mg$ $=$ $0.25\times 1kg\times 10m{s}^{-2}$ $=$ $2.5N$
Since the force applied is not more than the force of friction $F$$<$$f$, the block will not move, hence its acceleration will be $zero$.