Question

A large block attached to a spring is undergoing simple harmonic motion horizontally, with angular frequency ω and amplitude A. On top of the block there is a small mass m which has a coefficient of friction µ with the surface of the block. What is the smallest value of µ (in terms the given values, and the gravitational constant g) for which the small mass does not slide while sitting on top of the block?

Answer 1

Step-by-step explanation:

It is a problem based on simple harmonic motion and friction . maximum friction possible between large block and mass m is µ mg . During SHM , maximum acceleration is ω² A and force is mω² A .

friction must exceed it so that mass m may not slip over it during motion . so

µ mg ≥ mω² A

µ ≥ mω² A / mg

smallest value of µ

= mω² A / mg

= ω² A /g