Question

A first block with m(1)=2.00 kg lies at rest on a frictionless table. An ideal spring, with a spring constant of 100 N/m is attached to the wall and to the block. A second block with m(2)=0.50 kg is placed on top of the first block. The first block is gently pulled to a position x = + A and released from rest. There is a coefficient of static friction of 0.45 between the two blocks.

(a) What is the period of the oscillations if m(2) stays still on m(1) in SHM?

b) What is the largest amplitude of motion A that will allow the blocks to oscillate together without the second block sliding off?

Answer 1

a] Period T = 2pi*sqrt(Mnet/k)

= 2pi*sqrt(1.5/100)

= 0.7695 s

b] maximum acceleration of m2 = ug = 0.45*9.8 m/s^2

A*w^2 = 0.45*9.8

A = 0.45*9.8/w^2 = 0.45*9.8*(T/2pi)^2 = 0.45*9.8*(0.7695/2pi)^2

= 0.0661 m answer