A block of mass 15 kg is placed on a long trolley . The coefficient of static friction between the block and the trolley is `0.18` .The trolley accelerates from rest with `0.5 ms^(-2)` for 20 s and then moves with uniform velocity . Discuss the motion of the block as viewed by (a) a stationary observer on the ground (b) an observer moving with the trolley .

Explanation

Here , m = 15 kg
`mu = 0.18`
`a = 0.5 ms^(-2)`
t = 20 s
Force on the block due to motion of the trolley `P = ma = 15 xx 0.5 = 7.5 N `
Force of limitating friction on the block
` = F = mu R = mu mg`
`= 0.18 xx 15 xx 9.8 = 24.46 N `
This opposes the motion of the block . The block shall not move . The force of static friction F will adjust itself equal and opposite to P , the applied force .
Hence to a stationary observer on the ground , the block will appear to be at rest relative to the trolley . When trolley moves with uniform velocity . the block will continue to be stationary . Because in that case , forward force is zero . Force of friction alone is acting on the block .
(b) An observer moving with the trolly has accelerated motion . The observer is therefore non - inertial ., The law of inertia is no longer valid .