Question

A block of mass 15 kg is placed on a long trolley. The co-efficient of static friction between the block and 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 viewed by 

(a) a stationary observer on the ground. 

(b) an observer moving with the trolley

Answer 1

For an observer on ground, this is how he depicts the FBD of mass,

f = ma

Now let us check for any sliding.

f ≤ f_s … (i) [Condition for no sliding]

f_s = µmg = (0. 18) (15 × 10) = 27 N.

and f = ma ≡ 15(0. 5) = 7. 5 N.

Hence no sliding.

The observer will find the body to move with acceleration of 0.5 m/s.

Now since there is no sliding, there is no relative motion w. r. t. the trolley.

Hence observer on trolley will find the mass to be at rest.

Answer 2

(a) accelerated with acceleration 0.5 m/s² , 

(b) at rest.