A block of mass m witha given inital speed slides down a rough incline with cons

Question

A block of mass m witha given inital speed slides down a rough incline with constant speed. If a smaller block that has a mass of 4m were placed on the same incline with the same initial speed, it would

a. accelerate down the incline with an acceleration significantly less than that of the smaller block

b. accelerate down the incline with an acceleration significantly greater than that of the smaller block

c. slowly slide down the incline and then stop

d. not move

e. slide down at a constant speed

Explanation / Answer

Here ,

as the force of friction is given as

F = u * N

where N = mg * cos(theta)

and the gravity down the incline is mg * sin(theta)

Now, acceleration of the block is a

ma = mg * sin(theta) - u*mg * cos(theta)

a = g * sin(theta) - u * g * cos(theta)

the acceleration is inddependent of mass ,

as acceleration is zero for mass m ,

acceleration will also be zero for 4 m

e. slide down at a constant speed

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