Question

A straight horizontal track, lying along the x–axis, has a length 3l . The first segment of the track, of length 2l , is perfectly smooth, while the second segment, of length l , has a coefficient of friction, μ, with respect to a given object of mass M. This object, initially at rest, at the ‘starting point’ of the track, is acted upon by a force, Fx, which adjusts its value so that it maintains the object’s (along the axis) acceleration at a constant value, a (= 2 m/s² ), over the whole length (= 3 l) of the straight track. The work done, by this force, over the two segments of the track, would be (nearly) equal if μ equals

(1) 0.05

(2) 0.10

(3) 0.15

(4) 0.20

Answer 1

(4) 0.20

The force, needed over the first segment = Ma. 

Hence W₁ = work done over the first segment = Ma (2l)

Over the second segment, if F’ is the force needed, we have

F' - μMg = Ma

∴ F' = [ma + μMg]

Hence, W₂ = Work done over the second segment.