Question

A 2.41 kg block is pushed 1.42 m up a vertical wall with constant speed by a constant force of magnitude f applied at an angle of 59.9 ◦ with the horizontal. the acceleration of gravity is 9.8 m/s 2 . 2.41 kg 59 f .9 ◦ if the coefficient of kinetic friction between the block and wall is 0.521, find the work done by f.

Answer 1

Refer to the diagram shown below.

The weight of the block is
W = (2.41 kg)*(9.8 m/s²) = 23.618 N
The kinetic coefficient of friction is
μ = 0.521

The normal reaction is
N = f cos(59.9°) = 0.5015f N
The frictional resistive force is
R = μN = 0.521*(0.5015f N) = 0.2613f N

For dynamic force balance,
f sin(59.9°) = W + R
0.8652f = 23.618 + 0.2613f
0.6039f = 23.618
f = 39.109 N

The block moves by 1.42 m.
The work done is
W = (f sin(59.9° N)*(1.42 m)
     = 39.109*sin(59.9°)*1.42
     = 48.05 J

Answer: 48.0 J (nearest tenth