Question

A 4.50 kg wooden block slides 2.35 m down a wooden incline at constant velocity. (The coefficient of static friction is 0.40, and the coefficient of kinetic friction is 0.20.)

1. What is the angle of the incline? (Ans : 11.3 degrees)

2. Calculate the increase in the system's thermal energy. (Ans : 20.3 J)

Answer 1

The work done is expressed as follows:

Here, is the force exerted on the particle and is the displacement of the particle.

(a)

The free-body diagram is shown in the below figure.

$C:\Users\apparao.kante\Desktop\SSA.jpg$

The net force along the vertical direction is,

The net force along the horizontal direction is,

Substitute for in the above equation.

Thus, the angle is,

Rewrite the above equation for .

Substitute 0.200 for in the above equation.

Therefore, the angle of the incline is .

(b)

The thermal energy increases due to kinetic friction between the surfaces. As a result, the two surfaces are warmed. Hence, it is best to include both the block and the incline in the system.

(c)

The work done is calculated as follows:

Substitute for in the above equation.

Substitute 450 kg for m, for g, for , and 2.35 m for d in the above equation.

Therefore, the work done is .