Question

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 30° by a force of 10 N parallel to the inclined surface (Fig. 6.15).The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, calulate

(a) work done against gravity

(b) work done against force of friction

(c) increase in potential energy

(d) increase in kinetic energy

(e) work done by applied force.

Answer 1

(a) W_g = mg sinθ d = 1×10 × 0.5 ×10 = 50 J.

(b) W_f = μmg cosθ d = 0.1 ×10 × 0.866 × 10 = 8.66 J.

(c) ΔU = mgh = 1 ×10 × 5 = 50 J

(d) a = {F - (mg sinθ + μmg cosθ)} = [10 -5.87]

= 4.13 m/s² 

v = u + at or v² = u² + 2ad

ΔK = (1/2)mv² - (1/2)mu² = mad = 41.3J

(e) W = F d = 100 J