A block of mass 1 kg is pushed up a surface inclined to horizontal at

1.	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» (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

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»

(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.

(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