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.). The coefficient of friction between block and the in line is 0.1. if the block is pushed up by 10 m along the incline, calculate

(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

m = 1kg, θ = 30° , cos 30° = 0.866, sin 30° = 0.5 F = 10 N, μ = 0.1

Distance d = 10m

(a) W_g = mg sin θ d = 1 × 10 × 0.5 × 10 = 50 J

(b) W₁ = μmg cos θ d = 0.1 × 10 × 0.866 × 10

= 8.66 J

(c) ∆U = mgh = 1 × 10 × 5 = 50 J

(d) a = {F – (mg sin 30° + μmg cos 30°)}

\(a=\frac{[10.0-(5.0+0.87)]}{1.0}m/s^2\)

= 4.13 m/s²

Apply 3^rd kinematic equation of motion,

V² − u² = 2ad

Change in KE, ∆K = \(\frac{1}{2}mv^2-\frac{1}{2}mu^2\) = mad = 41.3 J

(e) Work done = Force × displacement

= 10 × 10J

= 100 J