As 1 kg block situated on a rough incline is connected to a spring of

1.	As 1 kg block situated on a rough incline is connected to a spring of spring constant 100 N m-1 as shown in Fig. The block is released from rest with the spring in the unstreched position. The block moves 10 cm down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has negligible mass and the pulley is frictionless.
Answer» From the fig; R = mg cosθ F = μR = μmg cosθ Net force on the block down the incline, = mg sinθ - F = mg sinθ - μmg cosθ = mg(sinθ - μ cosθ) Distance moved, x = 10 cm = 0.1 m In equilibrium, work done = P.E. of the streched spring Hence, mg(sinθ - m cosθ) × x = 1/2 kx² ⇒ 2 mg(sinθ - μ cosθ) = kx ⇒ 2 × 1 × 10(sin 37º - μ cos 37º) = 100 × 0.1 ⇒ 20(0.601 - μ × 0.798) = 10 μ = 0.126

As 1 kg block situated on a rough incline is connected to a spring of spring constant 100 N m-1 as shown in Fig. The block is released from rest with the spring in the unstreched position. The block moves 10 cm down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has negligible mass and the pulley is frictionless.

Answer»

From the fig; R = mg cosθ

F = μR = μmg cosθ

Net force on the block down the incline,

= mg sinθ - F = mg sinθ - μmg cosθ

= mg(sinθ - μ cosθ)

Distance moved, x = 10 cm = 0.1 m

In equilibrium, work done = P.E. of the streched spring

Hence, mg(sinθ - m cosθ) × x = 1/2 kx²

⇒ 2 mg(sinθ - μ cosθ) = kx

⇒ 2 × 1 × 10(sin 37º - μ cos 37º) = 100 × 0.1

⇒ 20(0.601 - μ × 0.798) = 10

μ = 0.126