Question

An object of mass 1.0 kg is at rest on a smooth inclined plane with height h, length 8 m,

Answer 1

The coefficient of kinetic friction for the rough horizontal surface is 0.66.

The given parameters;

• mass of the object, m = 1 kg
• length of the inclined plane, L = 8 m
• angle of inclination of the plane, θ = 30⁰
• distance traveled before hitting the spring, d₁ = 4 m
• distance traveled after hitting the spring, d₂ = 1.3 m
• the spring constant, k = 26.5 N/m

Apply work-energy theorem; the work done the force of friction is equal to the energy stored in the spring.

$F_kd_1 = \frac{1}{2} kd_2^2\\\\\mu_kmg cos(\theta)d_1 = \frac{1}{2} kd_2^2\\\\\mu_k(1 \times 9.8 \times cos(30)\times 4) = \frac{1}{2} \times 26.5 \times (1.3)^2\\\\33.95\mu_k = 22.39\\\\\mu_k = \frac{22.39}{33.95} \\\\\mu_k = 0.66$

Thus, the coefficient of kinetic friction for the rough horizontal surface is 0.66.

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