Question

 A wooden box with a mass of 10.0 kg rest on a ramp that is incline at an angle of 25° to the horizontal. A rope attached to the box runs parallel to the ramp and then passes over a frictionless bully. A bucket with a mass of M hangs at the end of the rope. The coefficient of static friction between the ramp in the box is 0.50. The coefficient of Connecticut friction between the ramp in the box is 0.35.

Suppose the box remains at rest relative to the ramp. What is the maximum magnitude of the friction force exerted on the box by the ramp?

Answer 1

The maximum magnitude of the friction force exerted on the box by the ramp is 44.41 N.

The given parameters;

• Mass of the box, m = 10 kg
• Inclination of the ramp, θ = 25⁰
• Coefficient of static friction, μ = 0.5
• Coefficient of kinetic friction, μk = 0.35

The normal force on the wooden box is calculated as follows;

$F_n = mg \times cos(\theta)\\\\F_n = 10 \times 9.8 \times cos(25)\\\\F_n = 88.8 2 \ N$

The maximum magnitude of the friction force exerted on the box by the ramp is calculated as follows;

$F_f = \mu \times F_n\\\\F_f = 0.5 \times 88.82 \\\\F_f = 44.41 \ N$

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