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Multiple Choice
Nick is pulling a crate across a horizontal floor with a rope angled 30° above the horizontal. The coefficients of kinetic and static friction are 0.2 and 0.3 respectively. If the crate is moving at a constant speed, what is the tension in the rope?
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Verified step by step guidance
1
Identify the forces acting on the crate: the gravitational force (weight), the normal force, the tension in the rope, and the frictional force.
Since the crate is moving at a constant speed, the net force in the horizontal direction is zero. This means the horizontal component of the tension must equal the frictional force.
Calculate the gravitational force using the formula: , where is the mass of the crate and is the acceleration due to gravity (9.8 m/s²).
Determine the normal force. Since the rope is angled, the vertical component of the tension affects the normal force. Use the equation: .
Calculate the frictional force using the kinetic friction coefficient: . Set this equal to the horizontal component of the tension: and solve for .