A box with mass m is dragged across a level floor with coefficient of kinetic friction μk by a rope that is pulled upward at an angle θ above the horizontal with a force of magnitude F. (a) In terms of m, μk, θ, and g, obtain an expression for the magnitude of the force required to move the box with constant speed. (b) Knowing that you are studying physics, a CPR instructor asks you how much force it would take to slide a 90-kg patient across a floor at constant speed by pulling on him at an angle of 25∘ above the horizontal. By dragging weights wrapped in an old pair of pants down the hall with a spring balance, you find that μk=0.35. Use the result of part (a) to answer the instructor's question.

Question

Physics

Jadyn Parsons

10 June, 01:02

A box with mass m is dragged across a level floor with coefficient of kinetic friction μk by a rope that is pulled upward at an angle θ above the horizontal with a force of magnitude F. (a) In terms of m, μk, θ, and g, obtain an expression for the magnitude of the force required to move the box with constant speed. (b) Knowing that you are studying physics, a CPR instructor asks you how much force it would take to slide a 90-kg patient across a floor at constant speed by pulling on him at an angle of 25∘ above the horizontal. By dragging weights wrapped in an old pair of pants down the hall with a spring balance, you find that μk=0.35. Use the result of part (a) to answer the instructor's question.

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Answers (1)

Know the Answer?

Brennan Nelson · Answer 1

a) F = μk mg Cosθ

b) F = 279.78 N

Explanation:

a) F = μk R

Based on the description in the question, the horizontal reaction is:

R = mg Cosθ

The force required to move the box with constant speed in terms of m, μk, θ, and g is:

F = μk mg Cosθ

b) If m = 90 kg

g = 9.8 m/s²

μk=0.35

θ = 25⁰

Force required to slide the 90-kg patient across a floor at constant speed by pulling on him at an angle of 25∘ above the horizontal will be:

F = μk mg Cosθ

F = 0.35 * 90 * 9.8 * cos25

F = 279.78 N