Question

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.

Answer 1

Answer:

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