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Chapter 6: Q72P (page 146)

A box of canned goods slides down a ramp from street level into the basement of a grocery store with acceleration0.75m/s2directed down the ramp. The ramp makes an angle of40°with the horizontal. What is the coefficient of kinetic friction between the box and the ramp?

Short Answer

Expert verified

μk=0.47

Step by step solution

01

Given data

  • The angle of inclination of the ramp, θ=40°.
  • The acceleration down the ramp is a=0.75m/s2.
02

Understanding the concept

The problem deals with Newton’s second law of motion, which states that the acceleration of an object can be written in terms of the net force acting upon the object and the mass of the object.Use Newton’s law of motion to calculate the kinetic friction.

Formula:

F=maFN=mgcosθ

03

Calculate the coefficient of kinetic friction between the box and the ramp

The normal force on the block on the inclined ramp is:

FN=mgcosθ

To calculate acceleration, use Newton’s second law of motion:

mgsinθ-fk=mamgsinθ-μkmgcosθ=ma

Substitute the values in the above expression, and we get,

9.8m/s2×sin40°-μk×9.8m/s2×cos40°=0.75m/s2μk=0.74

Thus, the coefficient of kinetic friction is0.74.

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Most popular questions from this chapter

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