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Chapter 3: Q3.4-20E (page 90)

An object at rest on an inclined plane will not slide until the component of the gravitational force down the incline is sufficient to overcome the force due to static friction. Static friction is governed by an experimental law somewhat like that of kinetic friction (Problem 18); it has a magnitude of at mostN, where m is the coefficient of static friction and Nis, again, the magnitude of the normal force exerted by the surface on the object. If the plane is inclined at an angle a, determine the critical value0for which the object will slide ifa>ao but will not move fora<ao.

Short Answer

Expert verified

Therefore, the object starts sliding down when tanαo>μ.

Step by step solution

01

Draw a diagram

02

Find the critical value

Here C is the center of mass of an object. As the object starting sliding down

mgsinαo>μN

However, μN=μmgcosαo

Hence the object starts sliding down whenmgsinαo>μmgcosαo

sinαo>μcosαo

Assume that the inclined plain is not vertical. Hence,cosαo≠0 . Then

sinαocosαo=tanαo

Both μand tanαoare positive,

so tanαo=tanαoandμ=μ

Therefore, the object starts sliding down when role="math" localid="1664209459647" tanαo>μ.

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