A hollow body of weight 30 lb is sitting on a ramp degree up from the horizontal

Question

A hollow body of weight 30 lb is sitting on a ramp degree up from the horizontal. If the ramp is frictionless, determine the smallest value of the angle which will allow the body to slide down the ramp. what will be the acceleration of the body down the ramp in (a)? If there is a coefficient of static friction of 0.4 between the ramp and the body, determine the smallest value of the angle which will allow the body to slide down the ramp. What will be the acceleration of the body down the ramp in (c)? With the ramp in (c) add 10 lb of lead shot to the hollow 30 lb body and calculate its acceleration down the ramp.

Explanation / Answer

a) since no friction, any theta > 0 will cause slipping.

b)

Accelration = g*sin theta

c)

Normal force = mg*cos theta

Friction force = 0.4*mg*cos theta

mg*sin theta = 0.4*mg*cos theta

Tan theta = 0.4

theta = atan (0.4) = 21.8 deg

d)

F = ma = mg*sin theta - u(k)*mg*cos theta

a = 32.2*sin21.8 - 0.3*32.2*cos21.8

= 2.988 ft/s^2

e)

Acceleration is independent of mass, So after 10 lb mass addition, a will remain 2.988 ft/s^2.

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