2) A 100-kg block on an inclined plane is attached to another block of mass m vi

Question

2) A 100-kg block on an inclined plane is attached to another block of mass m via a string, as in the figure. The coefficients of static and kinetic friction for the block and the incline are µs = 0.40 and µk = 0.20 and the plane is inclined 18° with horizontal. (a) Determine the range of values for m, the mass of the hanging block, for which the 100-kg block will not move unless disturbed, but if nudged, will slide down the incline. (b) Determine a range of values for m for which the 100-kg block will not move unless nudged, but if nudged will slide up the incline.

Explanation / Answer

sum of Fx=T-mA*g*sin(theta)=mA*a for known weight sum of Fy=eta-mA*g*cos(theta)=0 for known weight sum of Fy=mB*g-T=mB*a for unknown weight a=(mB-mA*sin(theta))/(mA+mB)*g if a is negative, known weight is falling down to figure out the unknown values just plug and chug: if known is falling down the slope, unknown is less than 100 kg; and vice versa T=(mA*mB*g)/(mA+mB)*(1+sin(theta)

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