1 A block of mass mb sits atop a at wooden plank of mass mp on a plane inclined an angle theta with respect to thehorizontal. The two are supported near the bottom of the plane by a spring of spring constant k that is in contactwith the plank but not the block. If the coecient of friction between the plank and the plane is µ1 and the coefficent of friction between the block and the plank is µ2 answer the following questions.

Question

1 A block of mass mb sits atop a at wooden plank of mass mp on a plane inclined an angle theta with respect to thehorizontal. The two are supported near the bottom of the plane by a spring of spring constant k that is in contactwith the plank but not the block. If the coecient of friction between the plank and the plane is µ1 and the coefficent of friction between the block and the plank is µ2 answer the following questions.
a. Find an expression for the maximum compression of the spring such that the plank and block remain at rest.
b. If the spring is compressed three times the amount you found in part (a) find the initial acceleration of theplank and the acceleration of the block given the following values: k = 4025N/m, mp = 1.2kg, mb = 4.3kg, µ1 = 0.12, µ2 = 0:07.