Two object on top of each other with friction

[David Hamshir]

Homework Statement

Question 1
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 coefficient 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.

Question 2
A spring of spring constant k is used to swing a mass m around in a circle. The equilibrium length of the spring l0, and when it swings the mass in a horizontal circle it stretches by an amount that is twice the amount it stretcheswhen the mass is just hanging on the spring. Find the velocity at which this happens and the angle that the springmakes with respect to vertical.

Homework Equations

F=ma
i know we have to find all the x and y components , but i am really confused with sins and cosines .

The Attempt at a Solution

when i attempted the first my professor kinda laughed at me
for the first question i found Normal force and then plugged it in into friction minus K = ma

i would really appreciate if you guys kindly answer these questions

 

[Doc Al]

for the first question i found Normal force and then plugged it in into friction minus K = ma

It's not clear to me what you did. Try this. Treat the block+plank as a single system. What forces act on that system? (Draw yourself a free body diagram.)

 

[David Hamshir]

Well can u kindly answer these two problems for me, and show all your steps please, i would really appreciate it sir , thank you so much