"In the diagram shown below, the lower block is acted on by a force, F, which has a magnitude of 74.4 N. The coefficient of kinetic friction between the lower block and the surface is 0.269. The coefficient of kinetic friction between the lower block and the upper block is also 0.269. What is the acceleration of the lower block, if the mass of the lower block is 3.27 kg and the mass of the upper block is 2.02 kg?"
I think I understand the system and the forces involved, and I was able to come up with the equations and substitute them, can someone just verify that my methods are correct?
Fnet = ma
The Attempt at a Solution
For object m2, on the bottom:
Fnet(x) = n2 - m2*g = 0 --> n2 = m2*g
Fnet(y) = Fa - u*n2 - T = ma --> T = Fa - u*n2 - m2*a [EQUATION #1]
For object m1, on the top:
Fnet(x) = n1 - m1*g = 0 --> n1 = m1*g
Fnet(y) = T - u*n1 = m1*a --> T = m1*a + u*n1 [EQUATION #2]
Substitute m1*g for n1 and m2*g for n2, then....
Equate equation #1 to equation #2 and isolate for acceleration, "a", so that:
a = Fa - u*g(m2 - m1) / (m1 + m2)
Since the two objects are connected in the pulley system, their accelerations will be the same.