M1 and M2 are two masses connected as shown. The pulley is light (massless) and frictionless. Find the mass M1, given that M2 (3.5 kg) accelerates downwards at 3.35 m/s^2, θ is 35o, and μk is 0.25.
The Attempt at a Solution
The total force (which is the total mass times the acceleration) is equal to the sum of the forces.
Gravity = M1g
Normal = M1g(sinθ)
Applied = M1a
Kinetic Friction = μkM1a
a(M1 + M2) = -M1g +M1g(sinθ) +M1a -μkM1a
M1a +M2a = M1g((sinθ)-1) +M1a -μkM1a
M2a = M1(g((sinθ)-1) -μka)
M1 = M2a/(g((sinθ)-1) -μka)
M1 = (3.5*3.35)/(9.81((sin35)-1) -0.25*3.35)
M1 = 11.725/(9.81(-.426)-0.8375)
M1 = -2.34 kg
A negative answer isn't even possible, but I tried putting in "2.34 kg" is an answer and that didn't work. I don't know what I'm doing wrong.
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