1. The problem statement, all variables and given/known data A block of mass m1 is at rest on an inclined plane that makes an angle (theta) with the horizontal. The coefficient of static friction between the block and the inclined planed is µs. A massless, inextensible string is attached to one end of the block, passes over a fixed pulley, pulley 1, around a second freely suspended pulley, pulley 2, and is finally attached to a fixed support. The pulleys are massless, but a second block of mass m2 is hung from the suspended pulley. Gravity acts downwards. Now assume that the block on the incline plane is sliding up the plane. The coefficient of kinetic friction is µk. Find the magnitude of the acceleration of the block on the inclined plane a_x1 Express your answer in terms of some or all of the variables m1, m2, theta, µk and g 2. Relevant equations F = ma 3. The attempt at a solution I choose coordinate systems. For block 1 I chose the positive X axis downward along the surface of the inclined plane and the positive Y axis up, perpendicular to the surface of the inclined plane with the x origin at the top of the incline. For block 2 I chose the positive Y-direction downwards with the origin at the ceiling. I made free-body diagrams of both block 1, 2 and the suspended pulley which gave me the following equations: I can treat the suspended pulley and block 2 as one system because the length between them is constant so they move with the same acceleration a_2 -T + µ_k m_1 gcos(theta) + m_1 gsin(theta) = m_1 a_x1 N = m_1 gcos(theta) -2T + m_2 g = m_2 a_2 The length of the cord connecting block 1 with the ceiling is constant. So after taking two derivatives of the length. I get the relation between a_x1 and a_2 which is a_1 = -2a_2 T = ((m_2*g- m_2*a_2)/2 ) T = µ_k*m_1*g*cos(theta) + m_1*g*sin(theta) - m_1*a_1 ((m_2*g-m_2*a_2 /2 ) = µ_k*m_1*g*cos(theta) + m_1*g*sin(theta) - m_1*a_1 2*(µ_k*m_1*g*cos(theta) + m_1*gsin(theta) - m_1*a_1 = (m_2*g-m_2*a_2) 2*(µ_k*m_1*g*cos(theta) + m_1*g*sin(theta)) - m_2*g = -m_2*a_2 + 2*m_1*a_1 substitute a_1 / -2 for a_2 and factor a_1 out 2*(µ_k*m_1*g*cos(theta) + m_1*g*sin(theta)) -m_2*g = (m_2/2 + 2*m_1) * a_1 a_1 = (2*(µ_k*m_1*g*cos(theta) + m_1*g*sin(theta))-m_2*g ) / (m_2/2 + 2*m_1) For some reason this answer is not correct and I have been looking for that reason for several hours but I can't seem to find it. I think its a math error rather than a physics error. Can someone help me out?