Determining Acceleration of Pulley System w/ Friction

AI Thread Summary
To determine the upward acceleration of mass m2 in the pulley system, the horizontal component of the applied force on mass m1 must be calculated using Fcos(θ), while the frictional force is determined by μ times the sum of the vertical forces. The tension in the string can be expressed as T = m2g + m2a, where a is the acceleration of m2. By equating the net forces acting on both masses and solving for acceleration, the relationship between the forces and the masses can be established. The solution involves substituting the tension back into the equations to find the desired acceleration of m2.
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Homework Statement


Mass m1= (25.70 kg) is on a horizontal surface, connected to mass m2= (5.90 kg) by a light string as shown. The pulley has negligible mass and no friction.
A force of 241.7 N acts on m1 at an angle of 33.30 degrees. The coeficient of kinetic friction between m1 and the surface is 0.237. Determine the upward acceleration of m2.

a picture of the problem and a partial explanation is given here: http://images.google.com/imgres?img...&sa=N&start=36&um=1&ei=TE8wSruPLaXYswO43JzWAw


Homework Equations


How do I find the acceleration?


The Attempt at a Solution


I found the horizontal component of the force pulling the masses. I know F=ma and that F(friction)=mu*normal force. But how do I use that? etc.
 
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The acceleration of m2 = ( T - m2g)/m2.
Frictional force = μ( Fsinθ + m1g )
Applied force = Fcosθ - T
Find the net force and acceleration of m1.
Equate it with m2 and find T. Substitute it in one of the equation to get acceleration.
 

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