Determining Acceleration of Pulley System w/ Friction

[lexi011]

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.

 

[rl.bhat]

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.

 

[nlightner]

I would approach this problem by first identifying all the given information and variables. From the problem, we know that there are two masses (m1 and m2) connected by a light string, a pulley with negligible mass and no friction, and a force acting on m1 at an angle of 33.30 degrees. We also know the coefficient of kinetic friction between m1 and the surface.

To determine the acceleration of m2, we can use Newton's second law, F=ma. However, since there is friction involved, we need to consider the forces acting on both masses separately.

For m1, the forces acting on it are the force of tension from the string, the force of friction from the surface, and the force acting at an angle of 33.30 degrees. We can break down the force acting at an angle into its horizontal and vertical components, and use trigonometry to find the horizontal component (F_h) which will be equal to the force of tension.

For m2, the only force acting on it is the force of tension from the string, which is equal to F_h from m1.

Next, we can set up an equation for the net force acting on each mass. For m1, it would be F_net = F_h - F(friction) - F_applied. For m2, it would be F_net = F_h.

We can then substitute in the known values and solve for the acceleration using F=ma. The acceleration of m2 will be the same as the acceleration of the system.

In summary, to find the acceleration of the pulley system with friction, we need to break down the forces acting on each mass, set up equations for the net force, and solve for the acceleration using F=ma.