Force-Pulley problem solving for accel

[bocobuff]

Homework Statement

A 30.7-kg block (m1) is on a horizontal surface, connected to a 6.3-kg block (m2) hanging vertically by a massless string. The pulley is massless and frictionless. A force of 224.9 N acts on m1 at an angle of 30.5degrees. The coefficient of kinetic friction (mu_k between m1 and the surface is 0.209. Determine the upward acceleration of m2.

Homework Equations

Fnet_x=m*a_x, Fnet_y=m*a_y, f_k=mu_k*Fn,

The Attempt at a Solution

I drew the free-body diagram with normal force, Fn, and gravity, m*g, and the y component of the applied Force, F_y=F*sin30.5, on the y-axis with the Fnet_y= Fn+F_y-m*g=0. On the x-axis I have tension from m2, T, and f_k=mu_k*Fn, and the x component, F_x=F*cos30.5. The Fnet_x=T+mu_k*Fn-F*cos30.5, and I don't have a numerical solution for this yet. I know from Fnet_y that Fn=m*g-F*sin30.5 and that I'm looking to solve for T from m2 because that will be the same T on m2 on the other side of the pulley. From there I can solve for the acceleration easily but I'm having a terrible time with eliminating variables and isolating T. Am I looking over a trig identity or a simple substitution somewhere? Any suggestions would be great, thanks.

 

[Hootenanny]

I've haven't looked at all your working to make sure that it's correct, but I will say that you shouldn't worry about having trigonometric functions in your equations, remember that sin(30.5) and cos(30.5) are just numbers. Just solves these two equations as you would any pair of simultaneous equations.

 

[baba89]

It seems like you are on the right track with your approach. To solve for T, you can use the equation Fnetx=T+muk*Fn-F*cos30.5 and substitute in the value for Fn that you found from Fnety. This will give you an equation with only one variable, T, which you can then solve for. Another approach could be to use the equation Fnetx=m2*ax, where ax is the acceleration of m2. From this, you can solve for ax and then use the equation ax=ay to find the upward acceleration of m2. Keep in mind that in this problem, the acceleration of m2 is equal to the acceleration of m1, since they are connected by a massless string and the pulley is frictionless. I hope this helps and good luck with your problem solving!