Tension on a string between two masses.

1. Oct 4, 2012

thatguythere

1. The problem statement, all variables and given/known data
The figure below shows an object of mass m1 = 1.1 kg on an inclined surface. The angle of the inclined surface is θ = 31° with the horizontal. The object m1 is connected to a second object of mass m2 = 6.10 kg on a horizontal surface below an overhang that is formed by the inclined surface. Further, an external force of magnitude Fext = 14 N is exerted on the object with mass m1. We observe both objects accelerate. Assuming the surfaces and the pulley are frictionless, and the pulley and the connecting string are massless, what is the tension in the string connecting the two objects?

2. Relevant equations
F=ma

3. The attempt at a solution
I would simply like someone to verify my free body diagrams, so that I know whether I am working with the proper forces or not. Also, does the normal force and the perpendicular force cancel out?

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Last edited: Oct 4, 2012
2. Oct 4, 2012

PhanthomJay

Your 2nd FBD is good. But not so on the first. You are missing the tension force, and what you are calling f_perp and f_parallel are the components of mg, which replace mg in your diagram.

3. Oct 4, 2012

thatguythere

So in this case, is F_parallel even applicable since the mass seems to be in equilibrium prior to the exerted force causing it to accelerate?

4. Oct 4, 2012

PhanthomJay

no, that is not correct, without the applied force, the block would slide down the plane and the string would go slack . But anyway, it is given that an external force is applied and the system is accelerating, so you must identify forces for that loading case.

5. Oct 4, 2012

thatguythere

So the forces acting upon m1 are f_ext = 14cos31 = 12.00
f_parallel = mgsin31 = 5.55
T = ?
And upon m2 T = ?
On m1 the normal force and perpendicular cancel out, as well the F_g and F_n on m2?

6. Oct 4, 2012

SarahBB

How did you figure this out? I have a similar problem and im having issues figuring it out any help would be appreciated.

7. Oct 4, 2012

thatguythere

I just cannot seem to find the proper forces on m1. I would think that I would end up with something like. For mass 1 Fx-T = 1.1a and for mass 2 T = 6.1a
Fx - (6.1a) = 1.1a
Fx = 7.2a
a = Fx/7.2

T = 6.1a

8. Oct 4, 2012

PhanthomJay

You should choose the x axis parallel to the incline and the y axis perpendicular to the incline. In this manner, f_ext is 14 up the plane.
yes, down the plane.
yes, T is still unknown at this point, and the sum of all these forces is equal to what, per Newton 2?
T = what , per Newton 2?
yes, why?

9. Oct 4, 2012

thatguythere

Victory!

10. Oct 4, 2012

PhanthomJay

Sweet!

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