physics hw....need help?

Question

Two packing crates of masses m1 = 10.0 kg and m2 = 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.26. The 5.00 kg crate lies on a smooth incline of angle 41.0°. Find the acceleration of the 5.00 kg crate.

______ m/s2 (up the incline)

Find the tension in the string.
______ N

need a detailed way to solve the problem, not just the answer...thank you sooo much

Answer 1

Consider the forces acting on m2:

1) Tension T (pulling up along the incline);
2) component of weight m2g(sinθ) (pulling down the incline)
3) Normal force N pushing perpendicularly
4) component of weight m2g(cosθ) (opposite of N)

We know that (3) and (4) must be equal in magnitude, so they cancel out. Therefore the NET force on m2 is:

F2_net = T − m2g(sinθ)

Now for forces on m1:

1) (m1)g [down]
2) T [up]

So NET force on m1 is:

F1_net = (m1)g - T

Next steps:
* Use F=ma (actually, a=F/m) to write an equation for the acceleration a1 of mass 1; and another equation for the acceleratation a2 of mass 2.
* Notice that the a1 _equals_ a2, since the two masses are tied together.
* Set the equation for a1 equal to the equation for a2.
* You should now have an equation that you can solve to get "T"
* You can then go back and plug "T" into the equation for a2, and therefore find a2