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Upward Acceleration

Mass m1 (34.50 kg) is on a horizontal surface, connected to mass m2 (5.90 kg) by a light string. The pulley has negligible mass and no friction. A force of 220.9 N acts on m1 at an angle of 34.50 degrees. The coefficient of kinetic friction between m1 and surface is .233. Determine the upward acceleration of m2.

I have attached an drawing.


Solution Preview

To do this, you must consider each block separately, and the forces acting upon each.

So, first let's consider the forces acting on block 1. Further, let's consider the x and y components separately.

BLOCK 1, x direction, with positive direction to the right:

Forces on block 1 in the x direction are:

- the x-component of the applied force F, which, from trigonometry, is F*cos(theta).
- the force of friction, which is to the left, so we'll call that -f_k
- the tension in the string, which is also pulling to the left, so we'll call that -T

These are the three ...

Solution Summary

The solution looks at this problem of upwards acceleration via a pulley by breaking it down into the two blocks and the force in the x and y direction on each in a helpful manner that makes it easy to follow the calculations to the conclusion.