Newton's Law of Motion Example # 4

Suppose now that a box is resting on an inclined plane that is attached via a massless cord and a frictionless pulley to a second box that is resting vertically. Assuming the surface is frictionless and that our system of objects will move to the right, we need to calculate the tension in the cord as well as the acceleration of the objects. In order to find our two unknowns, we need to set up two different equations with those two unknowns. Since we have two different objects, we can easily set up the equations, keeping in mind that the force of gravity acting on the box found on the inclined plane is less than usual because the box is at an angle. By rearranging one of the equations and representing one unknown in terms of the other, we can plug the result into the second equation and solve.

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