Question

A 200 pound box has two ropes attached to it. The rope on the left is being pulled with a force of 100 pounds at an angle with the horizontal which causes the box to be pulled to the left with a force of 37 pounds. The rope on the right is being pulled up at an angle of elevation of 63^o with a force which causes the box to be pulled to the right with a force of 53 pounds (hence the box is moving horizontally to the right). In which vertical direction is the box moving, up or down?

Answer 1

The direction of force (up or down) on the left rope is not specified, so let us consider it being pulled upwards, at some angle to the horizontal.

We calculate all the components of all the forces experienced on the box.

As you can see from the diagram, for the Left Rope F1 is the component facing upwards, and for the Right Rope F2 is the component of the force that faces up.

Thus, intuitively, and mathematically proved, the box will move vertically upwards.