A box is dragged along the floor. The rope that is acting on the box makes an angle A to the floor. How much force is being used to drag the box ?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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In the rope occurs a tension that is dragging the box and tends to lift the box. If the angle made by the rope to the floor is smaller, the force that is dragging the box will be greater. If the rope is parallel to the floor, the lifting component won't exist, at all.

The component of the tension that dragging the box is the horizontal component.

F horiz. = F*cos a

If the tension in the rope is 300 N and the angle made by the rope to the floor is 30 degrees, the horizontal component is:

F horiz. = 300 N*cos 30

F horiz. = 300*sqrt3/2

F horiz. = 150sqrt3 N

The vertical component of the tension, the lifting force is:

F vert = 300N*sin30

F vert = 150N

Now, we must take in consideration the friction that brakes the box when it is dragged on the floor.

The friction is opposite to the horizontal component of the tension from the rope, when the object is moving at constant speed.

Friction = - F horiz.

Friction = -150sqrt3 N

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