What amount of force must be applied to roll a 120-pound barrel up a 9-foot inclined plane to a height of 3 feet, ignoring friction?

To determine the amount of force required to roll a 120-pound barrel up a 9-foot inclined plane to a height of 3 feet, one must consider the relationship between the height of the incline and the length of the plane. The force needed to move the object up the incline can be calculated using the concept of gravitational force acting on the barrel, specifically the component of gravity acting parallel to the incline.

First, we can find the slope of the incline by using the height and the length of the incline. The height (rise) is 3 feet, while the length of the incline is 9 feet. The angle of the incline can be determined by using the sine function, but we'll focus instead on the direct relationship to the weight of the barrel.

The force required to lift the barrel directly upwards (ignoring friction) can be articulated through the sine of the angle of inclination. The formula for the force component acting upward along the incline is:

[ F = W \times \left(\frac{\text{height}}{\text{length}}\right) ]

Where:

• ( W ) is the weight of the barrel, which is 120 pounds.

• The height is 3 feet and the length is 9 feet