Question

If a 200-pound barrel must be lifted 4 feet to the bed of a box truck, an inclined plane will reduce the amount of effort required to move the barrel by half if the incline plane is

a.)2 ft long
b.)6 ft long
c.)8 ft long
d.)9 ft long

Answer 1

To reduce the effort required to lift a 200-pound barrel by half using an inclined plane, the plane needs to be twice as long as the lift height. Hence, the inclined plane must be 8 feet long to reduce the required effort by half for lifting the barrel 4 feet.

Step-by-step explanation:

The question addresses the concept of an inclined plane and how it can be used to reduce the effort required to lift a weight. An inclined plane allows you to exert a smaller force over a longer distance to achieve the same work as lifting the object directly up. The work done is the product of the force applied and the distance over which it is applied. If using an inclined plane cuts the effort required in half, the distance over which the force is applied must be twice the height the barrel is being lifted.

In this case, the barrel needs to be lifted 4 feet, so an inclined plane that accomplishes the same work with half the effort must be 8 feet long. Therefore, the correct option is (c) 8 ft long. This is because work is defined as force times distance. By making the distance over the inclined plane twice as long as the direct lift height, you effectively halve the force necessary to do the same amount of work, assuming no friction.