Question

A) A person applies 98 Newtons of force to a 20 kilogram box. They apply the force to the box over a 4-meter ramp, raising the box 2 meters from the ground. How much work is done? (1 point)

40 Joules

80 Joules

392 Joules

194 Joules

Answer 1

To calculate the work done, we can use the formula for work:

\[
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
\]

In this scenario:

- The force applied is 98 Newtons.
- The distance moved along the ramp is 4 meters.
- The angle (\(\theta\)) between the force applied (assuming it's along the ramp) and the direction of motion needs to be clarified. However, since the force is applied along the ramp, we can assume \(\theta = 0^\circ\), leading to \(\cos(0^\circ) = 1\).

Since the full inclination of the work is with respect to the distance traveled, and we are interested in vertical work, we can also calculate work in terms of vertical lifting:

The vertical lift (height) is 2 meters.

To find the gravitational force acting on the box:

\[
\text{Weight} = \text{mass} \times g = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N}
\]

However, since the applied force is less than the weight, we would consider the incline work done against gravity.

The work is therefore:

\[
\text{Work done} = \text{Force} \times \text{Distance Along the Ramp}
\]

So now substituting into the work formula:

\[
\text{Work} = 98 \, \text{N} \times 4 \, \text{m} = 392 \, \text{J}
\]

Thus, the total work done on the box is **392 Joules**.

**Final answer:** 392 Joules