An 80-N crate slides with constant speed a distance of 5.0 m downward along a rough slope that makes an angle of 30° with the horizontal.The work done by the force of gravity is:

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Quizplus · Accepted Answer

The work done by the force of gravity can be calculated using the formula $W = Fd\cos(\theta)$, where $F$ is the force of gravity (weight of the crate), $d$ is the distance moved, and $\theta$ is the angle between the force and the direction of motion. Since the crate is moving downward along the slope and gravity acts vertically downward, the angle to consider here is the slope's angle with the horizontal, which is 30 degrees. However, the effective component of gravity that does the work is along the slope, so we use the component of the gravitational force parallel to the slope. This component is $F\cos(30^\circ)$, but since the motion is directly down the slope, we actually use the full force of gravity for calculating work done along the slope, which simplifies to $W = Fd$, because the angle between the direction of gravity's force (downward) and the direction of motion (also downward along the slope) effectively becomes 0 degrees in terms of the component of force doing work, meaning $\cos(0^\circ) = 1$. Therefore, the calculation should directly use the gravitational force and the distance moved without needing to adjust for the angle in this context. The gravitational force is the weight of the crate, which is given as 80 N, and the distance is 5.0 m. Thus, the work done by gravity is $W = 80\, \text{N} \times 5.0\, \text{m} = 400\, \text{J}$. The work is positive because the force of gravity and the direction of motion are in the same direction, indicating that gravity is doing work on the object to move it downward.

An 80-N Crate Slides with Constant Speed a Distance of 5.0