A 2.0-kg block slides down a plane (inclined at 40° with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work?
A) +98 W
B) +63 W
C) zero
D) +75 W
E) −75 W

Question

Quizplus · Accepted Answer

The gravitational force doing work on the block can be calculated using the formula for power: $P = F \cdot v \cdot \cos(\theta)$, where $F$ is the force of gravity ($mg$), $v$ is the velocity, and $\theta$ is the angle of the incline. Since the block moves at a constant speed down the incline, the component of gravitational force doing work is $mg \sin(\theta)$. Thus, $P = mg \sin(\theta) \cdot v$. Given $m = 2.0 \, \text{kg}$, $g = 9.8 \, \text{m/s}^2$, $\theta = 40^\circ$, and $v = 5.0 \, \text{m/s}$, we find $P = 2.0 \cdot 9.8 \cdot \sin(40^\circ) \cdot 5.0 \approx 63 \, \text{W}$.

A 20-Kg Block Slides Down a Plane (Inclined at 40° with with the Horizontal)