A 400 -pound trailer is sitting on an exit ramp inclined at $31 ^ { \circ }$ on Highway 35 . How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.
A) $206.02$ pounds
B) $342.87$ pounds
C) $274.44$ pounds
D) $308.65$ pounds
E) $325.76$ pounds

Question

Quizplus · Accepted Answer

The force required to keep the trailer from rolling back down the ramp can be found using the formula for the component of the gravitational force acting along the ramp, which is $F = mg \sin(\theta)$, where $m$ is the mass of the trailer, $g$ is the acceleration due to gravity (approximately $32 \, \text{ft/s}^2$ on Earth), and $\theta$ is the angle of the incline. First, convert the weight of the trailer from pounds to mass in slugs (mass = weight/g), which gives $m = 400 \, \text{lbs} / 32 \, \text{ft/s}^2 = 12.5 \, \text{slugs}$. Then, calculate the force: $F = 12.5 \, \text{slugs} \times 32 \, \text{ft/s}^2 \times \sin(31^\circ) \approx 206.02 \, \text{pounds}$.

A 400 -Pound Trailer Is Sitting on an Exit Ramp 31∘31 ^ { \circ }31∘

A 400 -Pound Trailer Is Sitting on an Exit Ramp $31 ^ { \circ }$