A 400 -pound trailer is sitting on an exit ramp inclined at 31° 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 calculated 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 $9.8 \, \text{m/s}^2$ or $32 \, \text{ft/s}^2$ when working in imperial units), and $\theta$ is the angle of the incline. Since the weight of the trailer is given in pounds, a force unit, we can use it directly without needing to convert mass to weight. Thus, $F = 400 \times \sin(31^\circ)$. Calculating this gives a force of approximately $206.02$ pounds, which is the force required to keep the trailer from rolling back down the ramp.

A 400 -Pound Trailer Is Sitting on an Exit Ramp