Solve the problem.
-What is the minimum force required to prevent a ball weighing $26.6 \mathrm { lb }$ from rolling down a ramp inclined $12.4 ^ { \circ }$ with the horizontal?
A) $26 \mathrm { lb }$
B) $13 \mathrm { lb }$
C) $5.7 \mathrm { lb }$
D) $2.9 \mathrm { lb }$

Question

Quizplus · Accepted Answer

The minimum force required to prevent the ball from rolling down the ramp can be found by calculating the component of the ball's weight parallel to the ramp's surface. This force can be calculated using the formula $F = mg\sin(\theta)$, where $m$ is the mass of the ball, $g$ is the acceleration due to gravity (approximately $32.2 \mathrm{ft/s^2}$ for objects near the Earth's surface), and $\theta$ is the angle of the incline.First, convert the weight of the ball from pounds to mass in slugs using the relation $1 \mathrm{lb} = 1 \mathrm{slug} \cdot 32.2 \mathrm{ft/s^2}$:$$26.6 \mathrm{lb} = m \cdot 32.2 \mathrm{ft/s^2}$$$$m = \frac{26.6}{32.2} \mathrm{slugs}$$Then, calculate the force:$$F = mg\sin(\theta) = \frac{26.6}{32.2} \cdot 32.2 \cdot \sin(12.4^\circ)$$$$F \approx 5.7 \mathrm{lb}$$Therefore, the minimum force required to prevent the ball from rolling down the ramp is approximately $5.7 \mathrm{lb}$.

Solve the Problem 26.6lb26.6 \mathrm { lb }26.6lb From Rolling Down a Ramp Inclined

Solve the Problem $26.6 \mathrm { lb }$ From Rolling Down a Ramp Inclined