Question

what is the minimum force required to prevent a ball weighing 21.3 lb from rolling down a ramp inclined 26.5° with the horizontal?

a. 9.5 lb
b. 9.6 lb
c. 4.8 lb
d. 19.1 lb

Explanation:

Step1: Decompose the weight force

The weight of the ball \(W = 21.3\) lb. The force component along the ramp is \(F=W\sin\theta\), where \(\theta = 26.5^{\circ}\)

Step2: Calculate the force

Substitute \(W = 21.3\) lb and \(\theta=26.5^{\circ}\) into the formula \(F = W\sin\theta\).
We know that \(\sin(26.5^{\circ})\approx0.447\)
\(F=21.3\times\sin(26.5^{\circ})\)
\(F = 21.3\times0.447\)
\(F\approx9.5\) lb

Answer:

A. 9.5 lb