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 component of the weight force 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 \(F = W\sin\theta\).
\(\sin(26.5^{\circ})\approx0.447\)
\(F=21.3\times0.447\)
\(F = 21.3\times\frac{447}{1000}=\frac{21.3\times447}{1000}\)
\(21.3\times447=(20 + 1.3)\times447=20\times447+1.3\times447=8940+581.1 = 9521.1\)
\(F=\frac{9521.1}{1000}=9.5211\approx9.5\) lb

Answer:

A. \(9.5\) lb