Question

question 5 - multiple choice
an industrial water valve wheel at the hoover dam is designed to operate with 50 lb of effort force. the valve will undergo 350 lb of resistance force applied to a 3.0 in. diameter axle. what is the actual mechanical advantage (ama)? and what is the water valve wheel radius?
ama = 14 and de = 5.25 in.
ama = 7 and de = 10.50 in.
ama = 9 and de = 7.75 in.
ama = 10.5 and de = 7 in.

Explanation:

Step1: Calculate the Actual Mechanical Advantage (AMA)

The formula for AMA is \(AMA=\frac{F_{r}}{F_{e}}\), where \(F_{r}\) is the resistance force and \(F_{e}\) is the effort force.
Given \(F_{r} = 350\space lb\) and \(F_{e}=50\space lb\), then \(AMA=\frac{350}{50}=7\).

Step2: Calculate the radius of the water - valve wheel

For a wheel - and - axle system, \(AMA=\frac{r_{w}}{r_{a}}\), where \(r_{w}\) is the radius of the wheel and \(r_{a}\) is the radius of the axle.
The diameter of the axle \(d_{a}=3.0\space in\), so the radius of the axle \(r_{a}=\frac{d_{a}}{2}=\frac{3.0}{2}=1.5\space in\).
Since \(AMA = 7\) and \(AMA=\frac{r_{w}}{r_{a}}\), then \(r_{w}=AMA\times r_{a}\).
Substituting the values, \(r_{w}=7\times1.5 = 10.5\space in\).

Answer:

AMA = 7 and DE = 10.50 in.