A camper operates a manual water pump. The pump handle acts as a first-class lever pivotin… — Armed Services Vocational Aptitude Battery (ASVAB)

A camper operates a manual water pump. The pump handle acts as a first-class lever pivoting on a central pin. The distance from the handle's grip to the pivot pin is $32\text{ inches}$ , and the distance from the pivot pin to the pump rod connection is $4\text{ inches}$ . If the camper pushes down on the grip with $12\text{ pounds}$ of force, what is the upward force exerted on the pump rod?

$96\text{ pounds}$ Answer
B
$108\text{ pounds}$
C
$12\text{ pounds}$
D
$1.5\text{ pounds}$

Answer

The correct force exerted on the pump rod is

96\text{ pounds}

For a first-class lever, the mechanical advantage is calculated by dividing the effort arm by the load arm. Here,

32\text{ inches} / 4\text{ inches} = 8

. By multiplying the applied effort force of

12\text{ pounds}

by the mechanical advantage of 8, we find the resulting upward force is

96\text{ pounds}

Step-by-Step Solution

Calculate the mechanical advantage (MA) of the first-class lever.

\text{MA} = \frac{32\text{ inches}}{4\text{ inches}} = 8

The mechanical advantage is the ratio of the effort arm length to the load arm length.

Calculate the output force at the pump rod.

12\text{ pounds} \times 8 = 96\text{ pounds}

The output force (load) is the effort force multiplied by the mechanical advantage.

Key Concept

Mechanical Advantage in First-Class Levers

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