A landscaping worker uses a shovel to lift 30\text{ lbs} of soil. The worker's rear hand p… — Armed Services Vocational Aptitude Battery (ASVAB)

A landscaping worker uses a shovel to lift $30\text{ lbs}$ of soil. The worker's rear hand pushes down on the grip to act as the fulcrum, while the front hand lifts the shaft at a point $2\text{ feet}$ away from the rear hand. The soil is centered on the shovel's blade, which is $5\text{ feet}$ away from the rear hand. Ignoring the weight of the shovel itself, what is the minimum upward effort force the front hand must apply to lift the soil?

$75\text{ lbs}$ Answer
B
$50\text{ lbs}$
C
$45\text{ lbs}$
D
$12\text{ lbs}$

Answer

The minimum upward effort force required is

75\text{ lbs}

A shovel functions as a third-class lever, where the effort (front hand) is between the fulcrum (rear hand) and the load (soil). To find the required effort force, set the effort torque equal to the load torque:

\text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm}

. Substituting the given values yields

E \times 2 = 30 \times 5

. This simplifies to

2E = 150

, giving an effort force of

75\text{ lbs}

. Third-class levers always require an effort force greater than the load because they multiply distance at the expense of force.

Step-by-Step Solution

Identify the lever class and the pivot point (fulcrum).

The shovel acts as a third-class lever where the rear hand is the fulcrum.

Establishing the fulcrum is necessary to measure the lengths of the effort arm and load arm accurately.

Determine the lengths of the effort arm and the load arm relative to the fulcrum.

Effort Arm =

2\text{ feet}

(rear hand to front hand). Load Arm =

5\text{ feet}

(rear hand to blade).

Torque is calculated by multiplying force by its perpendicular distance from the fulcrum.

Apply the principle of moments (torque balance) to solve for the unknown effort force.

\text{Effort} \times 2 = 30 \times 5 \Rightarrow 2E = 150 \Rightarrow E = 75\text{ lbs}

For the lever to be balanced and lift the load, the effort torque must equal the load torque.

Key Concept

Torque balance in third-class levers

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