A sheet metal fabricator uses a custom compound lever tool to punch holes in aluminum pane… — Armed Services Vocational Aptitude Battery (ASVAB)

A sheet metal fabricator uses a custom compound lever tool to punch holes in aluminum panels. The tool consists of two connected levers:

1. The Handle (Lever A): A second-class lever with its fulcrum at the very top. The handle is $25\text{ inches}$ long overall. A vertical connecting rod is attached to this handle $5\text{ inches}$ away from the fulcrum.
2. The Punch Arm (Lever B): A first-class lever positioned horizontally. The connecting rod pulls down on one end, which is $8\text{ inches}$ away from its fulcrum. The punching die is located on the opposite side of the fulcrum, $2\text{ inches}$ away.

If the fabricator applies a perpendicular force of $24\text{ lbs}$ to the extreme end of the handle, what is the total downward force, in pounds, exerted by the punch die onto the aluminum panel?

Cevap: 480 lbs

Cevap

The correct answer is

480\text{ lbs}

In a compound lever system, the mechanical advantage of each lever multiplies sequentially to produce the final force. The handle (Lever A) provides a mechanical advantage of

25/5 = 5

. Therefore, the

24\text{ lbs}

input is multiplied by

5

, becoming

120\text{ lbs}

of force on the connecting rod. The punch arm (Lever B) provides a mechanical advantage of

8/2 = 4

. The

120\text{ lbs}

input to Lever B is then multiplied by

4

, resulting in a total output force of

480\text{ lbs}

at the punching die.

Adım Adım Çözüm

Calculate the input torque generated by the fabricator on Lever A.

24\text{ lbs} \times 25\text{ inches} = 600\text{ in-lbs}

Torque is determined by multiplying the applied force by the perpendicular distance from the fulcrum.

Determine the force exerted on the connecting rod by Lever A.

600\text{ in-lbs} / 5\text{ inches} = 120\text{ lbs}

In equilibrium, the input torque equals the output torque. The rod is attached

5\text{ inches}

from the fulcrum.

Calculate the input torque on Lever B caused by the connecting rod.

120\text{ lbs} \times 8\text{ inches} = 960\text{ in-lbs}

The connecting rod applies

120\text{ lbs}

of force at a distance of

8\text{ inches}

from Lever B's fulcrum.

Calculate the final output force at the punching die.

960\text{ in-lbs} / 2\text{ inches} = 480\text{ lbs}

The punching die is

2\text{ inches}

from the fulcrum, balancing the

960\text{ in-lbs}

of torque on the opposite side.

Anahtar Kavram

Compound Lever Systems and Torque Balance

Tahmini Süre:1m 30s

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