A worker uses an industrial paper cutter to slice through thick cardboard. The cutter oper… — Armed Services Vocational Aptitude Battery (ASVAB)

A worker uses an industrial paper cutter to slice through thick cardboard. The cutter operates as a second-class lever with the pivot (fulcrum) at one end of the blade. The cardboard is positioned $8\text{ inches}$ from the pivot and creates a cutting resistance of $120\text{ lbs}$ . If the worker pushes down on the handle at a distance of $40\text{ inches}$ from the pivot, what is the minimum downward effort force required to cut the cardboard?

$24\text{ lbs}$ Answer
B
$30\text{ lbs}$
C
$20\text{ lbs}$
D
$600\text{ lbs}$

Answer

The minimum downward effort force required is

24\text{ lbs}

In a second-class lever, the effort torque must equal the load torque. By multiplying the cutting resistance (

120\text{ lbs}

) by its distance from the fulcrum (

8\text{ inches}

), we find a load torque of

960\text{ inch-lbs}

. Dividing this torque by the total effort distance from the fulcrum (

40\text{ inches}

) gives a minimum effort force of

24\text{ lbs}

Step-by-Step Solution

Identify the lever class and the given variables.

This is a second-class lever. Load (

F_L

) =

120\text{ lbs}

, Load arm (

d_L

) =

8\text{ inches}

, Effort arm (

d_E

) =

40\text{ inches}

Correctly identifying the lever class ensures that the distances are properly measured from the fulcrum.

Apply the torque balance (principle of moments) equation.

F_E \times d_E = F_L \times d_L

For the lever to balance and cut the cardboard, the input effort torque must equal the output load torque.

Substitute the known values and solve for the effort force (

F_E

F_E \times 40 = 120 \times 8 \rightarrow 40 F_E = 960 \rightarrow F_E = 24\text{ lbs}

Calculating this equation yields the minimum effort force required.

Key Concept

Torque Balance in Second-Class Levers

Estimated Time:1m 0s

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