A carpenter uses a claw hammer to extract a stubborn nail from a wooden board. The hammer … — Armed Services Vocational Aptitude Battery (ASVAB)

A carpenter uses a claw hammer to extract a stubborn nail from a wooden board. The hammer acts as a first-class lever. The distance from the nail to the pivot point (fulcrum) on the hammer's head is $2\text{ inches}$ . The carpenter applies an effort force perpendicular to the handle at a distance of $16\text{ inches}$ from the pivot point. If a resistance force of $280\text{ pounds}$ is required to extract the nail, how many pounds of effort force must the carpenter apply?

Answer: 35 pounds

Answer

35 pounds

In a first-class lever, the mechanical advantage is determined by the ratio of the effort arm to the resistance arm. The hammer provides a mechanical advantage of

16 / 2 = 8

. Therefore, the effort force required is the load divided by 8, which is

280 / 8 = 35\text{ pounds}

. Using the fundamental torque balance equation (

F_1 \times d_1 = F_2 \times d_2

280 \times 2 = 560

, and

560 / 16 = 35

Step-by-Step Solution

State the torque balance equation for a lever.

F_E \times d_E = F_R \times d_R

For the lever to overcome the resistance, the torque applied by the effort must equal the torque exerted by the load.

Substitute the given values into the equation.

F_E \times 16 = 280 \times 2

The effort distance (

d_E

) is

16\text{ inches}

, the resistance force (

F_R

) is

280\text{ pounds}

, and the resistance distance (

d_R

) is

2\text{ inches}

Calculate the total torque of the resistance.

280 \times 2 = 560\text{ inch-pounds}

This represents the total rotational force required to loosen the nail.

Solve for the effort force (

F_E

F_E = 560 / 16 = 35\text{ pounds}

Dividing the total required torque by the longer effort arm gives the smaller effort force needed.

Key Concept

Torque Balance and Mechanical Advantage

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