A carpenter uses a claw hammer to pull a stubborn nail out of a wooden plank. The hammer h… — Armed Services Vocational Aptitude Battery (ASVAB)

A carpenter uses a claw hammer to pull a stubborn nail out of a wooden plank. The hammer head rests on the plank, creating a pivot point (fulcrum) that is exactly $2\text{ inches}$ away from the nail. The carpenter applies a perpendicular pulling force of $40\text{ lbs}$ on the hammer's handle, at a distance of $12\text{ inches}$ away from the pivot point. Assuming the hammer acts as a simple first-class lever, how much upward force is exerted on the nail?

A
$80\text{ lbs}$
B
$200\text{ lbs}$
$240\text{ lbs}$ Cevap
D
$480\text{ lbs}$

Cevap

The upward force exerted on the nail is

240\text{ lbs}

The claw hammer acts as a first-class lever where torque is balanced around the fulcrum. The formula for a balanced lever is

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

. Plugging in the given values yields

40 \times 12 = \text{Load} \times 2

, which simplifies to

480 = 2 \times \text{Load}

. Dividing both sides by 2 gives a load force of

240\text{ lbs}

Adım Adım Çözüm

Identify the lever arms for the hammer setup.

The effort arm (distance from the pulling hand to the fulcrum) is

12\text{ inches}

. The load arm (distance from the nail to the fulcrum) is

2\text{ inches}

Correctly identifying the distances from the fulcrum is necessary for calculating mechanical advantage and balancing torque.

Calculate the mechanical advantage (MA) of the lever.

\text{MA} = \text{Effort Arm} / \text{Load Arm} = 12 / 2 = 6

The mechanical advantage indicates how many times the lever multiplies the input force.

Calculate the total upward force exerted on the nail.

\text{Force on nail} = \text{Effort force} \times \text{MA} = 40 \times 6 = 240\text{ lbs}

The output load force is the product of the input effort and the mechanical advantage.

Anahtar Kavram

Mechanical Advantage and Torque Balance in First-Class Levers

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Cevap

Adım Adım Çözüm

Anahtar Kavram

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