A farmer uses a long, rigid pole to move a 180\text{-pound} boulder. The pole is positione… — Armed Services Vocational Aptitude Battery (ASVAB)

A farmer uses a long, rigid pole to move a $180\text{-pound}$ boulder. The pole is positioned over a smaller rock that serves as a fulcrum. The fulcrum is placed exactly $2\text{ feet}$ away from the boulder. The farmer pushes down on the opposite end of the pole, which is $6\text{ feet}$ away from the fulcrum. What is the minimum downward force the farmer must apply to lift the boulder?

A
$30\text{ pounds}$
B
$45\text{ pounds}$
$60\text{ pounds}$ Cevap
D
$540\text{ pounds}$

Cevap

The farmer must apply

60\text{ pounds}

of downward force.

The system acts as a first-class lever. To lift the boulder, the torque (force times distance) on the farmer's side of the fulcrum must match the torque on the boulder's side. The boulder creates a torque of

360\text{ ft-lbs}

(

180\text{ lbs} \times 2\text{ ft}

). To balance this over a

6\text{-foot}

distance, the required force is

360 / 6

, which equals

60\text{ pounds}

Adım Adım Çözüm

Set up the equation for a lever in equilibrium based on the principle of moments.

\text{Effort Force} \times \text{Effort Distance} = \text{Load} \times \text{Load Distance}

For a lever to lift a load, the torque generated by the effort must equal the torque exerted by the load.

Substitute the provided values into the equilibrium equation.

\text{Effort Force} \times 6\text{ ft} = 180\text{ lbs} \times 2\text{ ft}

The load is

180\text{ lbs}

at a distance of

2\text{ ft}

, and the effort is applied at a distance of

6\text{ ft}

Solve the equation for the Effort Force.

\text{Effort Force} = \frac{360\text{ ft-lbs}}{6\text{ ft}} = 60\text{ lbs}

Dividing the total torque of the load by the effort distance gives the required downward force.

Anahtar Kavram

Torque and Mechanical Advantage in 1st Class Levers

Tahmini Süre:45s

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