A dump truck bed pivots on a rear hinge, which acts as the fulcrum. A hydraulic cylinder p… — Armed Services Vocational Aptitude Battery (ASVAB)

A dump truck bed pivots on a rear hinge, which acts as the fulcrum. A hydraulic cylinder provides the upward effort force and is attached to the bed $2\text{ ft}$ from the rear hinge. The center of gravity of the loaded bed is located $6\text{ ft}$ from the rear hinge. If the total weight of the loaded bed is $12,000\text{ lbs}$ , what is the minimum purely vertical force the hydraulic cylinder must apply to begin lifting the horizontally resting bed?

A
$4,000 \text{ lbs}$
B
$12,000 \text{ lbs}$
C
$24,000 \text{ lbs}$
$36,000 \text{ lbs}$ Cevap

Cevap

The minimum purely vertical force the hydraulic cylinder must apply is

36,000 \text{ lbs}

In this 3rd class lever, the effort arm (

2\text{ ft}

) is significantly shorter than the load arm (

6\text{ ft}

). To balance the torque created by the

12,000\text{ lbs}

load (

12,000 \times 6 = 72,000\text{ ft-lbs}

), the hydraulic cylinder must apply a proportionally larger force of

36,000\text{ lbs}

at its

2\text{ ft}

distance (

36,000 \times 2 = 72,000

Adım Adım Çözüm

Identify the lever class and the pivot point.

The rear hinge is the fulcrum. The hydraulic cylinder provides the effort between the fulcrum and the load, making this a 3rd class lever.

To correctly apply the principles of torque, the locations of the effort and load relative to the fulcrum must be established.

Calculate the torque exerted by the loaded bed.

12,000 \text{ lbs} \times 6 \text{ ft} = 72,000 \text{ ft-lbs}

Torque is equal to force multiplied by the distance from the fulcrum.

Set up the torque balance equation for the effort force (

F_e

F_e \times 2 \text{ ft} = 72,000 \text{ ft-lbs}

To begin lifting the bed, the effort torque must be equal to the load torque.

Solve the equation for the effort force.

F_e = 36,000 \text{ lbs}

Dividing both sides by

2 \text{ ft}

isolates the required force.

Anahtar Kavram

Mechanical advantage and torque balance in a 3rd class lever

Tahmini Süre:1m 0s

Soru

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Adım Adım Çözüm

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