A maintenance crew uses a horizontal boom mounted on a utility truck to lift a 600 \text{ … — Armed Services Vocational Aptitude Battery (ASVAB)

A maintenance crew uses a horizontal boom mounted on a utility truck to lift a $600 \text{ N}$ generator. The boom pivots at a hinge on the truck bed. A vertical hydraulic cylinder supports the boom, attaching exactly $1.0 \text{ m}$ from the hinge. The generator hangs from the far end of the boom, $4.0 \text{ m}$ from the hinge. Assuming the weight of the boom itself is negligible, how much upward force must the hydraulic cylinder apply to hold the generator stationary, and what class of lever does this system represent?

$2400 \text{ N}$ ; third-class leverCevap
B
$150 \text{ N}$ ; second-class lever
C
$1800 \text{ N}$ ; third-class lever
D
$2400 \text{ N}$ ; first-class lever

Cevap

2400 \text{ N}

; third-class lever

The system represents a third-class lever because the effort force (the hydraulic cylinder) is applied between the fulcrum (the hinge) and the load (the generator). To maintain static equilibrium, the counterclockwise torque provided by the cylinder must perfectly equal the clockwise torque from the generator. The generator creates a torque of

600 \text{ N} \times 4.0 \text{ m} = 2400 \text{ N}\cdot\text{m}

. Therefore, the cylinder must apply

2400 \text{ N}

of force at a distance of

1.0 \text{ m}

to balance the system (

2400 \text{ N} \times 1.0 \text{ m} = 2400 \text{ N}\cdot\text{m}

Adım Adım Çözüm

Identify the lever class based on the arrangement of the fulcrum, effort, and load.

The effort force (hydraulic cylinder) is located between the fulcrum (hinge) and the load (generator). This arrangement defines a third-class lever.

Determining the lever arrangement is essential to properly visualize the system and answers the classification part of the question.

Set up the torque balance equation (principle of moments) around the fulcrum.

To remain stationary, upward torque must equal downward torque:

F_{\text{effort}} \times d_{\text{effort}} = F_{\text{load}} \times d_{\text{load}}

A lever in static equilibrium must have balanced rotational forces acting around its pivot point.

Substitute the known distances and forces into the equation to solve for the effort force.

F_{\text{effort}} \times 1.0 \text{ m} = 600 \text{ N} \times 4.0 \text{ m}

, which simplifies to

F_{\text{effort}} = 2400 \text{ N}

Applying the specific measurements yields the precise upward force required by the cylinder.

Anahtar Kavram

Third-Class Levers and Torque Balance

Tahmini Süre:1m 15s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru