A rescue crew uses a uniform 14-foot steel beam as a first-class lever to lift a 900\text{… — Armed Services Vocational Aptitude Battery (ASVAB)

A rescue crew uses a uniform $14$ -foot steel beam as a first-class lever to lift a $900\text{ lb}$ concrete slab. The beam itself weighs $240\text{ lbs}$ . They place a pivot block exactly $2\text{ feet}$ from the end where the concrete slab rests. How much downward effort force must the crew apply at the opposite end of the beam to perfectly balance the slab?

$50\text{ lbs}$ Cevap
B
$150\text{ lbs}$
C
$190\text{ lbs}$
D
$250\text{ lbs}$

Cevap

The correct answer is

50\text{ lbs}

, because the uniform beam's own weight assists the effort force in balancing the heavy slab.

The correct answer properly applies the principle of rotational equilibrium. The slab creates

1800\text{ lb-ft}

of counter-clockwise torque. The beam's center of gravity is

5\text{ feet}

to the right of the fulcrum, creating

1200\text{ lb-ft}

of clockwise torque. This means the effort force only needs to provide the remaining

600\text{ lb-ft}

of torque. At a distance of

12\text{ feet}

from the fulcrum, a

50\text{ lb}

force provides exactly

600\text{ lb-ft}

(

50 \times 12

Adım Adım Çözüm

Determine the moment arms (distances from the fulcrum) for all forces involved.

Load arm =

2\text{ ft}

. Effort arm =

14 - 2 = 12\text{ ft}

. The beam's center of gravity (CG) is at

7\text{ ft}

, making its distance to the fulcrum

7 - 2 = 5\text{ ft}

Torque is calculated as force multiplied by the perpendicular distance to the pivot point.

Calculate the counter-clockwise torque exerted by the concrete slab.

Torque =

900\text{ lbs} \times 2\text{ ft} = 1800\text{ lb-ft}

This is the primary torque that must be overcome to balance the lever.

Calculate the clockwise torque exerted by the beam's own weight.

Torque =

240\text{ lbs} \times 5\text{ ft} = 1200\text{ lb-ft}

Because the beam's CG is to the right of the fulcrum, its weight assists the downward effort force.

Set up the torque equilibrium equation and solve for the required effort force (

F

1800 = 1200 + (F \times 12)

. Solving for

F

12F = 600

, which gives

F = 50\text{ lbs}

For the lever to be perfectly balanced, the total counter-clockwise torque must equal the total clockwise torque.

Anahtar Kavram

Torque equilibrium in levers accounting for uniform mass distribution.

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Cevap

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