A uniform wooden plank is 16 feet long and weighs 120 pounds. It rests horizontally on two… — Armed Services Vocational Aptitude Battery (ASVAB)

A uniform wooden plank is $16$ feet long and weighs $120$ pounds. It rests horizontally on two supports. The left support is positioned at the extreme left end of the plank, and the right support is positioned $12$ feet away from the left end. If a $60$ -pound weight is placed on the extreme right end of the plank, how much upward force must the right support provide to maintain equilibrium?

A
$90$ pounds
B
$120$ pounds
$160$ poundsCevap
D
$180$ pounds

Cevap

160

pounds

The system is in equilibrium, meaning the torques must balance. Taking the left support as the pivot, the downward forces create a clockwise torque: the plank's weight (

120

lbs) acts at its center (

8

ft away) creating

960 \text{ lb-ft}

of torque, and the box (

60

lbs) acts at the end (

16

ft away) creating another

960 \text{ lb-ft}

. The total downward torque is

1920 \text{ lb-ft}

. The right support is located

12

feet away and must push upward to create an equal counter-clockwise torque. Therefore,

12 \times \text{Force} = 1920

, which means the required force is

160

pounds.

Adım Adım Çözüm

Set the left support as the pivot point (fulcrum).

All distances for torque calculations will be measured from the

0

-foot mark.

Choosing one of the unknown supports as the pivot eliminates its force from the torque equation, allowing us to solve directly for the other support.

Calculate the total clockwise torque acting on the plank.

Plank torque =

120 \text{ lbs} \times 8 \text{ ft} = 960 \text{ lb-ft}

. Weight torque =

60 \text{ lbs} \times 16 \text{ ft} = 960 \text{ lb-ft}

. Total clockwise torque =

1920 \text{ lb-ft}

The uniform plank's weight acts at its center of gravity (

8

feet from the left), and the external weight acts at the extreme right end (

16

feet from the left). Both create a downward, clockwise rotation around the left support.

Equate the clockwise torque to the counter-clockwise torque to solve for the right support's force.

F_{right} \times 12 \text{ ft} = 1920 \text{ lb-ft}

. Dividing by

12

gives

F_{right} = 160 \text{ lbs}

For the system to remain in static equilibrium, the upward (counter-clockwise) torque provided by the right support must exactly balance the downward (clockwise) torques.

Anahtar Kavram

Static Equilibrium and Principle of Moments

Soru

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