Two workers, Worker X and Worker Y, are carrying a heavy motor block using a rigid, 12-foo… — Armed Services Vocational Aptitude Battery (ASVAB)

Two workers, Worker X and Worker Y, are carrying a heavy motor block using a rigid, $12$ -foot wooden beam. Each worker supports one end of the beam on their shoulder. The motor block weighs $300$ pounds. Assume the weight of the beam is negligible. If the center of the motor block is placed on the beam exactly $3$ feet away from Worker X, how much of the block's weight is Worker Y supporting?

$75$ poundsAnswer
B
$100$ pounds
C
$150$ pounds
D
$225$ pounds

Answer

Worker Y is supporting

75

pounds of the motor block's weight.

The system is in static equilibrium. By setting Worker X as the pivot point (fulcrum), the motor block creates a downward torque of

300 \text{ pounds} \times 3 \text{ feet} = 900 \text{ foot-pounds}

. To keep the beam from rotating, Worker Y must exert an equal opposing torque at a distance of

12

feet (the entire length of the beam). Therefore, Worker Y's force is

900 \div 12 = 75 \text{ pounds}

. Because Worker Y is four times further from the load than Worker X is, Worker Y carries one-fourth of the weight.

Step-by-Step Solution

Identify the pivot point and the forces acting on the beam.

Let Worker X's shoulder be the pivot point. The forces are the

300

-pound downward load acting at a distance of

3

feet, and Worker Y's upward supporting force acting at a distance of

12

feet.

Setting one end as the pivot point allows us to isolate the unknown force at the other end using the principle of torque (moments).

Set up the static equilibrium equation where total torque equals zero.

The downward torque from the block must equal the upward torque from Worker Y:

300 \times 3 = F_Y \times 12

For the beam to be balanced and not rotate, the clockwise moments and counter-clockwise moments around the pivot must be equal.

Solve the equation for Worker Y's supporting force (

F_Y

900 = 12 \times F_Y

, which simplifies to

F_Y = 900 / 12 = 75

pounds.

Basic algebra is used to isolate the unknown variable.

Key Concept

Load distribution and static equilibrium (torques/moments)

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic