A landscaper is using a wheelbarrow to move a 120\text{-pound} rock. The rock's center of … — Armed Services Vocational Aptitude Battery (ASVAB)

A landscaper is using a wheelbarrow to move a $120\text{-pound}$ rock. The rock's center of gravity is positioned exactly $2\text{ feet}$ behind the wheel's axle, which acts as the fulcrum. The handles where the landscaper applies upward force are located $6\text{ feet}$ behind the wheel's axle. What upward lifting force must be applied at the handles to hold the wheelbarrow level?

A
$20\text{ pounds}$
$40\text{ pounds}$ Cevap
C
$60\text{ pounds}$
D
$360\text{ pounds}$

Cevap

The correct lifting force is

40\text{ pounds}

The correct answer is derived by balancing the torques around the fulcrum. The rock exerts a downward torque of

120\text{ pounds} \times 2\text{ feet} = 240\text{ foot-pounds}

. To keep the wheelbarrow level, the landscaper must exert an equal and opposite torque. By dividing the required torque (

240\text{ foot-pounds}

) by the distance of the handles from the fulcrum (

6\text{ feet}

), we find that

40\text{ pounds}

of upward force is required.

Adım Adım Çözüm

Identify the type of simple machine and the appropriate formula.

A wheelbarrow is a second-class lever. The principle of torque balance applies:

\text{Effort Force} \times \text{Effort Arm} = \text{Load Force} \times \text{Load Arm}

To find the unknown force, we must set the rotational forces (torques) equal to each other.

Determine the values for the load, load arm, and effort arm from the problem.

\text{Load Force} = 120\text{ pounds}

\text{Load Arm} = 2\text{ feet}

, and

\text{Effort Arm} = 6\text{ feet}

Correctly identifying distances relative to the fulcrum (the wheel's axle) is critical for calculating torque.

Substitute the values into the torque equation and solve for the Effort Force.

\text{Effort Force} \times 6 = 120 \times 2

. Simplifying gives

6 \times \text{Effort Force} = 240

. Dividing both sides by

6

gives

\text{Effort Force} = 40\text{ pounds}

This mathematically isolates the unknown variable to find the exact force required to balance the load.

Anahtar Kavram

Torque balance in a second-class lever dictates that the mechanical advantage is the ratio of the effort arm to the load arm.

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