Examkin

Soru

Zorluk: OrtaLevers and Fulcrums

A landscaping worker uses a shovel to lift 30 lbs30\text{ lbs} of soil. The worker's rear hand pushes down on the grip to act as the fulcrum, while the front hand lifts the shaft at a point 2 feet2\text{ feet} away from the rear hand. The soil is centered on the shovel's blade, which is 5 feet5\text{ feet} away from the rear hand. Ignoring the weight of the shovel itself, what is the minimum upward effort force the front hand must apply to lift the soil?

  1. 75 lbs75\text{ lbs}Cevap
  2. B
    50 lbs50\text{ lbs}
  3. C
    45 lbs45\text{ lbs}
  4. D
    12 lbs12\text{ lbs}

Cevap

The minimum upward effort force required is 75 lbs75\text{ lbs}.
A shovel functions as a third-class lever, where the effort (front hand) is between the fulcrum (rear hand) and the load (soil). To find the required effort force, set the effort torque equal to the load torque: Effort×Effort Arm=Load×Load Arm\text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm}. Substituting the given values yields E×2=30×5E \times 2 = 30 \times 5. This simplifies to 2E=1502E = 150, giving an effort force of 75 lbs75\text{ lbs}. Third-class levers always require an effort force greater than the load because they multiply distance at the expense of force.

Adım Adım Çözüm

1
Identify the lever class and the pivot point (fulcrum).
The shovel acts as a third-class lever where the rear hand is the fulcrum.
Establishing the fulcrum is necessary to measure the lengths of the effort arm and load arm accurately.
2
Determine the lengths of the effort arm and the load arm relative to the fulcrum.
Effort Arm = 2 feet2\text{ feet} (rear hand to front hand). Load Arm = 5 feet5\text{ feet} (rear hand to blade).
Torque is calculated by multiplying force by its perpendicular distance from the fulcrum.
3
Apply the principle of moments (torque balance) to solve for the unknown effort force.
Effort×2=30×5⇒2E=150⇒E=75 lbs\text{Effort} \times 2 = 30 \times 5 \Rightarrow 2E = 150 \Rightarrow E = 75\text{ lbs}.
For the lever to be balanced and lift the load, the effort torque must equal the load torque.

Anahtar Kavram

Torque balance in third-class levers
Bu soruyu puanla

Konular

Levers and Fulcrums

Bu konudan daha fazla soru