A technician uses a pair of long industrial tweezers to securely hold a sensitive electron… — Armed Services Vocational Aptitude Battery (ASVAB)

A technician uses a pair of long industrial tweezers to securely hold a sensitive electronic component. The tweezers pivot at the joined top end and have a total length of $40 \text{ cm}$ from the pivot to the gripping tips. The technician's fingers apply pressure at a point $8 \text{ cm}$ from the pivot. If the component requires a holding force of $50 \text{ N}$ at the tips, what effort force (in Newtons) must the technician apply?

Cevap: 250 N

Cevap

The technician must apply an effort force of 250 N.

In a third-class lever like tweezers, the effort is applied between the fulcrum and the load. Since the effort arm (

8 \text{ cm}

) is shorter than the load arm (

40 \text{ cm}

), the mechanical advantage is less than 1. This means a much larger effort force is required to generate a smaller load force at the tips. Using the torque balance equation

F_e \times d_e = F_l \times d_l

, we get

F_e \times 8 = 50 \times 40

. Solving this gives

250 \text{ N}

Adım Adım Çözüm

Identify the lever configuration and its parameters.

The tweezers are a third-class lever (fulcrum at one end, effort in the middle). Effort arm

d_e = 8 \text{ cm}

, load arm

d_l = 40 \text{ cm}

, load force

F_l = 50 \text{ N}

Correctly identifying the lever class ensures the correct distances are used relative to the fulcrum.

Set up the torque equilibrium equation.

F_e \times d_e = F_l \times d_l

For the lever to remain stable and provide the required grip, the effort torque must balance the load torque.

Calculate the required effort force.

F_e \times 8 = 50 \times 40 \Rightarrow 8 F_e = 2000 \Rightarrow F_e = 250 \text{ N}

To find the unknown variable by substituting the given values.

Anahtar Kavram

Torque Balance in Third-Class Levers

Soru

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