A maintenance worker uses a 50\text{-inch} rigid steel bar to lift one edge of a heavy gen… — Armed Services Vocational Aptitude Battery (ASVAB)

A maintenance worker uses a $50\text{-inch}$ rigid steel bar to lift one edge of a heavy generator. The fulcrum is positioned at the far end of the bar, and the worker applies an upward force at the opposite end. If the weight of the generator applies a downward force of $320\text{ pounds}$ at a point exactly $10\text{ inches}$ from the fulcrum, how much upward effort force (in pounds) must the worker apply to maintain static equilibrium?

Cevap: 64 pounds

Cevap

64 pounds

The problem describes a second-class lever setup where the fulcrum is at one end, the effort is at the opposite end, and the resistance (load) is located between them. According to the principle of moments (law of the lever), the system is in static equilibrium when the effort torque equals the resistance torque (

F_e \times d_e = F_r \times d_r

). The effort arm length is the total length of the bar (

50\text{ inches}

), and the resistance arm length is the distance from the pivot to the load (

10\text{ inches}

). Substituting the values gives

F_e \times 50 = 320 \times 10

, which simplifies to

50F_e = 3200

. Dividing both sides by 50 yields an effort force of

64\text{ pounds}

Adım Adım Çözüm

Identify the lever class and the lengths of the moment arms.

The setup is a second-class lever. The effort arm (

d_e

) is

50\text{ inches}

and the resistance arm (

d_r

) is

10\text{ inches}

Correctly identifying the distances from the fulcrum to the forces is required to calculate torques.

Set up the torque balance equation.

F_e \times d_e = F_r \times d_r

For the lever to be in static equilibrium, the effort torque must equal the resistance torque.

Substitute the known values and solve for the effort force (

F_e

F_e \times 50 = 320 \times 10 \rightarrow 50F_e = 3200 \rightarrow F_e = 64

Isolating the unknown variable determines the exact force required.

Anahtar Kavram

The Law of the Lever (Torque Balance)

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

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