A painter uses a flathead screwdriver to pry open a tightly sealed paint can. The rim of t… — Armed Services Vocational Aptitude Battery (ASVAB)

A painter uses a flathead screwdriver to pry open a tightly sealed paint can. The rim of the can acts as the fulcrum. The tip of the screwdriver is inserted $2\text{ inches}$ under the lid from the fulcrum, while the handle extends $8\text{ inches}$ in the opposite direction from the fulcrum. If opening the lid requires an upward force of $40\text{ pounds}$ , how much downward effort force must the painter apply to the handle?

A
8 pounds
B
40 pounds
10 poundsCevap
D
160 pounds

Cevap

10 pounds

The screwdriver is functioning as a first-class lever. To find the required effort, the torque of the load must be balanced by the torque of the effort. The load torque is

40\text{ pounds} \times 2\text{ inches} = 80\text{ inch-pounds}

. Dividing this torque by the effort arm of

8\text{ inches}

yields an effort force of

10\text{ pounds}

Adım Adım Çözüm

Identify the lever class and the lengths of the load arm and effort arm.

The screwdriver acts as a first-class lever. The load arm (distance from the fulcrum to the tip) is 2 inches. The effort arm (distance from the fulcrum to the handle) is 8 inches.

Accurate arm lengths from the fulcrum are required to calculate the torque balance.

Apply the principle of moments (torque balance equation).

Effort Force × Effort Arm = Load Force × Load Arm

For the lever to move the load, the torque applied by the effort must equal the torque of the load.

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

Effort Force × 8 = 40 × 2. Effort Force × 8 = 80. Effort Force = 10 pounds.

Solving the equation provides the exact downward force needed on the handle.

Anahtar Kavram

In a first-class lever, the mechanical advantage is determined by the ratio of the effort arm to the load arm. A longer effort arm reduces the force required to lift a load.

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