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Zorluk: OrtaLevers and Fulcrums

An automotive technician operates a hydraulic floor jack by pressing down on its handle. The handle pivots on a fixed pin at one end. The technician applies a steady downward force of 30 lbs30\text{ lbs} at the opposite end of the handle. The total length of the handle from the pivot pin to the point of effort is 24 inches24\text{ inches}. The handle pushes down on a pump piston that is located 1.5 inches1.5\text{ inches} from the pivot pin. What is the total force, in pounds, applied to the pump piston? (Assume the handle is horizontal and ignore friction.)

Cevap: 480 lbs

Cevap

480
The jack handle operates as a lever with the fulcrum at one end. Because the effort is applied much further from the fulcrum than the load, the lever multiplies the applied force. The mechanical advantage is the ratio of the effort arm to the load arm (24/1.5=1624 / 1.5 = 16). Multiplying the 30 lbs30\text{ lbs} of effort by a mechanical advantage of 16 yields a 480 lbs480\text{ lbs} force on the piston.

Adım Adım Çözüm

1
Identify the lever components.
Fulcrum = pivot pin; Effort Force (E) = 30 lbs; Effort Arm (d_E) = 24 inches; Load Arm (d_L) = 1.5 inches.
To apply the torque balance equation, all distances must be measured from the fulcrum.
2
Set up the torque balance equation.
E×dE=L×dLE \times d_E = L \times d_L
In a static lever system, the torque generated by the effort equals the torque generated by the load.
3
Substitute the given values.
30×24=L×1.530 \times 24 = L \times 1.5
To prepare the equation for solving the unknown load force (L).
4
Solve for the load force.
720=1.5L  ⟹  L=480 lbs720 = 1.5L \implies L = 480\text{ lbs}
Dividing the effort torque by the load arm distance yields the resulting force applied to the piston.

Anahtar Kavram

Torque Balance and Mechanical Advantage
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Konular

Levers and Fulcrums

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