A mechanic presses a brake pedal with a force of 25\text{ pounds}. The pedal pivots on a h… — Armed Services Vocational Aptitude Battery (ASVAB)

A mechanic presses a brake pedal with a force of $25\text{ pounds}$ . The pedal pivots on a hinge at the top. The mechanic's foot applies the force $16\text{ inches}$ from the pivot point. The brake's pushrod, which transfers the force to the master cylinder, is attached to the pedal $4\text{ inches}$ from the pivot point. Calculate the force, in pounds, applied to the pushrod.

Cevap: 100 pounds

Cevap

100 pounds

The brake pedal functions as a second-class lever. To find the force transmitted to the pushrod, use the principle of moments where Effort Force × Effort Distance = Load Force × Load Distance. By substituting the known values, we get

25\text{ lbs} \times 16\text{ inches} = F_{\text{load}} \times 4\text{ inches}

. Multiplying

25

16

yields

400\text{ inch-pounds}

of torque. Dividing this torque by the load distance of

4\text{ inches}

reveals that a force of

100\text{ pounds}

is applied to the pushrod.

Adım Adım Çözüm

Identify the known variables from the problem.

Effort Force = 25 lbs, Effort Distance = 16 in, Load Distance = 4 in.

Organizing the known values is the first step to applying the lever equation.

Apply the mechanical advantage principle for levers.

Effort Force × Effort Distance = Load Force × Load Distance

In a state of equilibrium, the torque applied by the effort must equal the torque applied to the load.

Substitute the known values into the equation.

25 × 16 = Load Force × 4

This sets up the equation to isolate the unknown load force.

Calculate the effort torque.

400 = Load Force × 4

Multiplying the effort force by its distance from the pivot gives the total torque in inch-pounds.

Solve for the final load force.

Load Force = 100

Dividing the total torque by the load's distance from the pivot gives the force applied to the pushrod.

Anahtar Kavram

Torque and Mechanical Advantage in Second-Class Levers

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