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Zorluk: Çok zorLevers and Fulcrums

A mechanic uses a 60-inch straight pry bar to lift a 300 lb machinery crate. Initially, they place a pivot block 12 inches from the crate, pressing down on the opposite end to lift the load. To lift the crate higher on the next attempt, they move the pivot block so it is 20 inches from the crate, again pressing down on the opposite end. By how much does the required effort force change, and what is the new mechanical advantage of the lever?

  1. The effort force increases by 75 lbs; the new mechanical advantage is 2.Cevap
  2. B
    The effort force increases by 40 lbs; the new mechanical advantage is 3.
  3. C
    The effort force increases by 150 lbs; the new mechanical advantage is 0.5.
  4. D
    The effort force increases by 50 lbs; the new mechanical advantage is 2.4.

Cevap

The effort force increases by 75 lbs; the new mechanical advantage is 2.
The correct answer accurately calculates that moving the pivot increases the load arm to 20 inches and shrinks the effort arm to 40 inches. This cuts the mechanical advantage in half (from 4 to 2), doubling the required effort force from 75 lbs to 150 lbs, which is an increase of 75 lbs.

Adım Adım Çözüm

1
Identify the lever class and the formula for torque balance.
This is a first-class lever. The formula is: Effort Force × Effort Arm = Load Force × Load Arm. The Mechanical Advantage (MA) is Effort Arm / Load Arm.
The fulcrum (pivot block) is located between the applied effort and the load.
2
Calculate the initial effort force and mechanical advantage (State 1).
Load Arm = 12 inches. Effort Arm = 60 - 12 = 48 inches. MA = 48 / 12 = 4. Initial Effort Force = 300 / 4 = 75 lbs.
The total length of the bar is 60 inches, so the effort arm is the remainder of the bar after subtracting the load arm.
3
Calculate the new effort force and mechanical advantage (State 2).
New Load Arm = 20 inches. New Effort Arm = 60 - 20 = 40 inches. New MA = 40 / 20 = 2. New Effort Force = 300 / 2 = 150 lbs.
Moving the pivot 8 inches away from the load increases the load arm and correspondingly decreases the effort arm.
4
Determine the change in the required effort force.
150 lbs (New) - 75 lbs (Initial) = 75 lbs increase.
The question asks for the difference between the two required forces.

Anahtar Kavram

Torque balance and changing fulcrum positions on a first-class lever.
Tahmini Süre:2m 0s
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Konular

Levers and Fulcrums

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