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Zorluk: OrtaInclined Planes

A logistics team can use either a 12-foot12\text{-foot} ramp or a 24-foot24\text{-foot} ramp to slide heavy crates onto a loading platform that is 4 feet4\text{ feet} above the ground. Assuming friction is negligible, which of the following statements is true regarding the use of the 24-foot24\text{-foot} ramp compared to the 12-foot12\text{-foot} ramp?

  1. The required effort force is halved, but the crate must be pushed twice as far, resulting in the same amount of total work.Cevap
  2. B
    The required effort force is halved, and the total work done to move the crate is also reduced by half.
  3. C
    The greater surface area of the 24-foot24\text{-foot} ramp decreases the friction applied to the crate, which reduces the total work required.
  4. D
    Since the crate's mass is supported over a longer distance, its overall weight decreases, making it easier to lift.

Cevap

The longer ramp reduces the effort force by half because it is twice as long, but because the pushing distance is doubled, the total work remains exactly the same.
An inclined plane trades distance for reduced force. Doubling the ramp's length doubles the mechanical advantage, thus halving the effort force required. However, because the force must be applied over twice the distance to reach the same vertical height, the total work (Force × Distance) remains exactly the same, obeying the law of conservation of energy.

Adım Adım Çözüm

1
Calculate the ideal mechanical advantage (IMA) of both ramps.
The 12-foot12\text{-foot} ramp has an IMA of 33 (12/412/4), and the 24-foot24\text{-foot} ramp has an IMA of 66 (24/424/4).
IMA is found by dividing the slope length by the vertical height. It determines the factor by which effort force is reduced.
2
Compare the effort forces required for each ramp.
Because the 24-foot24\text{-foot} ramp has twice the IMA of the 12-foot12\text{-foot} ramp (66 vs 33), it requires exactly half the effort force to push the same crate.
Effort force is inversely proportional to mechanical advantage.
3
Analyze the total work done in both scenarios.
Work equals force multiplied by distance (W=F×dW = F \times d). Applying half the force over twice the distance yields identical total work.
Simple machines do not change the total amount of work required; they only trade increased distance for decreased force.

Anahtar Kavram

Conservation of work and ideal mechanical advantage (IMA) on an inclined plane.
Tahmini Süre:1m 0s
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Konular

Inclined Planes

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