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Zorluk: KolayWedges

A woodworker uses a steel splitting wedge to split a heavy log. The wedge has a length of 88 inches and a maximum thickness of 22 inches. If a lateral splitting force of 400400 lbs is needed to split the log, what ideal effort force must be applied to the top of the wedge? (Assume no friction)

  1. A
    400400 lbs
  2. B
    800800 lbs
  3. 100100 lbsCevap
  4. D
    16001600 lbs

Cevap

The ideal effort force is 100100 lbs.
The correct answer is found by first calculating the ideal mechanical advantage (IMA) of the wedge, which is its length divided by its thickness (8/2=48 / 2 = 4). Because the wedge multiplies the input force by a factor of 44, the required effort force is the splitting force divided by the IMA (400 lbs/4=100 lbs400 \text{ lbs} / 4 = 100 \text{ lbs}).

Adım Adım Çözüm

1
Calculate the ideal mechanical advantage (IMA) of the wedge.
IMA=LengthThickness=82=4IMA = \frac{\text{Length}}{\text{Thickness}} = \frac{8}{2} = 4
The mechanical advantage of a wedge depends on the ratio of its length to its maximum thickness.
2
Calculate the required ideal effort force using the IMA.
Effort Force=Load ForceIMA=4004=100 lbs\text{Effort Force} = \frac{\text{Load Force}}{IMA} = \frac{400}{4} = 100 \text{ lbs}
A wedge multiplies the effort force by its mechanical advantage to produce the required load force.

Anahtar Kavram

Wedges provide a mechanical advantage equal to their length divided by their maximum thickness, which reduces the effort force required to split an object.
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Konular

Wedges

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