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Zorluk: ZorWedges

A hydraulic log splitter is designed to drive a steel wedge into a large piece of timber. The wedge has a length of 20 cm20\text{ cm} and a maximum thickness of 5 cm5\text{ cm}. Assuming an ideal system with no friction, if the hydraulic cylinder applies a downward effort force of 2,000 N2,000\text{ N} to the wedge, which of the following statements correctly identifies the theoretical lateral splitting force exerted on the timber and the underlying physical principle regarding the work done?

  1. The lateral splitting force is 8,000 N8,000\text{ N}; the wedge multiplies the effort force, but the total work output cannot exceed the total work input from the cylinder.Cevap
  2. B
    The lateral splitting force is 8,000 N8,000\text{ N}; the wedge multiplies the effort force and therefore decreases the total amount of work required to split the timber.
  3. C
    The lateral splitting force is 500 N500\text{ N}; the mechanical advantage is determined by dividing the thickness by the length, which divides the effort force.
  4. D
    The lateral splitting force is 8,000 N8,000\text{ N}; the force is multiplied because the larger surface area of the wedge decreases the frictional force opposing the motion.

Cevap

The correct answer states that the theoretical lateral splitting force is 8,000 N8,000\text{ N} and that the total work output cannot exceed the work input.
The correct answer accurately calculates the Ideal Mechanical Advantage by dividing the length by the thickness (20/5=420 / 5 = 4), resulting in an output force of 4×2,000=8,000 N4 \times 2,000 = 8,000\text{ N}. It also correctly identifies that while the wedge multiplies the effort force, it does not reduce the total amount of work done, adhering to the conservation of energy.

Adım Adım Çözüm

1
Calculate the Ideal Mechanical Advantage (IMA) of the wedge.
IMA=LengthThickness=20 cm5 cm=4IMA = \frac{\text{Length}}{\text{Thickness}} = \frac{20\text{ cm}}{5\text{ cm}} = 4
The mechanical advantage of a wedge is the ratio of its penetration length to its maximum thickness.
2
Determine the theoretical lateral splitting force (Output Force).
Fout=Fin×IMA=2,000 N×4=8,000 NF_{out} = F_{in} \times IMA = 2,000\text{ N} \times 4 = 8,000\text{ N}
In an ideal machine, the output force is the product of the input effort force and the mechanical advantage.
3
Evaluate the principles of work and energy.
Total work input ≥\geq Total work output. Simple machines never reduce the amount of work required.
The Law of Conservation of Energy dictates that while a simple machine can reduce the required effort force by increasing the distance over which it is applied, it cannot reduce the total work done.

Anahtar Kavram

Mechanical Advantage of Wedges and Conservation of Work
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Konular

Wedges

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