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Zorluk: ZorFriction and Resistance

An automotive engineer is designing a mechanical disc brake system to stop a heavy rotating axle. The engineer is evaluating two brake pad designs made of the exact same friction material: Design X utilizes a single large brake pad, while Design Y utilizes a smaller brake pad with exactly half the surface area of Design X. During a braking event, the hydraulic system applies an identical clamping force (normal force) to the pad in both designs. Assuming the coefficient of kinetic friction remains constant, which of the following best describes the resulting kinetic frictional resistance and the reasoning behind it?

  1. A
    Design Y produces significantly less kinetic frictional resistance because its smaller contact area interacts with fewer surface imperfections on the brake disc.
  2. Both designs produce the same kinetic frictional resistance because the total frictional force depends on the applied clamping force and the coefficient of friction, regardless of the contact area.Cevap
  3. C
    Design X produces greater kinetic frictional resistance because the larger pad contains more mass, which converts the identical hydraulic pressure into a heavier total braking force.
  4. D
    Design Y produces more kinetic frictional resistance because concentrating the hydraulic force into a smaller area increases the pad's inertia, multiplying the reaction force.

Cevap

Both brake pad designs produce the identical amount of kinetic frictional resistance because macroscopic friction is independent of the contact surface area.
The correct answer accurately applies the standard physical model of kinetic friction, where the total frictional force (FkF_k) is solely the product of the coefficient of kinetic friction (μk\mu_k) and the normal force (FnF_n). Because both brake pad designs are made of identical material and are subjected to the exact same hydraulic clamping force, the resulting kinetic friction is identical. In solid mechanics, sliding friction does not depend on the macroscopic surface area in contact.

Adım Adım Çözüm

1
Identify the primary equation used to calculate kinetic friction.
Fk=μk×FnF_k = \mu_k \times F_n
This formula establishes that kinetic frictional force (FkF_k) depends strictly on the coefficient of kinetic friction (μk\mu_k) and the normal force (FnF_n).
2
Evaluate the variables given in the scenario for both designs.
Both designs possess the same normal force (identical clamping force) and the same coefficient of friction (exact same friction material).
The prompt explicitly states the hydraulic system applies an identical clamping force and the materials are the same.
3
Determine the impact of the differing surface areas on the total frictional force.
The surface area does not affect the calculation. Both designs yield the exact same frictional resistance.
Surface area is not a variable in the standard kinetic friction formula; increased area distributes the force resulting in lower pressure, while decreased area concentrates the force resulting in higher pressure, keeping total friction constant.

Anahtar Kavram

Independence of kinetic friction from surface area
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Konular

Friction and Resistance

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