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Difficulty: MediumFriction and Resistance

An automotive engineer is redesigning a vehicle's disc brake system to optimize heat dissipation. In the new design, the surface area of the brake pads is exactly doubled. However, the hydraulic system is calibrated to apply the exact same total normal force (clamping force) against the spinning rotor as the original design. Assuming the brake pad material and rotor material remain identical, how will the new design theoretically affect the kinetic frictional force generated during braking?

  1. A
    The kinetic frictional force will double, because there is twice as much brake pad material in contact with the rotor.
  2. The kinetic frictional force will remain unchanged, because it depends on the normal force and materials, not the contact area.Answer
  3. C
    The kinetic frictional force will be reduced by half, because the clamping force is spread out over a larger surface area.
  4. D
    The kinetic frictional force will increase, because the larger pads produce a stronger reaction force against the rotor's inertia.

Answer

The kinetic frictional force will remain unchanged, because it depends on the normal force and materials, not the contact area.
According to the standard model of dry friction (Coulomb friction), the kinetic frictional force between two solid surfaces is directly proportional to the normal force pressing them together and the materials involved (the coefficient of friction), but it is completely independent of the apparent area of contact. Since the normal force and materials are unchanged, the friction remains the same.

Step-by-Step Solution

1
Identify the factors that determine kinetic frictional force.
Kinetic friction (FkF_k) is determined by the formula Fk=μkFNF_k = \mu_k F_N, where μk\mu_k is the coefficient of kinetic friction and FNF_N is the normal force.
Establishing the mathematical relationship is necessary to see which variables affect the outcome.
2
Evaluate the changes made in the new design.
The surface area doubled, but the normal force (clamping force) and the materials (which determine μk\mu_k) remained exactly the same.
To apply the friction formula, we must know if the variables within it have changed.
3
Determine the effect on the total frictional force.
Because neither the normal force nor the coefficient of friction changed, the calculated frictional force remains identical, proving it is independent of surface area.
This confirms the theoretical principle of dry friction.

Key Concept

Friction and Contact Area Independence
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Topics

Friction and Resistance

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