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Zorluk: OrtaFriction and Resistance

A heavy winch is dragging a 200 kg200\text{ kg} rectangular steel block across a flat, horizontal concrete surface at a constant velocity of 5 m/s5\text{ m/s}. The coefficient of kinetic friction between the steel and the concrete is 0.40.4. (Assume gravitational acceleration g=10 m/s2g = 10\text{ m/s}^2). What is the approximate kinetic frictional force opposing the block's motion, and how would this force change if the block were turned to slide on a face with only half the original surface area?

  1. 800 N800\text{ N}; the frictional force would remain exactly the same.Cevap
  2. B
    80 N80\text{ N}; the frictional force would remain exactly the same.
  3. C
    800 N800\text{ N}; the frictional force would be halved.
  4. D
    1,000 N1,000\text{ N}; the frictional force would remain exactly the same.

Cevap

The kinetic frictional force is 800 N800\text{ N}, and it would remain exactly the same if the surface area were halved.
The correct answer accurately calculates the normal force by multiplying mass and gravity (200×10=2000 N200 \times 10 = 2000\text{ N}), then applies the friction coefficient (2000×0.4=800 N2000 \times 0.4 = 800\text{ N}). Furthermore, it correctly applies the principle that sliding friction is unaffected by the size of the contact area, so the force remains constant regardless of which face the block slides on.

Adım Adım Çözüm

1
Calculate the weight (which equals the normal force) of the block.
W=mg=200 kg×10 m/s2=2000 NW = mg = 200\text{ kg} \times 10\text{ m/s}^2 = 2000\text{ N}. Since the surface is horizontal, the normal force N=2000 NN = 2000\text{ N}.
Kinetic friction is directly proportional to the normal force pressing the surfaces together.
2
Calculate the kinetic frictional force.
Fk=μk×N=0.4×2000 N=800 NF_k = \mu_k \times N = 0.4 \times 2000\text{ N} = 800\text{ N}.
The formula for kinetic friction requires multiplying the normal force by the coefficient of kinetic friction.
3
Evaluate the effect of changing the surface area.
The frictional force remains 800 N800\text{ N}.
Amontons' Second Law of Friction states that the force of friction is independent of the apparent area of contact. The pressure increases on the smaller area, but the total normal force remains unchanged.

Anahtar Kavram

Kinetic friction depends solely on the normal force and the materials in contact (coefficient of friction), and is completely independent of the contact surface area and velocity.
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Konular

Friction and Resistance

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