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Zorluk: ZorFriction and Resistance

A logistics team is evaluating the force required to slide various solid steel crates across a dry, level concrete warehouse floor at a constant velocity. Assume the coefficient of kinetic friction remains constant for all steel-on-concrete contact.

Rank the following sliding scenarios from the GREATEST kinetic frictional resistance to the LEAST kinetic frictional resistance.

  1. 1Sliding a 200-pound crate that rests on its smallest face (2 square feet of contact area).
  2. 2Sliding a 150-pound crate that rests on its largest face (10 square feet of contact area).
  3. 3Sliding a 100-pound crate that rests on its smallest face (2 square feet of contact area).
  4. 4Sliding a 50-pound crate that rests on its largest face (10 square feet of contact area).

Cevap

The correct sequence from greatest to least frictional resistance is the 200-pound crate, followed by the 150-pound crate, the 100-pound crate, and finally the 50-pound crate.
According to the laws of sliding friction, kinetic frictional force depends entirely on the coefficient of friction and the normal force (the object's weight on a level surface). It is completely independent of the surface area in contact. Therefore, the friction is determined solely by the weight of the crates. Arranging them strictly from heaviest to lightest correctly orders them from greatest to least frictional resistance.

Adım Adım Çözüm

1
Identify the governing mathematical relationship for kinetic friction.
The formula for kinetic friction is Fk=μk×FNF_k = \mu_k \times F_N, where μk\mu_k is the coefficient of kinetic friction and FNF_N is the normal force.
This establishes which physical properties actually affect sliding resistance.
2
Determine the impact of surface area on the calculation.
The apparent contact area (2 sq ft vs 10 sq ft) is not a variable in the friction equation.
According to Amontons' Second Law of Friction, dry sliding friction is independent of the apparent area of contact.
3
Calculate the normal force for each scenario.
On a level floor, the normal force is exactly equal to the weight of the object. The normal forces are 200 lbs, 150 lbs, 100 lbs, and 50 lbs.
The weight dictates how hard the two surfaces are pressed together.
4
Order the scenarios based on the normal force.
Highest to lowest normal force: 200 lbs, 150 lbs, 100 lbs, 50 lbs.
Because kinetic friction is directly proportional to normal force, ordering by weight correctly orders by total frictional resistance.

Anahtar Kavram

Amontons' Laws of Friction (Surface Area Independence)
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Konular

Friction and Resistance

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