Friction is always present in real motion. When friction does work, mechanical energy decreases and is converted into thermal energy.
Basic Knowledge
Frictional force f is a force that acts along a contact surface in the direction opposing motion:f = μN
μ(mu): coefficient of kinetic friction(a constant determined by the properties of the surfaces), N: normal force(N).
The work done by friction on an object is negative work, decreasing the object's mechanical energy:ΔE = E₂ - E₁ = -f × d
(-f×d: magnitude of frictional force × distance traveled. The sign is negative)
Mechanical energy lost through friction is converted into thermal energy. The total amount of energy does not change(law of conservation of energy).
Static friction balances the force attempting to move an object up to the maximum static friction f₀ = μ₀N, but when the maximum value is exceeded, the object begins to move.
Frictional force f（A contact force opposing motion. f = μN）
Coefficient of kinetic friction μ（A constant determining the magnitude of friction. It depends on the types of surfaces）
Normal force N（A supporting force acting perpendicularly from a surface on an object）
Loss of mechanical energy（When friction is present, ΔE = -f×d < 0）
Conversion into thermal energy（Lost mechanical energy becomes heat）
Law of conservation of energy（Total energy remains unchanged even when its form changes）
Further Study (Background and Significance)
When friction is present, the law of conservation of mechanical energy cannot be used, but the following equation is used instead:E₁ - E₂ = f × d(thermal energy produced)
In other words, “the difference between the initial and final mechanical energies = frictional heat.” This method can solve relationships among speed, height, frictional force, and distance.
The coefficient of kinetic friction differs according to the material and roughness of the surfaces. It is about 0.02 on ice and about 0.6〜0.8 for concrete and rubber. Skiing and skating intentionally create conditions with extremely small coefficients of friction.
Brakes also use frictional energy conversion. They slow a vehicle by converting kinetic energy into heat through friction between brake pads and wheels. Electric vehicles use regenerative braking to convert kinetic energy back into electrical energy and store it in the battery.
- f = μN(kinetic frictional force)
- Friction does work → mechanical E decreases
- Amount lost = f × d(frictional force × distance traveled)
- Lost mechanical E = thermal energy
- Total energy is conserved(law)
- With friction: E₁ - f×d = E₂
- Without friction: E₁ = E₂(the conservation law can be used)
Points to Note (Common Confusions)
① “The law of conservation of mechanical energy does not hold” does not mean “the law of conservation of energy has been violated.” Total energy is always conserved. ② The work done by friction is -f×d(always negative). Friction is not the force “doing work” but the force “taking away energy.” ③ The normal force N does no work in the direction parallel to the surface(because it is perpendicular to the surface). ④ The coefficient of static friction(before motion begins) is generally greater than the coefficient of kinetic friction.
Practice
- An object of mass 2 kg was slid 5 m across a floor with a coefficient of kinetic friction of 0.3. Find the work done by friction(g = 10 m/s²).
- If the object's initial speed above was 6 m/s, find its speed after 5 m.
- An object of mass 1 kg slid down an 8 m-high slope(with friction). Its speed upon reaching the ground was 10 m/s. Find the mechanical energy lost through friction(g = 10 m/s²).