Savchenko Problem 2.1.45
Physics · mechanics · thermodynamics
Problem
A coin is placed on a plane whose slope tangent is equal to the coefficient of friction. In the horizontal direction along the plane, the coin was given a velocity v. Find the steady speed of the coin.Intuitive explanation
The key insight is recognizing that when the slope angle equals the friction coefficient (both equal to ), the coin experiences a special balance between gravity and friction. Since you give it an initial horizontal velocity, friction will act to slow it down, but gravity's component along the slope will also influence the motion. The steady speed occurs when the net force along the slope becomes zero—where gravity's pull and friction's resistance reach equilibrium, independent of the initial velocity direction.
Intuitive explanation
The key insight is recognizing that when the slope angle equals the friction coefficient (both equal to ), the coin experiences a special balance between gravity and friction. Since you give it an initial horizontal velocity, friction will act to slow it down, but gravity's component along the slope will also influence the motion. The steady speed occurs when the net force along the slope becomes zero—where gravity's pull and friction's resistance reach equilibrium, independent of the initial velocity direction.