Question

С горки высотой һ и с основанием r съезжают санки, которые останавливаются, пройдя по горизонтали путь S. Найти коэффициент трения μ, считая его одинаковым на всем пути.​

Answer 1

Бадаьсьдсьв в сбдвьвьсбжсщсьвььа
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Answer 2

Problem Analysis

We are given that sleds slide down a hill with a height of h and a base of r. The sleds come to a stop after traveling a distance S on a horizontal surface. We need to find the coefficient of friction μ, assuming it is the same throughout the entire path.

Solution

To solve this problem, we can use the principle of conservation of mechanical energy. The potential energy lost by the sleds as they slide down the hill is converted into kinetic energy, and then into work done against friction to bring the sleds to a stop.

The potential energy lost by the sleds is given by the formula:

ΔPE = mgh

where m is the mass of the sleds, g is the acceleration due to gravity, and h is the height of the hill.

The kinetic energy of the sleds when they reach the horizontal surface is given by the formula:

KE = (1/2)mv^2

where v is the velocity of the sleds.

The work done against friction to bring the sleds to a stop is given by the formula:

W = μmgS

where μ is the coefficient of friction, m is the mass of the sleds, g is the acceleration due to gravity, and S is the distance traveled on the horizontal surface.

Since the potential energy lost is equal to the work done against friction, we can equate the two equations:

mgh = μmgS

Simplifying the equation, we find:

μ = (h/S)

Now we can substitute the given values of h and S into the equation to find the coefficient of friction μ.

Calculation

From the given information, we have: - Height of the hill (h) = һ - Base of the hill (r) = r - Distance traveled on the horizontal surface (S) = S

Substituting these values into the equation, we find:

μ = (h/S) = (һ/S)

Therefore, the coefficient of friction μ is equal to (һ/S).

Answer

The coefficient of friction μ, assuming it is the same throughout the entire path, is equal to (һ/S).

Please note that the given information does not provide specific values for h, r, and S, so we cannot calculate the exact value of μ without those values.