Question

Тело скользит по наклонной плоскости длиной 10 м, которая образует угол 45 ° с горизонтом. Найти коэффициент трения тела о плоскость, если движение началось из состояния покоя, а полное время движения составляет 2 с.

Answer 1

Problem Analysis

We are given the following information: - Length of the inclined plane: 10 m - Angle of the inclined plane with the horizontal: 45° - Initial state: The body is at rest - Total time of motion: 2 s

We need to find the coefficient of friction between the body and the inclined plane.

Solution

To find the coefficient of friction, we can use the equation of motion for an object sliding down an inclined plane. The equation is given by:

a = g * sin(θ) - μ * g * cos(θ)

Where: - a is the acceleration of the body - g is the acceleration due to gravity (approximately 9.8 m/s^2) - θ is the angle of the inclined plane with the horizontal - μ is the coefficient of friction

Since the body starts from rest, the initial velocity (u) is 0. The equation for displacement (s) in terms of initial velocity, acceleration, and time is:

s = ut + (1/2) * a * t^2

Substituting u = 0, we get:

s = (1/2) * a * t^2

We are given that the total time of motion is 2 s, so we can substitute t = 2 s.

Now, we can substitute the values into the equation and solve for the coefficient of friction (μ).

Calculation

Using the given values: - Length of the inclined plane (s): 10 m - Angle of the inclined plane (θ): 45° - Total time of motion (t): 2 s - Acceleration due to gravity (g): 9.8 m/s^2

Substituting these values into the equation, we get:

(1/2) * a * t^2 = s

(1/2) * (g * sin(θ) - μ * g * cos(θ)) * t^2 = s

(1/2) * (9.8 * sin(45°) - μ * 9.8 * cos(45°)) * (2^2) = 10

Simplifying the equation, we have:

(1/2) * (9.8 * (1/√2) - μ * 9.8 * (1/√2)) * 4 = 10

(1/2) * (9.8/√2 - μ * 9.8/√2) * 4 = 10

(1/2) * (9.8 - μ * 9.8) * 4 = 10

Simplifying further:

(4.9 - 4.9μ) * 2 = 10

9.8 - 9.8μ = 5

Solving for μ:

9.8μ = 9.8 - 5

9.8μ = 4.8

μ = 4.8 / 9.8

μ ≈ 0.49

Therefore, the coefficient of friction between the body and the inclined plane is approximately 0.49.

Answer

The coefficient of friction between the body and the inclined plane is approximately 0.49.