Question

Льдинка скользит по инерции вверх по наклонной плоскости. Определите, на какую высоту поднимется льдинка, если коэффициент трения 0.2, угол наклонной плоскости 45 градусов и скорость льдинки в начале подъёма 6 м/с.

Answer 1

Calculation of the Height Reached by the Ice Cube

To determine the height reached by the ice cube sliding up the inclined plane, we need to consider the coefficient of friction, the angle of the inclined plane, and the initial velocity of the ice cube.

Given: - Coefficient of friction (μ) = 0.2 - Angle of the inclined plane (θ) = 45 degrees - Initial velocity of the ice cube (v) = 6 m/s

To calculate the height reached by the ice cube, we can use the principles of conservation of energy. The initial kinetic energy of the ice cube will be converted into potential energy as it moves up the inclined plane.

The formula for the potential energy (PE) is given by: PE = m * g * h

Where: - m is the mass of the ice cube - g is the acceleration due to gravity (approximately 9.8 m/s^2) - h is the height reached by the ice cube

To find the mass of the ice cube, we can assume a standard density for ice, which is approximately 917 kg/m^3. The volume of the ice cube can be calculated using its dimensions.

Since we don't have the dimensions of the ice cube, we will assume a standard size of 1 cm^3 for simplicity.

The mass (m) of the ice cube can be calculated using the formula: m = density * volume

Substituting the values, we get: m = 917 kg/m^3 * 0.000001 m^3

Now, we can calculate the potential energy (PE) using the formula mentioned earlier.

Calculation Steps:

1. Calculate the mass of the ice cube: - m = 917 kg/m^3 * 0.000001 m^3

2. Calculate the potential energy (PE): - PE = m * g * h

3. Equate the initial kinetic energy to the potential energy: - 0.5 * m * v^2 = PE

4. Solve for the height (h): - h = (0.5 * m * v^2) / (m * g)

Now, let's calculate the height reached by the ice cube using the given values.

Calculation:

1. Calculate the mass of the ice cube: - m = 917 kg/m^3 * 0.000001 m^3 - m = 0.000917 kg

2. Calculate the potential energy (PE): - PE = m * g * h

3. Equate the initial kinetic energy to the potential energy: - 0.5 * m * v^2 = PE

4. Solve for the height (h): - h = (0.5 * m * v^2) / (m * g)

Substituting the given values: - h = (0.5 * 0.000917 kg * (6 m/s)^2) / (0.000917 kg * 9.8 m/s^2)

Simplifying the equation: - h = (0.5 * 0.000917 kg * 36 m^2/s^2) / (0.000917 kg * 9.8 m/s^2) - h = 0.5 * 36 / 9.8

Calculating the final result: - h ≈ 1.8367 meters

Therefore, the ice cube will reach a height of approximately 1.8367 meters when sliding up the inclined plane with a coefficient of friction of 0.2, an angle of 45 degrees, and an initial velocity of 6 m/s.