Question

Шайба скользит с ледяной горки высотой H=5м, наклоненной к горизонту под углом α=45º. Коэффициент трения шайбы о лед равен 0,2. Горка плавно переходит в горизонтальную ледяную поверхность. Какой путь пройдет шайба до остановки по горизонтальной поверхности?

Answer 1

По крайней мере осталось совсем чуть-чуть до ответа

Answer 2

Calculation of the Distance Traveled by the Puck

To calculate the distance traveled by the puck on the horizontal surface, we can use the principles of conservation of energy and the work-energy theorem.

The initial potential energy of the puck at the top of the inclined plane can be calculated using the formula:

Potential energy = mass x gravity x height Potential energy = mgh

Given that the height of the inclined plane is 5m and the mass of the puck is not provided, we cannot calculate the exact potential energy. However, we can proceed with the calculations using the general formula.

The potential energy is converted into kinetic energy as the puck slides down the inclined plane. The kinetic energy can be calculated using the formula:

Kinetic energy = 0.5 x mass x velocity^2 Kinetic energy = (1/2)mv^2

Since the puck is sliding without any external forces acting on it, the work done by friction is equal to the change in kinetic energy. The work done by friction can be calculated using the formula:

Work done by friction = force of friction x distance Work done by friction = μmgd

Where: - μ is the coefficient of friction between the puck and the ice (given as 0.2) - m is the mass of the puck - g is the acceleration due to gravity (approximately 9.8 m/s^2) - d is the distance traveled by the puck on the horizontal surface

Equating the work done by friction to the change in kinetic energy, we have:

μmgd = (1/2)mv^2

Simplifying the equation, we get:

d = (1/2)μg(v^2/m)

To find the value of v^2/m, we can use the conservation of energy principle:

Potential energy at the top = Kinetic energy at the bottom

mgh = (1/2)mv^2

Simplifying the equation, we get:

v^2/m = 2gh

Substituting this value back into the equation for d, we have:

d = (1/2)μg(2gh) d = μgh

Given that the height of the inclined plane (H) is 5m and the angle of inclination (α) is 45 degrees, we can calculate the distance traveled by the puck on the horizontal surface (d).

Please note that the mass of the puck is not provided, so we cannot calculate the exact distance. However, we can proceed with the calculations using the general formula.

Using the given values: - H = 5m - α = 45 degrees - μ = 0.2 - g = 9.8 m/s^2

We can calculate the distance traveled by the puck on the horizontal surface (d) as follows:

d = μgh d = 0.2 x 9.8 x 5 d = 9.8 meters

Therefore, the puck will travel approximately 9.8 meters on the horizontal surface before coming to a stop.

Please note that the exact distance traveled by the puck may vary depending on the mass of the puck, which is not provided in the question.