Question

На сани, стоящие на гладком льду, с некоторой высоты прыгает человек массой 50 кг. Проекция скорости человека на горизонтальное направление в момент соприкосновения с санями 2 м/с. Скорость саней с человеком после прыжка составила 1.5 м/с. Определите массу саней.

Answer 1

Calculation of the mass of the sled

To determine the mass of the sled, we can use the principle of conservation of momentum. According to this principle, the total momentum before the jump is equal to the total momentum after the jump.

The momentum of an object is given by the product of its mass and velocity. Therefore, we can write the equation:

Initial momentum = Final momentum

The initial momentum is the product of the mass of the person and their horizontal velocity before the jump. The final momentum is the product of the combined mass of the person and the sled and their horizontal velocity after the jump.

Let's denote the mass of the person as m, the velocity of the person before the jump as v1, the mass of the sled as M, and the velocity of the sled with the person after the jump as v2.

According to the given information, we have:

- Mass of the person, m = 50 kg - Velocity of the person before the jump, v1 = 2 m/s - Velocity of the sled with the person after the jump, v2 = 1.5 m/s

Using the principle of conservation of momentum, we can write the equation as:

m * v1 = (m + M) * v2

Now, we can substitute the given values into the equation and solve for the mass of the sled, M.

50 kg * 2 m/s = (50 kg + M) * 1.5 m/s

Simplifying the equation:

100 kg*m/s = (50 kg + M) * 1.5 m/s

Dividing both sides of the equation by 1.5 m/s:

100 kg*m/s / 1.5 m/s = 50 kg + M

66.67 kg = 50 kg + M

Subtracting 50 kg from both sides of the equation:

66.67 kg - 50 kg = M

M = 16.67 kg

Therefore, the mass of the sled is approximately 16.67 kg.