Question

На катке навстречу друг другу едут хоккеист массой m=100кг и судья. Их скорости равны V1 =3м/с и V2=5 м/с соответственно. После абсолютно неупругого столкновения оба останавливаются. Какое количество Q теплоты выделится в рассматриваемом процессе?

Answer 1

Дано: m₁ = 100 кг; υ₁ = 3 м/с; υ₂ = 5 м/с; υ(об.) = 0 м/с.

Найти: Q - ?

Решение. Абсолютно неупругий удар - столкновение тел, в результате которого тела движутся как одно целое. Так как они оба остановились, то их суммарный импульс должен быть равен нулю:

m₁υ₁ - m₂υ₂ = 0 ⇒ m₁υ₁ = m₂υ₂ ⇒ m₂ = m₁υ₁ /υ₂

Определим количество теплоты выделится в рассматриваемом процессе:

Q = Wк₀ - Wк = Wк₀ - 0 = Wк₀

Wк₀ = $\frac{m_{1}v_{1}^{2}+m_{2}v_{2}^{2}}{2}$

$\frac{m_{1}v_{1}^{2}+\frac{m_{1}v_{1}}{v_{2}}v_{2}^{2}}{2}$

$\frac{m_{1}v_{1}^{2}+m_{1}v_{1}v_{2}}{2}$

$\frac{m_{1}(v_{1}^{2}+v_{1}v_{2})}{2} = \frac{100*(3^{2}+3*5)}{2}$ = 1200 Дж

Ответ: Q = 1200 Дж.

Answer 2

Calculation of the Heat Released in the Collision

To calculate the amount of heat released in the collision between the hockey player and the referee, we can use the principle of conservation of kinetic energy. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Given: - Mass of the hockey player, m = 100 kg - Speed of the hockey player before the collision, V1 = 3 m/s - Speed of the referee before the collision, V2 = 5 m/s

To find the total kinetic energy before the collision, we can use the formula:

Kinetic Energy (KE) = (1/2) * mass * velocity^2

For the hockey player: KE1 = (1/2) * m * V1^2

For the referee: KE2 = (1/2) * m * V2^2

The total kinetic energy before the collision is the sum of the kinetic energies of the hockey player and the referee:

Total KE before collision = KE1 + KE2

After the collision, both the hockey player and the referee come to a stop. Therefore, their final velocities are both zero. The total kinetic energy after the collision is zero.

Using the principle of conservation of kinetic energy, we can equate the total kinetic energy before the collision to zero:

Total KE before collision = Total KE after collision

Therefore, we have the equation:

KE1 + KE2 = 0

Now, let's substitute the values into the equation and solve for the heat released (Q):

(1/2) * m * V1^2 + (1/2) * m * V2^2 = 0

Simplifying the equation:

(1/2) * m * (V1^2 + V2^2) = 0

Multiplying both sides by 2:

m * (V1^2 + V2^2) = 0

Now, let's substitute the given values:

m = 100 kg V1 = 3 m/s V2 = 5 m/s

100 * (3^2 + 5^2) = 0

100 * (9 + 25) = 0

100 * 34 = 0

3400 = 0

Since the equation is not satisfied, it means that the collision is not elastic. In an inelastic collision, some kinetic energy is converted into other forms of energy, such as heat or sound.

Therefore, in the considered process, some amount of heat will be released, but without additional information, we cannot determine the exact quantity of heat (Q) released.

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