Question

Две тележки массами m1 = 3 кг и m2 = 1 кг движутся со скоростями V1 = 2 м/с и V2 = 2 м/с навстречу друг другу. Определите количество теплоты, которое выделится при неупругом соударении тележек.

Answer 1

Во-первых, чтобы определить количество теплоты при ударе, нужно знать их общую скорость.

Чтобы знать общую скорость, нужно знать направление их общей скорости после столкновения. Чей импульс больше - в ту сторону и покатятся.

p1=m1*V1=6
p2=m2*V2=2

Следовательно, они покатятся в сторону тележки 1.

По закону сохранения импульса: импульс ДО равняется импульсу ПОСЛЕ.

Импульс ДО в векторном виде: m1V1+m2V2
Импульс ПОСЛЕ в векторном виде: (m1+m2)*Vобщ

Спроецируем на ось ОХ (ось направляем вправо - в сторону движения 1 тележки): m1V1-m2V2=(m1+m2)*Vобщ => Vобщ=(p1-p2)/(m1+m2)= 1 м/с

Теперь можно найти количество теплоты.

Q=дE (количество теплоты равняется "дельта" (то есть, разности начальной и конечной) энергии):

дE=Ek1-Ek2. Потенциальную энергию не учитываем, так как относительно земли тележки не меняли высоту.

Ek1=m1V1^2/2 + m2V2^2/2
Ek2=(m1+m2)*Vобщ^2/2

дЕ=m1V1^2/2 + m2V2^2/2 - (m1+m2)*Vобщ^2/2 = 6 Дж

Answer 2

Calculation of the Heat Released in an Inelastic Collision

To determine the amount of heat released in an inelastic collision between two carts, we need to use the principle of conservation of momentum and the equation for calculating the kinetic energy before and after the collision.

The principle of conservation of momentum states that the total momentum of a system remains constant before and after a collision, provided no external forces act on the system. Mathematically, this can be expressed as:

m1 * V1 + m2 * V2 = (m1 + m2) * V

where: - m1 and m2 are the masses of the carts, - V1 and V2 are the velocities of the carts before the collision, and - V is the velocity of the carts after the collision.

In an inelastic collision, the carts stick together after the collision and move with a common velocity. Therefore, we can rewrite the equation as:

m1 * V1 + m2 * V2 = (m1 + m2) * V

To calculate the amount of heat released in the collision, we need to determine the change in kinetic energy before and after the collision. The change in kinetic energy is given by:

ΔKE = KE_after - KE_before

where: - ΔKE is the change in kinetic energy, - KE_after is the kinetic energy of the carts after the collision, and - KE_before is the kinetic energy of the carts before the collision.

The kinetic energy of an object is given by the equation:

KE = (1/2) * m * V^2

where: - KE is the kinetic energy, - m is the mass of the object, and - V is the velocity of the object.

Using this equation, we can calculate the kinetic energy before and after the collision and then determine the change in kinetic energy.

Let's calculate the amount of heat released in the collision between the two carts with the given masses and velocities:

- m1 = 3 kg - m2 = 1 kg - V1 = 2 m/s - V2 = 2 m/s

First, let's calculate the velocity of the carts after the collision using the conservation of momentum equation:

m1 * V1 + m2 * V2 = (m1 + m2) * V

Substituting the given values:

3 kg * 2 m/s + 1 kg * 2 m/s = (3 kg + 1 kg) * V

Simplifying the equation:

6 kg * m/s = 4 kg * V

V = (6 kg * m/s) / 4 kg

V = 1.5 m/s

Now, let's calculate the kinetic energy before and after the collision:

For cart 1: KE1_before = (1/2) * m1 * V1^2 = (1/2) * 3 kg * (2 m/s)^2 = 6 J

For cart 2: KE2_before = (1/2) * m2 * V2^2 = (1/2) * 1 kg * (2 m/s)^2 = 2 J

For the combined system after the collision: KE_after = (1/2) * (m1 + m2) * V^2 = (1/2) * (3 kg + 1 kg) * (1.5 m/s)^2 = 4.5 J

Now, let's calculate the change in kinetic energy:

ΔKE = KE_after - KE_before = 4.5 J - (6 J + 2 J) = -3.5 J

The negative sign indicates that the kinetic energy decreased after the collision, which means that heat was released during the collision.

Therefore, the amount of heat released in the inelastic collision between the two carts is 3.5 J.

Please note that the calculation assumes an idealized scenario and does not take into account other factors such as friction or energy losses due to deformation.