Question

Шары массами 6 и 4 кг, движущиеся навстречу друг другу со скоростью 2 м/с каждый относительно Земли, соударяются, после чего движутся вместе. Определите, какое количество теплоты выделится в результате соударения.

Answer 1

Дано m1=6 кг  m2=4 кг   V=2 м/с   Q-?
по закону сохранения импульса
m1*V -m2*V=(m1+m2)*U
U=V*(m1-m2)/(m1+m2)=2*2/10=0,4 м/с
Q= m1*V^2/2 +m2*V^2/2 - (m1+m2)*U^2/2=6*4/2+4*4/2-10*0,16/2=12+8-0,8=19,2Дж

Answer 2

Calculation of the Heat Released in the Collision

To determine the amount of heat released in the collision between two spheres, we can use the principle of conservation of kinetic energy. According to this principle, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Let's denote the masses of the spheres as m1 = 6 kg and m2 = 4 kg, and their velocities before the collision as v1 = 2 m/s and v2 = -2 m/s (since they are moving towards each other). The negative sign indicates opposite directions.

The total kinetic energy before the collision is given by the sum of the kinetic energies of the two spheres:

KE_before = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2.

After the collision, the two spheres stick together and move with a common velocity, denoted as v_final. The total kinetic energy after the collision is given by:

KE_after = (1/2) * (m1 + m2) * v_final^2.

Since the total kinetic energy is conserved, we can equate the two expressions:

(1/2) * m1 * v1^2 + (1/2) * m2 * v2^2 = (1/2) * (m1 + m2) * v_final^2.

Now we can solve this equation to find the value of v_final.

Calculation Steps:

1. Substitute the given values into the equation: - m1 = 6 kg - m2 = 4 kg - v1 = 2 m/s - v2 = -2 m/s

2. Calculate the total kinetic energy before the collision, KE_before: - KE_before = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2

3. Calculate the total kinetic energy after the collision, KE_after: - KE_after = (1/2) * (m1 + m2) * v_final^2

4. Equate KE_before and KE_after to solve for v_final.

5. Once we have v_final, we can calculate the heat released in the collision using the formula: - Heat released = (1/2) * (m1 + m2) * (v_final^2 - v1^2).

Let's perform the calculations step by step.

Calculation:

1. Given values: - m1 = 6 kg - m2 = 4 kg - v1 = 2 m/s - v2 = -2 m/s

2. Calculate KE_before: - KE_before = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2 - KE_before = (1/2) * 6 kg * (2 m/s)^2 + (1/2) * 4 kg * (-2 m/s)^2 - KE_before = 12 J + 8 J - KE_before = 20 J

3. Calculate KE_after: - KE_after = (1/2) * (m1 + m2) * v_final^2 - KE_after = (1/2) * (6 kg + 4 kg) * v_final^2 - KE_after = 10 kg * v_final^2

4. Equate KE_before and KE_after: - 20 J = 10 kg * v_final^2

5. Solve for v_final: - v_final^2 = 20 J / 10 kg - v_final^2 = 2 m^2/s^2 - v_final = √(2 m^2/s^2) - v_final ≈ 1.41 m/s

6. Calculate the heat released: - Heat released = (1/2) * (m1 + m2) * (v_final^2 - v1^2) - Heat released = (1/2) * (6 kg + 4 kg) * ((1.41 m/s)^2 - (2 m/s)^2) - Heat released = 10 kg * (1.99 m^2/s^2 - 4 m^2/s^2) - Heat released = 10 kg * (-2.01 m^2/s^2) - Heat released ≈ -20.1 J

Therefore, the amount of heat released in the collision is approximately -20.1 J. The negative sign indicates that heat is released from the system during the collision.

Please note that the negative sign indicates the direction of heat flow, not the actual value of the heat released. Heat is considered a form of energy, and the negative sign indicates that energy is leaving the system.

Let me know if you need any further assistance!