Две игрушечные тележки массами 180 г и 90 г движутся навстречу друг другу со скоростями 0,1 м/с и 0,15 м/с соответственно и после столкновения сцепляются. Определите скорость тележек сразу после их сцепки. Какое количество исходной кинетической энергии системы перешло во внутреннюю после их столкновения?
The solution to this problem involves using conservation of momentum and conservation of energy principles.
First, we can determine the total system (two carts) momentum before the collision:
P1 = m1v1 + m2v2, where m1 and m2 are the masses of the carts and v1 and v2 are the velocities.
Plugging in the values, we get:
P1 = (0.18 kg)(0.1 m/s) + (0.09 kg)(0.15 m/s) = 0.03 kg·m/s
After the collision, the carts stick together and move with a common velocity, vf. To find vf, we use the conservation of momentum equation:
P1 = P2 = (m1+m2)vf
Plugging in the values again, we get:
0.03 kg·m/s = (0.18 kg + 0.09 kg)vf
Solving for vf, we get vf = 0.03 kg·m/s / (0.18 kg + 0.09 kg) = 0.1 m/s
Therefore, the speed of the carts after the collision is 0.1 m/s.
To calculate the amount of kinetic energy lost during the collision, we can use the conservation of energy equation:
KEi = KEf + ΔKEinternal, where KEi is the initial kinetic energy, KEf is the final kinetic energy, and ΔKEinternal is the change in internal kinetic energy (i.e. the energy lost during the collision).
Since there is no external work done on the system, the initial kinetic energy is equal to the final kinetic energy. Therefore, we can rewrite the equation as:
KEi = KEf + ΔKEinternal = 0
Solving for ΔKEinternal, we get:
ΔKEinternal = KEi - KEf = (½)mvi2 - (½)mvf2 = (½)(0.18 kg)(0.1 m/s)2 - (½)(0.18 kg + 0.09 kg)(0.1 m/s)2 = -0.6 mJ
Therefore, after the collision, 0.6 mJ of kinetic energy is converted into internal energy in the system. This is why the carts stick together after the collision instead of bouncing off each other.
