car 1 is moving at 10 m/s and hits car 2 if they have a perfectly elastic collision and the masses are 1700 kg and 3000kg respectively what is the final velocity of the second car ?
To find the final velocity of the second car after the collision, we can use the principle of conservation of momentum.
Conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. In this case, the two cars make up the isolated system.
The momentum of an object is defined as the product of its mass and velocity. Thus, the initial momentum of car 1 is given by:
Initial momentum of car 1 = mass of car 1 * velocity of car 1 = 1700 kg * 10 m/s = 17,000 kg.m/s
Similarly, the initial momentum of car 2 is given by:
Initial momentum of car 2 = mass of car 2 * velocity of car 2 = 3000 kg * 0 m/s (since car 2 is initially at rest) = 0 kg.m/s
Since it is given that the collision is perfectly elastic, the total momentum before and after the collision remains the same. Therefore, the initial momentum of the system is equal to the final momentum of the system after the collision:
Initial momentum of system = Final momentum of system
Therefore,
17,000 kg.m/s + 0 kg.m/s = Final momentum
The final momentum of the system is the sum of the momenta of the two cars after the collision. Let's assume the final velocity of car 1 is V1 and the final velocity of car 2 is V2.
Final momentum = mass of car 1 * V1 + mass of car 2 * V2
Substituting the masses and rearranging the equation, we get:
17,000 kg.m/s = 1700 kg * V1 + 3000 kg * V2
Since the collision is perfectly elastic, we can also use the principle of conservation of kinetic energy, which states that the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision.
The initial kinetic energy of the system is given by:
Initial kinetic energy = (1/2) * mass of car 1 * (velocity of car 1)^2 + (1/2) * mass of car 2 * (velocity of car 2)^2
= (1/2) * 1700 kg * (10 m/s)^2 + (1/2) * 3000 kg * (0 m/s)^2
= 85,000 J
The final kinetic energy of the system can be written as follows:
Final kinetic energy = (1/2) * mass of car 1 * (final velocity of car 1)^2 + (1/2) * mass of car 2 * (final velocity of car 2)^2
= (1/2) * 1700 kg * V1^2 + (1/2) * 3000 kg * V2^2
Since the collision is perfectly elastic, the initial kinetic energy is equal to the final kinetic energy:
Initial kinetic energy = Final kinetic energy
Substituting the values, we get:
85,000 J = (1/2) * 1700 kg * V1^2 + (1/2) * 3000 kg * V2^2
We now have two equations:
17,000 kg.m/s = 1700 kg * V1 + 3000 kg * V2
85,000 J = (1/2) * 1700 kg * V1^2 + (1/2) * 3000 kg * V2^2
Solving these two equations simultaneously will give us the values of V1 and V2, which represent the final velocities of car 1 and car 2 after the collision.