A) To find the velocity of the 3170 kg car before the collision, we can use the conservation of momentum principle. The principle states that the total momentum of a system remains constant if no external forces act on the system. In this case, the two cars form a closed system and no external forces are acting on them.
Given:
m1 = 2110 kg (mass of first car)
v1 = 10.2 m/s (velocity of first car)
m2 = 3170 kg (mass of second car)
v2f = 5.03 m/s (velocity of both cars after collision)
Using the conservation of momentum formula:
m1v1 + m2v2 = (m1 + m2)vf
2110 kg * 10.2 m/s + m2v2 = (2110 kg + 3170 kg) * 5.03 m/s
21632.2 + m2v2 = 5234.3 + 5.03 m/s
21632.2 = 5234.3 + m2v2
subtracting 5234.3 from both sides
16397.9 = m2v2
dividing both sides by m2
v2 = 16397.9/3170
v2 = 5.15 m/s
The velocity of the 3170 kg car before the collision is 5.15 m/s
B) To find the decrease in kinetic energy during the collision, we can use the conservation of energy principle. The principle states that the total energy of a closed system remains constant.
Given:
m1 = 2110 kg (mass of first car)
v1 = 10.2 m/s (velocity of first car)
m2 = 3170 kg (mass of second car)
v2 = 5.15 m/s (velocity of second car before collision)
vf = 5.03 m/s (velocity of both cars after collision)
Initial kinetic energy of first car = 1/2 * m1 * v1^2 = 1/2 * 2110 kg * 10.2 m/s^2 = 11096.2 J
Initial kinetic energy of second car = 1/2 * m2 * v2^2 = 1/2 * 3170 kg * 5.15 m/s^2 = 8073.36 J
Initial total kinetic energy = 11096.2 J + 8073.36 J = 19169.56 J
Final kinetic energy of both cars = 1/2 * (m1 + m2) * vf^2 = 1/2 * (2110 kg + 3170 kg) * 5.03 m/s^2 = 16100.57 J
Decrease in kinetic energy = Initial total kinetic energy - Final kinetic energy = 19169.56 J - 16100.57 J = 3068.99 J
The decrease in kinetic energy during the collision is 3068.99 J