A 2170 kg car moving east at 10.5 m/s collides with a 3230 kg car moving east. The cars stick together and move east as a unit after the collision at a velocity of 6.00 m/s.
a) What is the velocity of the 3230 kg car before the collision?
Answer in units of m/s.
016 (part 2 of 2) 10.0 points
b) What is the decrease in kinetic energy during the collision?
To solve part a) we need to apply the conservation of momentum principle, which states that the total momentum before the collision is equal to the total momentum after the collision.
Given:
Mass of car 1 (m1) = 2170 kg
Velocity of car 1 (v1) = 10.5 m/s
Mass of car 2 (m2) = 3230 kg
Velocity of the combined cars (vf) = 6.00 m/s
Using the principle of conservation of momentum, we can write the equation as:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Substituting the given values, we have:
(2170 kg * 10.5 m/s) + (3230 kg * v2) = (2170 kg + 3230 kg) * 6.00 m/s
Simplifying the equation:
22785 kg·m/s + (3230 kg * v2) = 5400 kg * 6.00 m/s
Now, isolate v2 to solve for the velocity of the 3230 kg car before the collision:
3230 kg * v2 = (5400 kg * 6.00 m/s) - 22785 kg·m/s
3230 kg * v2 = 32400 kg·m/s - 22785 kg·m/s
3230 kg * v2 = 9605 kg·m/s
v2 = 9605 kg·m/s / 3230 kg
v2 ≈ 2.97 m/s
Therefore, the velocity of the 3230 kg car before the collision is approximately 2.97 m/s.
To solve part b):
The decrease in kinetic energy during the collision can be calculated by finding the difference in kinetic energy before and after the collision. The formula for kinetic energy is:
KE = 0.5 * mass * velocity^2
Before the collision, the combined kinetic energy of the cars is:
KE_before = 0.5 * (2170 kg + 3230 kg) * 10.5 m/s^2
Simplifying,
KE_before = 0.5 * 5400 kg * (10.5 m/s)^2
KE_before = 0.5 * 5400 kg * 110.25 m^2/s^2
KE_before = 297675 J
After the collision, the kinetic energy of the combined cars is:
KE_after = 0.5 * (2170 kg + 3230 kg) * 6.00 m/s^2
Simplifying,
KE_after = 0.5 * 5400 kg * (6.00 m/s)^2
KE_after = 0.5 * 5400 kg * 36 m^2/s^2
KE_after = 97200 J
Finally, the decrease in kinetic energy is:
ΔKE = KE_before - KE_after
ΔKE = 297675 J - 97200 J
ΔKE ≈ 200,475 J
Therefore, the decrease in kinetic energy during the collision is approximately 200,475 Joules.