Two cars are on a collision course. One is going right 18 m/s and has a mass of 860kg. The other is going left at 24 m/s and has a mass of 840 kg.
1. Find the total initial momentum of the two cars
For this question I did
first car: 860(18) = 15480
second car: 840(-24) = -15480
15480 - - 15480 = 36000 N•s
2. The cars collide and stick to each other. Find the velocity immediately after the collision.
3. What's the change in kinetic energy of the two-car system?
to find the total you add, not subtract.
first car = 15480 yes
second car = -20160 so disagree
p = 15480-20160 = - 4680
total mass = 1700 kg
1700 v = -4680
v = - 2.75 m/s
(1/2)860(18^2)+(1/2)840(24^2)-(1/2)(1700)(2.75)^2
To find the total initial momentum of the two cars, you correctly used the formula for momentum, which is mass times velocity. Let's look at the calculations step by step:
1. Total initial momentum:
- For the first car: Momentum = mass × velocity = 860 kg × 18 m/s = 15480 kg·m/s (to be precise, the units are kg·m/s, not N·s)
- For the second car: Momentum = mass × velocity = 840 kg × (-24 m/s) = -20160 kg·m/s
- To find the total initial momentum, you correctly subtracted the momentum of the second car from that of the first car: 15480 kg·m/s - (-20160 kg·m/s) = 35640 kg·m/s. (Please note that you made a minor calculation error here, as the correct result is 35640 kg·m/s, not 36000 kg·m/s.)
2. After the collision, the two cars stick together, meaning they move as one combined body. To find the velocity immediately after the collision, you need to apply the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision:
Total initial momentum = Total final momentum
Since the cars stick together, their masses are combined:
Total mass = mass of the first car + mass of the second car = 860 kg + 840 kg = 1700 kg
Let the velocity after the collision be V. Then, the momentum after the collision is:
Total final momentum = Total mass × V = 1700 kg × V
Setting the initial and final momentum equal to each other:
35640 kg·m/s = 1700 kg × V
Now, you can solve for V:
V = 35640 kg·m/s / 1700 kg ≈ 20.94 m/s
Therefore, the velocity immediately after the collision is approximately 20.94 m/s.
3. To find the change in kinetic energy of the two-car system, you need to calculate the initial and final kinetic energy separately, and then find the difference:
Initial kinetic energy is given by the formula: KE = 0.5 × mass × velocity^2
- For the first car: KE = 0.5 × 860 kg × (18 m/s)^2 ≈ 139,320 J
- For the second car: KE = 0.5 × 840 kg × (-24 m/s)^2 ≈ 241,920 J
Total initial kinetic energy = KE of the first car + KE of the second car ≈ 139,320 J + 241,920 J ≈ 381,240 J
After the collision, the two cars stick together, so the final kinetic energy is the sum of their masses times the square of the final velocity:
Total final kinetic energy = 1700 kg × (20.94 m/s)^2 ≈ 724,218 J
The change in kinetic energy is then:
Change in kinetic energy = Total final kinetic energy - Total initial kinetic energy
= 724,218 J - 381,240 J ≈ 342,978 J
Therefore, the change in kinetic energy of the two-car system is approximately 342,978 J.