How Is Velocity and Impulse Determined in a Two-Car Collision?

[cary5]

1. A car of mass 1500 kg traveling at 20 m/s hits a parked car of mass 2000
kg. The two cars stick together.
a. Find the velocity of the cars after the collision
b. Determine the impulse

i know that the momentom befor the collition is 30,000 how can i use that to find the Vf

 

[yinx]

use conservation of momentum to find the final velocity.

total initial momentum = total final momentum

 

[cary5]

use conservation of momentum to find the final velocity.

total initial momentum = total final momentum

ok so hier is wat i did
Pbefor=Pafte
30,000=3500*Vf
8.57=Vf

and since the change in p is the same befor and after then the change in p would be 0 and therefor the impuls would be 0

m i rite?

 

[yinx]

thats right

 

[rwisz]

a. To find the velocity of the cars after the collision, we can use the law of conservation of momentum, which states that the total momentum of a system remains constant before and after a collision. In this case, the initial momentum of the system is 30,000 kg*m/s (since the two cars are sticking together), and the final momentum is equal to the mass of the combined cars (3500 kg) multiplied by the final velocity (Vf). So we can set up the equation: 30,000 kg*m/s = 3500 kg * Vf. Solving for Vf, we get a final velocity of approximately 8.57 m/s.

b. The impulse can be calculated using the formula I = F * t, where I is the impulse, F is the average force applied during the collision, and t is the time over which the force was applied. We can find the average force by using the equation F = m * (Vf - Vi)/t, where m is the mass of the car (1500 kg) and Vi is the initial velocity (20 m/s). We know that the time of the collision is very short, so we can assume it to be around 0.1 seconds. Plugging in the values, we get F = 1500 kg * (8.57 m/s - 20 m/s)/0.1 s, which gives us an average force of approximately -114,300 N (the negative sign indicates that the force is in the opposite direction of the initial velocity). Therefore, the impulse is approximately -11,430 N*s, or 11,430 kg*m/s in the opposite direction of the initial velocity.