Analyze each of the following collisions involving bumper cars. Case 1: Your car

Question

Analyze each of the following collisions involving bumper cars.
Case 1: Your car (total mass 60 kg) is moving at 4.4 m/s when it smashes into a stationary car (total mass 62 kg), which bounces off. After the collision, your car is still moving forward at 1.2 m/s. Find the speed of the car with which you collided.
(in m/s)

Case 2: This time, your car (total mass 60 kg) is moving at 3.6 m/s when it smashes into a the back end of another car (total mass 82 kg) moving in the same direction as you but at the slower speed of 1.9 m/s. Somehow, your bumpers lock and you move off together. Find the speed of the car to which you are now connected.
(in m/s)

Case 3: Now, your car (total mass 60 kg) is moving in the positive direction at 3.3 m/s and you are racing toward a head-on collision. The car approaching you has a mass of 81 kg and is moving in the opposite direction at 4.4 m/s. After the collision you find yourself moving backward at 2.1 m/s. What is the speed of the other car?
(in m/s)

Case 4: OK, now you're all mixed up and you slam into the wall with your car (total mass 60 kg) moving at 4.0 m/s. You bounce straight back at 2.9 m/s and somehow determine that the time of contact with the wall was 28.7 ms. What is the magnitude of the force that was exerted on your car?
(in N)

Explanation / Answer

Here ,

1)

let the speed is v

using coneravtion of momentum

60 * 4.4 = 1.2 * 60 + 62 * v

v = 3.1 m/s

the speed of car is 3.1 m/s

2)

let the speed of cars is v

using conservation of momentum

60 * 3.6 + 82 * 1.9 = (60 + 82) * v

v = 2.62 m/s

the speed of cars is 2.62 m/s

3)

let the speed of other car is v

3.3 * 60 - 81 * 4.4 = - 2.1 * 60 + 82 * v

v = -0.4 m/s

the speed of other car is 0.4 m/s in negative direction

4)

magnitude of force = change in momentum/time

magnitude of force = 60 *(4 - (-2.9))/.0287

magnitude of force = 14425 N

the magnitude of force acting on car is 14425 N

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