Let\'s ride the bumper cars! Analyze each of the following collisions involving
ID: 1392688 • Letter: L
Question
Let's ride the bumper cars! Analyze each of the following collisions involving bumper cars.Case 1: Your car (total mass 85 kg) is moving at 4.8 m/s when it smashes into a stationary car (total mass 87 kg), which bounces off. After the collision, your car is still moving forward at 1.8 m/s. Find the speed of the car with which you collided.
Case 2: This time, your car (total mass 85 kg) is moving at 4.4 m/s when it smashes into a the back end of another car (total mass 64 kg) moving in the same direction as you but at the slower speed of 1.8 m/s. Somehow, your bumpers lock and you move off together. Find the speed of the car to which you are now connected.
Case 3: Now, your car (total mass 85 kg) is moving in the positive direction at 5.0 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 3.8 m/s. After the collision you find yourself moving backward at 4.0 m/s. What is the speed of the other car?
Case 4: OK, now you're all mixed up and you slam into the wall with your car (total mass 85 kg) moving at 3.9 m/s. You bounce straight back at 2.8 m/s and somehow determine that the time of contact with the wall was 23.6 ms. What is the magnitude of the force that was exerted on your car?
Let's ride the bumper cars! Analyze each of the following collisions involving bumper cars.
Case 1: Your car (total mass 85 kg) is moving at 4.8 m/s when it smashes into a stationary car (total mass 87 kg), which bounces off. After the collision, your car is still moving forward at 1.8 m/s. Find the speed of the car with which you collided.
Case 2: This time, your car (total mass 85 kg) is moving at 4.4 m/s when it smashes into a the back end of another car (total mass 64 kg) moving in the same direction as you but at the slower speed of 1.8 m/s. Somehow, your bumpers lock and you move off together. Find the speed of the car to which you are now connected.
Case 3: Now, your car (total mass 85 kg) is moving in the positive direction at 5.0 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 3.8 m/s. After the collision you find yourself moving backward at 4.0 m/s. What is the speed of the other car?
Case 4: OK, now you're all mixed up and you slam into the wall with your car (total mass 85 kg) moving at 3.9 m/s. You bounce straight back at 2.8 m/s and somehow determine that the time of contact with the wall was 23.6 ms. What is the magnitude of the force that was exerted on your car?
Explanation / Answer
(1) We apply the conservation of momentum
m1V1i+m2V2i = m1V1f + m2V2f where V1i is the velocity of car 1 initially or before collision, V2i is the velocity of car 2 i.e. stationary car before collision
Similarly f is the finanl velocity of car 1 and 2 after collision.
(85*4.8) +(87*0) = (85*1.8) +(87*V2f)
V2f = 2.93 m/s in the forward direction.
(2) apply same
(85*4.4) +(64*1.8) = (85+64)Vf
Vf = 3.28 m/s
(3) this time both have opposite direction
therefore (85*5) - (81*3.8) = -(85*4) +(81*V2f)
V2f = 5.64 m/s
(4) we know that
Impulse = Change in momentum
impulse = force*time = chnae in momentum
Force*(23.6*10-3) = (85*3.9) -(-85*2.8)
Force = 24.13 KN
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