A 1200 kg car is traveling at 3.0 m/s and strikes a wall. The car bounces off the wall with a velocity of 4.0 m/s in the opposite direction. If the car is in contact with the wall for 0.10 seconds, then the magnitude of the average force of the wall on the car is
Question
A 1200 kg car is traveling at 3.0 m/s and strikes a wall. The car bounces off the wall with a velocity of 4.0 m/s in the opposite direction. If the car is in contact with the wall for 0.10 seconds, then the magnitude of the average force of the wall on the car is
Solution
To solve this problem, we need to use the formula for force, which is the change in momentum divided by the change in time.
Step 1: Calculate the initial momentum of the car. Momentum is mass times velocity. So, the initial momentum is 1200 kg * 3.0 m/s = 3600 kg*m/s.
Step 2: Calculate the final momentum of the car. The car is moving in the opposite direction after hitting the wall, so its velocity is -4.0 m/s. The final momentum is 1200 kg * -4.0 m/s = -4800 kg*m/s.
Step 3: Calculate the change in momentum. This is the final momentum minus the initial momentum. So, the change in momentum is -4800 kgm/s - 3600 kgm/s = -8400 kg*m/s.
Step 4: Calculate the force. Force is the change in momentum divided by the change in time. So, the force is -8400 kg*m/s / 0.10 s = -84000 N.
The negative sign indicates that the force is directed in the opposite direction of the initial motion of the car. However, since the problem asks for the magnitude of the force, we can ignore the negative sign. So, the magnitude of the average force of the wall on the car is 84000 N.
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