When it crashes into a bridge support that does not move, a car goes from 105 km/hkm/h to 0 in 1.23 mm.Part AWhat is the impulse delivered to the 70-kgkg driver by the seat belt, assuming the belt makes the driver's motion identical to the car's motion? Assume that the initial direction of motion of the car is the positive direction.Express your answer to two significant figures and include the appropriate units.
Question
When it crashes into a bridge support that does not move, a car goes from 105 km/hkm/h to 0 in 1.23 mm.Part AWhat is the impulse delivered to the 70-kgkg driver by the seat belt, assuming the belt makes the driver's motion identical to the car's motion? Assume that the initial direction of motion of the car is the positive direction.Express your answer to two significant figures and include the appropriate units.
Solution
To solve this problem, we need to first convert the speed from km/h to m/s, then calculate the change in momentum (which is the impulse), and finally apply Newton's second law.
Step 1: Convert speed from km/h to m/s 105 km/h = 105,000 m/3600 s = 29.17 m/s
Step 2: Calculate the change in momentum (impulse) The initial momentum of the driver is mass * velocity = 70 kg * 29.17 m/s = 2041.9 kgm/s. The final momentum of the driver is 0 (since the car and the driver come to a stop). Therefore, the change in momentum (or impulse) is final momentum - initial momentum = 0 - 2041.9 kgm/s = -2041.9 kg*m/s.
Step 3: Apply Newton's second law According to Newton's second law, the force exerted on the driver by the seat belt is equal to the rate of change of momentum (impulse) divided by the time it takes for the change to occur. However, the problem does not ask for the force, but the impulse, which we have already calculated.
So, the impulse delivered to the 70-kg driver by the seat belt is -2041.9 kg*m/s. The negative sign indicates that the impulse is in the opposite direction of the initial motion of the car.
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