Consider two identical cars (1400 Kg) moving along a road at a speed of 20 m/s.
ID: 1991254 • Letter: C
Question
Consider two identical cars (1400 Kg) moving along a road at a speed of 20 m/s. The blue car is stopped by the car’s brakes in 25 m while the green car is stopped by a concrete barrier in 1.2 m. The drivers of the two cars are the same mass (70 kg). The driver of the blue car is stopped by the seat belt in the same motion as the car. The driver of the green car is stopped by a seat belt/air bag in 0.150 sec.Compare the change in momentum of each car.
Compare the impulse received in stopping for each driver.
Calculate the average force exerted on each driver in stopping.
Explain whether a larger mass driver in the green car would experience a larger stopping force relative to their weight if they are stopped in the same time. (i.e. if they had twice the mass would they feel twice the force, or less, or more?)
Explanation / Answer
a) as the mass of the car and the respective drivers are same and each car has the same speed initially , thus it concludes that both of them will have same change in momentum( mass x velocity) . initially it is 1470 x 20 = 29400 kgm/s and when they brake it drops to zero.
so impulse = change in momentum = 29400 kgm/s for both the cars.
b) avg force exerted for the blue driver = ma, where a is the decleration of his body due to opposing force by seat belt. the rate of decleration will be same as the car as both are stopped at same time and both have same speed initially.
a= v2/ 2s, here s= 25m , v= 20 m/s, thus a= 8 m/s2 rate of decleration.
so force = 70 x 8 N= 560 N on blue driver
c) for green driver we can calculate force exerted by change in momentum per unit time.
force = [( 70 x 20)/ 0.015] N = 93333.33 N on green driver
we see the time taken for green car to stop is irrelevant here. actually car stops sooner than the driver.
d) obviously, a larger mass will experience larger force for it to stop since the momentum of the larger mass body will be higher( so will be the change in momentum). that is the reason why a truck causes more damge to a car in case of an accident because its momentum is high by virtue of its mass so its exerts greater force.