Answer to Question #104311 in Classical Mechanics for Arjo

Question

1. Two identical cars, mass 1.0 tonnes, traveling at 30.0 kph in opposite directions, collide. During the collision, the front of each the cars crumples and becomes 15 cm shorter. So let's say that each car decelerates to rest over 15 cm. What is the magnitude of the average acceleration?

a) Magnitude of average acceleration?
b) Magnitude of average external force?

2. In the car that decelerates from 30 kph to rest over 15 cm are two 70 kg passengers. One wears a seat belt and decelerates over 30 cm (with respect to the ground) (two significant figures). The other is not wearing a seat belt and decelerates over 5 cm* (with respect to the ground). What are the magnitudes of the average external forces acting on the two passengers during their decelerations? (Careful with significant figures: do both answers have the same precision?)

a) With a seat belt? _____ kN
b) Without a seat belt? _____ kN

Answer 1

1.

Converting 30km/hr into m/s

$u=\dfrac{25}{3}\ m/s \\v=0$

$v^2-u^2=2aS$

$-625/9=2\times a\times0.15$

$a=-231.5 m/s^2$

$F=ma=1000\times231.5 =231.5 k N$

2.

$u=\dfrac{25}{3}\ m/s \\v=0$

$v^2-u^2=2aS\\$

For the one person without seat belt S=0.15 m and for the men with the seat belt S=0.30 m

$a_1=- 115.75m/s^2\\a_2=-231.5m/s^2\\$

Force = ma

$F_1=-115.75\times70=8102.5 N\\F_2=-231.5\times70=16205 N$