Question

1.How does inertia affect a person who is not wearing a seatbelt during a collision?

Answer 1

1) Inertia is the tendency of an object in motion to keep moving in straight line with constant velocity, or to remain at rest if the object was initially at rest. A person in a moving car is moving together with the car, so his inertia is his tendency to keep moving with constant velocity. During a collision, therefore, if the person is not wearing a seatbelt, he will continue to move forrward due to his inertia (while the car will stop due to the crash), and eventually he will hit the windscreen of the car.

2) The more the kinetic energy, the larger the distance needed to stop the car. In fact, calling vi the initial speed of the car, vf the final velocity (which is zero, because we want the car to stop), a the deceleration of the car and S the stopping distance, we can use the following relationship:
$v_f^2-v_i^2=2aS$
Since vf=0, we can rewrite the stopping distance as
$S=- \frac{v_i^2}{2a}$
The vehicle in the two situations is the same, so we see that the larger the initial velocity (which means more kinetic energy), the larger the stopping distance. In particular, in this case the velocity in the second situation (60 mph) is twice the velocity in the first situation (30 mph), so the stopping distance in the second situation is $2^2=4$ times larger than in the first situation.

3) The large vehicle has a larger mass than the small vehicle, so it also has greater kinetic energy, which is given by:
$K= \frac{1}{2} mv^2$
where m is the mass of the car and v is its velocity. Due to its larger mass, the large vehicle has a greater inertia: it means it would take more effort to stop it. In fact, the work done to stop the car is W=FS, where F is the force of the brakes and S is the stopping distance. For the work-energy theorem, this work is equal to the initial kinetic energy of the car:
$\frac{1}{2} mv^2=FS$
If we assume the brakes in the two cars can apply the same force, then we see that the larger the mass m, the larger the stopping distance S.

4) The best way for the driver to prepare to enter the sharp curve is to decrease the velocity: in fact, decreasing the velocity (and so, decreasing the kinetic energy) will allow him to stay in the curved path more easily. If the car is going too fast, it will tend to go straight away (due to its inertia), and it won't be able to do the curve.

5) The damages produced by a car crash depend on the energy involved in the accident: the more the energy released, the larger the damages. In particular, since we are talking about kinetic energy
$K= \frac{1}{2} mv^2$
we see that the larger the mass of the vehicle, the greater the energy involved and so the larger the damages; and similarly, the larger the speed of the vehicle v, the greater the energy involved and so the larger the damages of the car crash.