Question

The windshield of a speeding car hits a hovering insect. Consider the time interval from just before the car hits the insect to just after the impact. (a) For which choice of system is the change of momentum zero? (b) Is the magnitude of the change of momentum of the bug bigger than, the same as, or smaller than that of the car? (c) Is the magnitude of the change of velocity of the bug bigger than, the same as, or smaller than that of the car?

Short answer

a) Thecar and insect system is the change of momentum zero.

b) The magnitude of thechange of momentum of the bug is the same as the car.

c) The magnitude of thechange of velocity of the bug is bigger than that of the car

Step-by-step solution

Significance of Conservation of momentum

The quantity termed momentum, which describes motion, never changes in an isolated collection of objects, according to a general law of physics.

Applying the law of conservation of momentum

(a)

Here, a car and hovering insect is a system where the change of momentum is zero.

$∆P_c=-∆P_i...................................\left(1\right)$

Where $∆P_c$is the change of momentum of a car, $∆P_i$is the change of momentum of an insect.

Checking change of momentum of car and bug

(b)

As per the law of conservation of momentum, the change of momentum of the car is the same as the change of momentum of the bug, as shown in equation (1).

Checking magnitude of change of velocity of car and bug 

(c)

The equation of change momentum is given as,

$$\begin{gathered} ∆P=m\left(v_2-v_1\right) \\ ∆P=m∆v \end{gathered}$$

As

role="math" localid="1653981898191" $$\begin{gathered} M\square m \\ Weget \\ ∆v\square ∆v \end{gathered}$$

Where M is the mass of the car, m is the mass of the bug, V is the speed of the car, and v is the speed of the bug.

As per the law of conservation of momentum, the magnitude of the change of velocity of the bug is going to be bigger because the bug is going to have a much smaller mass as compared to a car

Thus, the magnitude of the change of velocity of the bug is bigger than that of the car.