Question

5. {Chapter 6 Suppose you are traveling down the road in your car at highway speeds on a nice
summer day and the momentum of an unlucky bug is suddenly changed as it splatters onto your front
window
a. How do the forces that act on the bug and the car compare? Explain.
b. How does the impulse on the bug compare to the impulse on the car? Explain in detail.
c. Which object (bug or car) undergoes the greatest change in momentum? Explain.
d. What type of collision is this defined as? Explain.

Answer 1

Answer:

a) The 2 forces are equal

b) The impulse is the same

c) The change in momentum is the same

d) Inelastic

Explanation:

a)

According to Newton's third law of motion:

"When an object A exerts a force on an object B (action force), then object B exerts an equal and opposite force on object A (reaction force)"

In this problem, we can identify:

- The car as object A

- The bug as object B

Therefore:

- The force exerted by the car on the bug is the action force

- The force exerted by the bug on the car is the reaction force

According to Newton's third law of motion, these two forces are equal in magnitude, and opposite in direction.

b)

The impulse exerted on an object is equal to the product between the force exerted on it and the time taken:

$I=F\Delta t$

where

I is the impulse

F is the force exerted

$\Delta t$ is the time during which the force is applied

In this problem:

- The force F exerted on both the car and the bug is the same (according to what we said in part a)

- The time interval $\Delta t$ is the same for the two objects

Therefore, the impulse exerted on the bug is the same as the impulse on the car.

c)

The change in momentum of an object is defined as:

$\Delta p = m \Delta v$ (1)

where

m is the mass of the object

$\Delta v$ is the change in velocity of the object

However, according to the impulse theorem, the change in momentum of an object is also equal to the impulse it has experienced:

$\Delta p = I$

Therefore, since the impulse experienced by the bug and the car is the same (part b), this means that the change in momentum of the bug and the car is the same (and so by looking at eq.(1), we can conclude that the bug will experience a larger change in velocity, since its mass is smaller than that of the car).

d)

There are two types of collision:

• Elastic collision: in an elastic collision, both the total momentum and the total kinetic energy of the system are conserved
• Inelastic collision: in an inelastic collision, only the total momentum is conserved, while the total kinetic energy is not (part of the energy is converted into thermal energy due to the presence of friction forces)

In particular, inelastic collision occurs when the two objects stick together after the collision.

In this situation, we see that the bug and the car stick together after the collision: this means that the total kinetic energy of the system is not conserved, and therefore, this is an example of inelastic collision.