Suppose you are traveling in a bus at highway speed on a nice summer day and the momentum of an unlucky bug is suddenly changed as it splatters onto the from window.
a. Compared to the force that acts on the bug, how much force acts on the bus? (more) (the same) (less)
b. The time of impact is the same for both the bug and the bus. Compared to the impulse on the bug, this means the impulse on the bus is (more) (the same) (less).
c. Although the momentum of the bus is very large compared to the momentun of the bug, the change in momentum of the bus, compared to the change of momentun, of the bug is (more) (the same) (less).
d. Which undergoes the greatest acceleration? (bus) (both the same) (bug)
e. Which therefore, suffers the greater damage? (bus) (both the same (the bug of course!)
1. the same
a. The force that acts on the bug is the same as the force that acts on the bus. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So when the bug splatters onto the front window of the bus, the force between the bug and the window is equal in magnitude but opposite in direction to the force between the window and the bug.
b. The impulse experienced by an object is equal to the change in momentum it undergoes. Since the force acting on the bug and the bus is the same (as explained in part a), and the time of impact is also the same, the impulse on both the bug and the bus will be the same. Therefore, the impulse on the bus is the same as the impulse on the bug.
c. The change in momentum of an object is equal to the impulse it receives or the force multiplied by the time of impact. Since the impulse on the bug and the bus is the same (as explained in part b), and the mass of the bus is much larger than the mass of the bug, the change in momentum of the bug will be significantly greater than the change in momentum of the bus. Therefore, the change in momentum of the bug is more than the change in momentum of the bus.
d. According to Newton's second law of motion (F = ma), the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. As the mass of the bug is much smaller than the mass of the bus, and the force is the same (as explained in part a), the bug will experience a much greater acceleration than the bus. Therefore, the bug undergoes the greatest acceleration.
e. When a collision occurs, the damage suffered by an object depends on the magnitude of the forces involved. Since the bug experiences a greater acceleration (as explained in part d), it will experience a larger force during the collision with the window, leading to greater damage. Therefore, the bug suffers the greater damage.
Jeje
For (a), consider Newton's third law.
For (d), consider accleration in the form of the equation:
a = (Vf - Vi) / t
where a is acceleration, Vf is final veloctiry, Vi is initial velocity, and t is the elapsed time.
Or more simply, consider acceleration to be a change in velocity: which had a greater change in velocity, the bug or the bus?