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 front window. a) Compared t... 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 front window. a) Compared to the force that acts on the bug, how much force acts on the bus? (more) (the same) (less) b) Although the momentum of the bus is very large compared to the momentum of the bug, the change in momentum of the bus compared to the change in momentum of the bug is (more) (the same) (less) c) Which experiences the greater acceleration (HINT: think of Newton’s 2nd Law)? (bus) (both the same) (bug) d) Which, therefore, suffers the greater damage? (bus) (both the same) (the bug of course!)
Understand the Problem
The question explores the concepts of force, momentum, and acceleration as they relate to a collision between a bus and a bug. It requires understanding Newton's laws of motion, particularly the second and third laws, to compare the forces, changes in momentum, and accelerations experienced by the bus and the bug during the impact.
Answer
a) The same, b) The same, c) Bug, d) The bug of course!
Here are the answers to your questions:
a) The same b) The same c) Bug d) The bug of course!
Answer for screen readers
Here are the answers to your questions:
a) The same b) The same c) Bug d) The bug of course!
More Information
Here's the breakdown:
a) Force: According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. Therefore, the force exerted by the bug on the bus is equal in magnitude to the force exerted by the bus on the bug.
b) Change in Momentum: The change in momentum is the same for both. Momentum is conserved in a closed system. The bus and bug form a closed system. Therefore, the change in momentum of the bug is equal in magnitude but opposite in direction to the change in momentum of the bus.
c) Acceleration: Acceleration is inversely proportional to mass (Newton's Second Law: F=ma). Since the force is the same on both the bug and the bus, but the bug has a much smaller mass, the bug experiences much greater acceleration.
d) Damage: Because the bug experiences greater acceleration, it suffers greater damage.
Tips
A common mistake is thinking the bus experiences a greater force due to its size, but Newton's Third Law states the force is equal. Also, many people confuse momentum and change in momentum. Although the bus has far greater momentum, the change in momentum is equal to that of the bug.
Sources
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