Suppose a bug spatters upon your windshield as you drive down the road. Which sustains the greater change of momentum?
A) the bug
B) insufficient information
C) both the same
D) the car
The correct answer and explanation is:
The correct answer is C) both the same.
Explanation:
Momentum is defined as the product of an object’s mass and its velocity. When two objects collide, the law of conservation of momentum states that the total momentum before and after the collision remains the same in an isolated system. Additionally, Newton’s third law states that for every action, there is an equal and opposite reaction. This means the forces that the two objects exert on each other are equal in magnitude but opposite in direction.
When a bug hits a car’s windshield, the bug experiences a sudden change in velocity, usually going from its initial speed to nearly zero relative to the car. The car also experiences an impact force from the bug. Even though the mass of the car is much larger than the bug’s mass, the change in velocity of the car is extremely small due to its large mass. The bug, with very small mass, undergoes a very large change in velocity. The momentum change of each object is the product of mass and velocity change.
Because the forces are equal and opposite, the magnitude of the change in momentum experienced by the bug and the car are equal. The difference lies in how noticeable this change is. The bug undergoes a large change in velocity, resulting in a large relative momentum change for its small mass. The car undergoes an imperceptibly small change in velocity but with a much larger mass, so the product of mass and velocity change (momentum change) is the same as that of the bug but in the opposite direction.
In summary, despite the bug being squashed and the car hardly slowing down, both sustain the same magnitude of momentum change due to Newton’s third law and the conservation of momentum principles.