A. be greater for the bug
B. be greater for your car
C. depend on wind speed
D. be the same for the bug and the car
While driving down the highway a bug splatters into your windshield. The change in momentum would _______.?
depends on the size of the bug.
While driving down the highway a bug splatters into your windshield. The change in momentum would _______.?
You may not realize this but this is actually a question about Newton鈥檚 third law. And, in my 20 years of experience as a teacher guess which law I have found is the most misunderstood.
So, let us look at this question. Change in momentum means that either the mass or the velocity of an object changes. In the case here we presume that neither the bug nor the car lost any mass. That leaves only the velocity that changes.
To change velocity a force is required. That force has to be applied for a certain amount of time. The product of force and time (Ft) is called 鈥榠mpulse鈥? We can make an equation here: Ft = (change in) mv. If I could I would have put a triangle, which is the symbol that means 鈥榗hange in鈥? in front of the 鈥榤v鈥?
Newton鈥檚 third law states that whenever a force is applied to one object, another object must apply an equal force in the opposite direction. This means that the force applied by the car to the bug must be exactly equal to the force applied by the bug to the car, and, of course, the forces are in opposite directions.
If we agree that the time during which these forces were applied is the time it took for the bug and all its parts to come to a stop, then we can also agree that the time during which these forces were applied is the same for the bug as for the car.
This means that Ft (the impulse) for the car equals the Ft (the impulse) for the bug. And, if the impulses are equal so, therefore, is the change in momentum for both the bug and the car.
While it is easy to see that the Ft for the bug and car must be the same, a lot of people have a difficult time understanding how the change in momentum for the bug and car can be equal. So let鈥檚 look at the momentum of the car and bug more carefully.
When the bug hits the car the change in the mass of the car is zero and the change in the car鈥檚 velocity is, well, very close to zero too! But, it really is not zero. It鈥檚 close, I agree, but not zero. So, while the car has a large mass it has a very small change in velocity. Thus, for the car the change in momentum is nearly zero.
Now, look at the change in momentum of the bug. The bug鈥檚 tiny mass actually has a very large change in velocity. A large change in velocity multiplied by the very tiny mass means that the change in momentum of the bug is very small as well.
Here is how: to calculate the velocity of the bug you have to know both the bug鈥檚 speed and direction. And, we have to calculate this twice, once before the collision and again after the collision. When we get both numbers we put them into this equation: change in momentum = p2 鈥?p1. Which means, 鈥榗hange in momentum鈥?equals the 鈥榮econd momentum鈥?minus the 鈥榝irst momentum鈥?
Since the directions of the two momentums are opposite we are effectively adding the two momentums together. Since we agreed that the change in mass is zero we are really adding the two velocities of the bug, the velocity before the collision and the velocity after the collision. (Remember that when you subtract a negative number you are actually adding.)
