Do Forces, Impulse, and Momentum Change Equally in a Collision?

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In summary,a. The bug and the windshield have the same impact forces, and the impulse is the same.b. The bug's momentum is greater after the collision, due to the change in velocity.c. The change in speed is the same.d. The momentum of the bug is greater.
  • #1
mattfelner
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I'm a bit stumped on the following, as I'm not sure how to distinguish between the following. Thanks to all those who shed some light.

A bug and a windshield of a fast moving car collide. Indicate and explain whether each statement is true or false.

a. The forces of impact on the bug and the windshield are the same size.
True? I suppose because of Newton's third law the force would be indentical.

b. The impulse on the bug and the car are the same size.
I'm a bit confused. I know FxT=Impulse=Change In Momentum. I would suppose that the big's momentum loss would be greater, but I'm only speaking from a practical/obvious POV.

c. The change in speed of the bug and the car is the same
Falso. Perhaps their related somehow, but I know that's false.

d. The changes in momentum of the bug and the car are the same size?
I would say true, because wouldn't the system after the collision have to somehow equal the momentum of the two separate systems before it? I assume this could only be achieved if the momentum's were related.

Thank you to all
 
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  • #2
a) I think Newton's Third Law is a good way to argue that. The force of the bug on the windshield must be the same magnitude as the force of the windshield on the bug.

b) Impulse is change in momentum. Since linear momentum is absolutely conserved, and since we are considering only the bug and the car, whatever momentum one of them loses must be gained by the other one - otherwise, there'd be a net gain or loss.

c) We know the change in momentum is the same for the two, so the change in the product of the mass times the velocity must be the same for the two. Since the mass of the windshield and the bug are both constant (a good assumption for the windshield, probably not for the bug, but let's not get disgusting here...), the difference must come in the change in velocity. Since the mass of the bug is (presumably, unless you live in Florida) much less than the mass of the windshield, the change in velocity of the bug must be correspondingly greater.

The question, however, doesn't ask about velocity but speed, and this could make a difference - I'll leave you to puzzle out why it doesn't.

d) Already answered in part b.
 
  • #3
thanks so much
 

What is momentum?

Momentum is a physics concept that refers to the quantity of motion an object has. It is a product of an object's mass and velocity. In simple terms, an object with a larger mass and higher velocity will have a greater momentum.

How is momentum calculated?

The formula for momentum is p = m x v, where p is momentum, m is mass, and v is velocity. Momentum is measured in units of kilogram-meters per second (kg*m/s).

What is the law of conservation of momentum?

The law of conservation of momentum states that the total momentum of a closed system remains constant. This means that in a collision between two objects, the total momentum before and after the collision will be the same. In other words, momentum cannot be created or destroyed, only transferred between objects.

How does momentum relate to Newton's laws of motion?

Momentum is closely related to Newton's laws of motion. Newton's first law states that an object will remain at rest or in motion unless acted upon by an external force. This means that an object will maintain its momentum unless an external force is applied to it. Additionally, Newton's second law, which states that force equals mass times acceleration, can be rewritten as F = ma = m x (Δv/Δt) = m x (change in momentum). This shows that force and momentum are directly related.

Why is momentum important?

Momentum is important because it helps us understand how objects move and interact with each other. It also has practical applications, such as in sports and transportation, where momentum is used to increase speed and efficiency. Additionally, the conservation of momentum is a fundamental principle in physics and is used in various fields, such as mechanics and thermodynamics.

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