# Solve Negative/Positive Homework: Momentum-Impulse Theorem

• gold123456th
In summary, using the Momentum-Impulse Theorem with initial velocity of 100m/s and final velocity of 0m/s, the calculated average force of the bullet on the wearer is +1.00kN in the positive direction. However, the textbook's answer of -1.00kN suggests that the force acts against the bullet, implying that the force applied by the vest to stop the bullet is actually the average force imparted on the wearer.
gold123456th

## Homework Statement

Suppose a 6.00g bullet traveling at 100m/s strikes a bulletproof vest and comes to rest in about 600microseconds. What average force will it impart to the happy wearer?

## Homework Equations

Use the Momentum-Impulse Theorem
I took the initial direction of the bullet as the positive direction.

## The Attempt at a Solution

By using the momenum-impulse theorem, where vi = 100m/s and vf = 0m/s, I calculated the force to be -1.00kN. However, the negative sign tell me that this force is against the bullet, which should be the force that the vest apply to stop the bullet, not the force the bullet imparted to the wearer. The force that the bullet will impart on the wearer should be in the positive direction, which is the initial direction of the bullet. Therefore, I think the average force that the bullet imparted to the wearer should be +1.00kN. Nevertheless, the answer in the textbook for this question is -1.00kN, so I don't know whose right, the textbook or me.

I would say you were right.
If you take the direction of the bullet to be +ve then the force obviously acts in that direction on the victim.

I understand your confusion and the importance of clarifying this concept. The negative sign in the calculated force indicates that the force is in the opposite direction to the initial direction of the bullet, as you correctly pointed out. This means that the force is acting on the bullet, not on the wearer. However, according to Newton's third law, for every action, there is an equal and opposite reaction. Therefore, the force acting on the bullet is also the force that the bullet imparts on the wearer. So, both the textbook and you are correct in stating that the force imparted on the wearer is 1.00kN, but the negative sign indicates the direction of this force. It is important to note that the momentum-impulse theorem only calculates the force acting on the object, not the direction of the force. I hope this clarifies your understanding of this concept.

## What is the Momentum-Impulse Theorem?

The Momentum-Impulse Theorem is a physics principle that relates the change in momentum of an object to the impulse applied to it. It states that the impulse exerted on an object is equal to the change in momentum of the object.

## How do you solve negative/positive homework using the Momentum-Impulse Theorem?

To solve negative/positive homework using the Momentum-Impulse Theorem, you first need to identify the initial and final momentum of the object. Then, calculate the impulse by finding the difference between the final and initial momentum. Finally, use the Momentum-Impulse Theorem to solve for the unknown variable, such as mass or velocity.

## What are some real-life applications of the Momentum-Impulse Theorem?

The Momentum-Impulse Theorem has many real-life applications, such as in sports where the force of impact is important, like in basketball or football. It is also used in car safety technology, such as airbags, which reduce the force of impact in a collision. Additionally, the Momentum-Impulse Theorem is used in rocket science to calculate the necessary impulse for a spacecraft to reach a certain velocity.

## Can the Momentum-Impulse Theorem be used for objects in motion with changing mass?

Yes, the Momentum-Impulse Theorem can be used for objects in motion with changing mass. In this case, the change in momentum is equal to the impulse applied plus the change in mass multiplied by the velocity.

## Is there a difference between positive and negative momentum in the Momentum-Impulse Theorem?

Yes, there is a difference between positive and negative momentum in the Momentum-Impulse Theorem. Positive momentum indicates that the object is moving in the same direction as the applied force, while negative momentum indicates that the object is moving in the opposite direction of the force. This affects the calculation of impulse and can result in different solutions.

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