# [Linear momentum] When to use which equation.

• hiuting
In summary, when dealing with inelastic collisions, you can use the formula (mbullet)(vinitial) = (mbullet + mblock)(vfinal) or the equation (m1)(vi)bullet = (m1+m2)(vf)system. These equations are equivalent and will give the same final velocity for the system. This is because in an inelastic collision, the two objects stick together and form a combined mass, resulting in a shared final velocity.
hiuting

## Homework Statement

I'm confused about when to use which formula.
I thought for inelastic collisions,
for example, when a bullet is shot into a block,
I should use
(mbullet)(vinitial) = (mbullet + mblock)(vfinal)

but it turns out that I must use

why do i have to use this one?

## The Attempt at a Solution

eqn w/ velocities you use

They should really be the same equation. (m1)(vi)+(m2)(vi)=(m1)(vf)+(m2)(vf) will reduce to the top equation you wrote if the block "m2" is initally at rest (vi=0) and upon impact they stick and form a system. Thus they have a combined mass (m1+m2) and the same final velocity (vf). So it reduces to:

(m1)(vi)bullet = (m1+m2)(vf)system

kjohnson said:
They should really be the same equation. (m1)(vi)+(m2)(vi)=(m1)(vf)+(m2)(vf) will reduce to the top equation you wrote if the block "m2" is initally at rest (vi=0) and upon impact they stick and form a system. Thus they have a combined mass (m1+m2) and the same final velocity (vf). So it reduces to:

(m1)(vi)bullet = (m1+m2)(vf)system

then v1 final and v2 final are the same??

Yes, this is true because they stick together to form a system. They must have the same velocity.

## 1. What is linear momentum?

Linear momentum is a physical quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity. In other words, it represents the amount of motion an object has in a certain direction.

## 2. When should I use the equation p = mv?

The equation p = mv is used to calculate the linear momentum of an object in a straight line. It is commonly used in situations where an object is moving at a constant speed in a single direction.

## 3. When is the equation p = mΔv useful?

The equation p = mΔv is useful when an object's velocity is changing over time. It takes into account the initial and final velocities of an object and can be used to calculate the change in linear momentum.

## 4. What is the significance of momentum conservation?

Momentum conservation is a fundamental law of physics that states that the total momentum of a closed system remains constant. This means that in any interaction between objects, the total momentum before the interaction is equal to the total momentum after the interaction.

## 5. How do I know which equation to use for a specific problem?

The equation to use for a specific problem depends on the given information and the type of motion involved. If an object is moving at a constant speed in a straight line, use p = mv. If the velocity is changing over time, use p = mΔv. In situations involving multiple objects, use the principle of momentum conservation to determine the equations to use.

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