## Objects Of Variable Mass

The concept of momentum plays a fundamental role in explaining the behavior of variable-mass objects such as a rocket ejecting fuel or a staraccreting gas. In analyzing such an object, one treats the object’s mass as a function that varies with time: *m*. The momentum of the object at time *t* is therefore *p* = *m**v*. One might then try to invoke Newton’s second law of motion by saying that the external force *F* on the object is related to its momentum *p* by *F* = *dp*/*dt*, but this is incorrect, as is the related expression found by applying the product rule to

## The Conservation Of Momentum

In much the same way knocking balls in pool against one another transfers energy from one ball to the next, objects that collide with one another transfer momentum. According to the law of conservation of momentum, the total momentum of a system is conserved.

You can create a total momentum formula as the sum of the momenta for the objects before the collision, and set this as equal to the total momentum of the objects after the collision. This approach can be used to solve most problems in physics involving collisions.

## Conservation In A Continuum

In fields such as fluid dynamics and solid mechanics, it is not feasible to follow the motion of individual atoms or molecules. Instead, the materials must be approximated by a continuum in which there is a particle or fluid parcel at each point that is assigned the average of the properties of atoms in a small region nearby. In particular, it has a density and velocity **v** that depend on time *t* and position **r**. The momentum per unit volume is **v**.

Consider a column of water in hydrostatic equilibrium. All the forces on the water are in balance and the water is motionless. On any given drop of water, two forces are balanced. The first is gravity, which acts directly on each atom and molecule inside. The gravitational force per unit volume is **g**, where **g** is the gravitational acceleration. The second force is the sum of all the forces exerted on its surface by the surrounding water. The force from below is greater than the force from above by just the amount needed to balance gravity. The normal force per unit area is the pressure*p*. The average force per unit volume inside the droplet is the gradient of the pressure, so the force balance equation is

- . }\equiv }+\mathbf \cdot }\,.}

- , p}}}=c^\nabla ^p\,,}

where *c* is the speed of sound. In a solid, similar equations can be obtained for propagation of pressure and shear .

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## Newtons Second Law In Terms Of Momentum

When Newtonâs second law is expressed in terms of momentum, it can be used for solving problems where mass varies, since Î

Î p stays the same will decrease **F**net. This is another example of an inverse relationship. Similarly, a padded dashboard increases the time over which the force of impact acts, thereby reducing the force of impact.

Cars today have many plastic components. One advantage of plastics is their lighter weight, which results in better gas mileage. Another advantage is that a car will crumple in a collision, especially in the event of a head-on collision. A longer collision time means the force on the occupants of the car will be less. Deaths during car races decreased dramatically when the rigid frames of racing cars were replaced with parts that could crumple or collapse in the event of an accident.

## What Is The Momentum Formula

The formula for the calculations from both the methods is as follow:

**When Mass & Velocity Given:**

The formula when \ & \ is given is as follows:

$$ p = m \times v $$

\ is the mass of object

\ is the velocity of object

You can try our online velocity calculator to exactly determine the velocity/speed of the moving object.

**When Time & Force Given:**

The formula when \ & \ is given is as follows:

$$ p = F \times t $$

\ is the time taken by the object

Also, our online momentum calculator considers these momentum equations for the momentum calculations.

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## Making Connections: Force And Momentum

Force and momentum are intimately related. Force acting over time can change momentum, and Newtons second law of motion, can be stated in its most broadly applicable form in terms of momentum. Momentum continues to be a key concept in the study of atomic and subatomic particles in quantum mechanics.

This statement of Newtons second law of motion includes the more familiar Fnet = *m*a as a special case. We can derive this form as follows. First, note that the change in momentum p is given by p = .

If the mass of the system is constant, then = *m*v.

So that for constant mass, Newtons second law of motion becomes

\displaystyle}_}=\frac}=\frac}}

Because \frac}}=\mathbf\\, we get the familiar equation Fnet = *m*a **when the mass of the system is constant**.

Newtons second law of motion stated in terms of momentum is more generally applicable because it can be applied to systems where the mass is changing, such as rockets, as well as to systems of constant mass. We will consider systems with varying mass in some detail however, the relationship between momentum and force remains useful when mass is constant, such as in the following example.

## Vector Components And Momentum

As a vector quantity, momentum can be broken down into component vectors. When you are looking at a situation on a three-dimensional coordinate grid with directions labeled *x*, *y*, and *z. *For example, you can talk about the component of momentum that goes in each of these three directions:

px=mvxpy=mvypz=mvz

These component vectors can then be reconstituted together using the techniques of vector mathematics, which includes a basic understanding of trigonometry. Without going into the trig specifics, the basic vector equations are shown below:

p=px+py+pz=mvx+mvy+mvz

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## Selected Solutions To Problems & Exercises

1. 1.50 × 104 kg m/s 625 to 1 6.66 × 102 kg m/s

3. 8.00 × 104 m/s 1.20 × 106 kg · m/s Because the momentum of the airplane is 3 orders of magnitude smaller than of the ship, the ship will not recoil very much. The recoil would be 0.0100 m/s, which is probably not noticeable.

5. 54 s

- College Physics. : OpenStax College.
**Located at**: .**License**:*CC BY: Attribution*.**License Terms**: Located at License

## How To Calculate Momentum Of An Object

Momentum is defined as the mass of an object when it is motion. Simplifying the momentum is included in few steps below. The following simple steps will guide you to solve the momentum of an object. So, have a look at the below lines

- First, get mass of the object and velocity in the given question.
- Multiply the mass and velocity of the object.
- Result is called object momentum.

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## Example: A Pool Ball Bouncesit Hits The Edge With A Velocity Of 8 M/s At 50 And Bounces Off At The Same Speed And Reflected Angleit Weighs 016 Kgwhat Is The Change In Momentum

Let’s break the velocity into x and y parts. Before the bounce:

- vx = 8 × cos
*…going along* - vy = 8 × sin
*…going up*

After the bounce:

- vx = 8 × cos
*…going along* - vy = 8 ×sin
*…going down*

The x-velocity does not change, but the y-velocity changes by:

vy = × sin

And the change in momentum is:

**p** = m **v**

p = 0.16 kg × 16 × sin m/s

p = 1.961… kg m/s

## Example 2 Calculating Force: Venus Williams Racquet

During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier womens match, reaching a speed of 58 m/s . What is the average force exerted on the 0.057-kg tennis ball by Venus Williams racquet, assuming that the balls speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms ?

#### Strategy

This problem involves only one dimension because the ball starts from having no horizontal velocity component before impact. Newtons second law stated in terms of momentum is then written as

\displaystyle}_}=\frac}

As noted above, when mass is constant, the change in momentum is given by *p* = *m**v* = *m* .

In this example, the velocity just after impact and the change in time are given thus, once *p* is calculated, }_}=\frac} can be used to find the force.

#### Solution

To determine the change in momentum, substitute the values for the initial and final velocities into the equation above.

\begin\Delta& =& m\\ & =& \\ & =& 3.306\text\cdot\text\approx3.3\text\cdot\text\end\\

Now the magnitude of the net external force can determined by using }_}=\frac}:

\begin\mathbf_}& =& \frac}}=\frac\cdot\text}\text}\\ & =& 661\text\approx660\text\end\\

where we have retained only two significant figures in the final step.

#### Discussion

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## Faqs On Momentum Calculator

**1. What is the formula and unit of momentum?**

Momentum formula is given as p = m * v

Where p is the momentum, m is the mass of the object and v is the velocity

The SI unit of momentum is kg.m/s.

**2. How do you find velocity with mass and momentum? **

The formula to find velocity of an object with momentum and mass is defined as v = p / m.

**3. What is the momentum of a child and wagon if the total mass of the child and wagon is 22 kg and the velocity is 1.5 m/s?**

Mass m = 2 kg

Mass of a child is 33 kg.m/s

**4. What are the two types of momentum?**

The two kinds of momentum are linear momentum and angular momentum. A spinning object has angular momentum. If an object is travelling with a velocity then it has linear momentum.

**5. How is momentum used in everyday life?**

Momentum is the product of mass and velocity. One of the example of momentum is throw a cricket ball and tennis ball with same speed or velocity. Then more force is required to stop the cricket ball when compared to the tennis ball. So, force is directly proportional to its mass.

#### Favorite Calculators

## Momentum And Newtons Second Law

The importance of momentum, unlike the importance of energy, was recognized early in the development of classical physics. Momentum was deemed so important that it was called the quantity of motion. Newton actually stated his *second law of motion* in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. Using symbols, this law is

\displaystyle}_}=\frac},

where Fnet is the net external force, p is the change in momentum, and *t* is the change in time.

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## Impulse And Momentum Calculator

This impulse and momentum calculator will help you analyze any object in motion. You will learn how to calculate impulse in three ways:

- knowing the change in velocity of a body,
- knowing the time a force acts on this body and
- simply from the change of momentum.

Keep reading to learn the impulse equation, and never worry about calculating momentum again!

## How To Calculate Impulse

**initial**and

**final momentum**values into our calculator to find the impulse directly from the impulse formula J = p.

**mas**s and

**velocity change**of an object to calculate the impulse from the equation J = mv.

**force**and

**time change**instead. Our impulse and momentum calculator will use the J = Ft formula.

The concept of impulse is connected to kinetic energy – make sure to read about it as well!

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## Example: What Is The Momentum Of A 1500 Kg Car Going At Highway Speed Of 28 M/s

**p** = m **v**

**p** = 1500 kg ×**28 m/s**

**p** = 42,000 kg m/s

The unit for momentum is:

- kg m/s , or
- N s

They are the same! **1 kg m/s = 1 N s**

We will use both here.

More examples:

0.0075 × 1000 = 7.5 kg m/s | |

Tennis Ball | 0.057 × 50 = 2.85 kg m/s |
---|---|

Soccer Ball | 0.45 × 28 = 12.6 kg m/s |

Basket Ball | 0.6 × 3 = 1.8 kg m/s |

Hammer | 0.4 × 7 = 2.8 kg m/s |

Runner | 80 × 2.5 = 200 kg m/s |

Car | 1500 × 28 = 42,000 kg m/s |

Momentum has **direction**: the **exact same direction** as the velocity.

But many examples here only use speed to keep it simple.

## How Do You Calculate The Change In Momentum Of An Object

There are two possible ways depending on the problem.

1) The change in momentum of an object is its mass times the change in its velocity. #\Delta p=m*=m*# .

are the final and initial velocities. Remember to use the right signs when substituting #v_f# and #v_i#

Example) A 3kg mass initially moving 4m/s to the right rebounds off of a wall and begins travelling to the left at 2m/s.

Taking “right” to be the positive direction: #v_i# = 2m/s, and m=3kg. Substituting, #\Delta p=3kg*(-2# #=-18# kg m/s

2) The change in the momentum of an object can also be found by considering the force acting on it. If a force, #F# , acts on an object for a time, #\Delta t# , the change in the objects momentum is #\Delta p= F*\Delta t# .Remember to use the right sign when substituting #F# . For example, a force to the left could be negative.

Lastly, if your object is moving both horizontally and vertically then #\Delta p# has a vertical and horizontal component. If this is the case, the above equations still work for each component separately, Ex) To find the horizontal component of #\Delta p# use the horizontal component of #v_i, v_f#

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## How To Calculate Momentum

wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 10 people, some anonymous, worked to edit and improve it over time.There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 25,178 times.

Momentum is the measurement of the quantity of an object’s motion. You can find momentum if you know the velocity and the mass of the object. It will be easy once you understand the formula.XResearch source

## Conservation Of Momentum Example

When dealing with conservation of momentum problems, you consider the initial and final states of each of the objects in the system. The initial state describes the states of the objects just before the collision occurs, and the final state, right after the collision.

If a 1,500 kg car with moving at 30 m/s in the +*x* direction crashed into another car with a mass of 1,500 kg, moving 20 m/s in the *x* direction, essentially combining on impact and continuing to move afterwards as if they were a single mass, what would be their velocity after the collision?

Using the conservation of momentum, you can set the initial and final total momentum of the collision equal to one another as *p*Ti = *p*Tfor *p*A + *p*B = *p*Tf for the momentum of car A, *p*A and momentum of car B, *p*B*.* Or in full, with *m*combined as the total mass of the combined cars after the collision:

Where *v*f is the final velocity of the combined cars, and the “i” subscripts stand for initial velocities. You use 20 m/s to for the initial velocity of car B because it’s moving in the *x* direction. Dividing through by *m*combined gives:

And finally, substituting the known values, noting that *m*combined is simply *m*A + *m*B, gives:

Note that despite the equal masses, the fact that car A was moving faster than car B means the combined mass after the collision continues to move in the +*x* direction.

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## Overview Of Momentum And What Is The Formula Of Change In Momentum

In this section, you will be able to learn more about the Momentum formula and how to use this particular formula to solve some of the most important questions in the exam. Momentum is a really important topic for the students and they definitely need to be aware of the formula. This section deals with the exact formula for momentum and it also tells you about the change in momentum and how can one calculate it.

## How To Use This Free Online Calculator:

The calculations becomes very easy with this online momentum calculator. Simply follow the detailed points for calculations:

Swipe on!

For calculations from the velocity, just stick to the following points:

**Inputs:**

- First of all, choose the parameter which you want to calculate .
- Then, enter in all the designated fields according to the selected calculation parameter.
- Finally. Hit the calculate button.

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## Understanding Momentum In Physics

- M.S., Mathematics Education, Indiana University
- B.A., Physics, Wabash College

Momentum is a derived quantity, calculated by multiplying the mass, *m* , times velocity, *v* . This means that the momentum has a direction and that direction is always the same direction as the velocity of an object’s motion. The variable used to represent momentum is *p*. The equation to calculate momentum is shown below.

## Momentum Impulse And The Impulse

Linear momentum is the product of a systemâs mass and its velocity. In equation form, linear momentum **p** is

You can see from the equation that momentum is directly proportional to the objectâs mass and velocity . Therefore, the greater an objectâs mass or the greater its velocity, the greater its momentum. A large, fast-moving object has greater momentum than a smaller, slower object.

Momentum is a vector and has the same direction as velocity **v**. Since mass is a scalar, when velocity is in a negative direction , the momentum will also be in a negative direction and when velocity is in a positive direction, momentum will likewise be in a positive direction. The SI unit for momentum is kg m/s.

Momentum is so important for understanding motion that it was called the *quantity of motion* by physicists such as Newton. Force influences momentum, and we can rearrange Newtonâs second law of motion to show the relationship between force and momentum.

Recall our study of Newtonâs second law of motion . Newton actually stated his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. The change in momentum is the difference between the final and initial values of momentum.

In equation form, this law is

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