## Magnitude Of A Single Force Vector

To calculate the magnitude of force vectors, you use the components along with Pythagoras theorem. Think of the *x* coordinate of the force as the base of a triangle, the *y* component as the height of the triangle, and the hypotenuse as the resultant force from both components. Extending the link, the angle the hypotenuse makes with the base is the direction of the force.

If a force pushes 4 Newtons in the x-direction and 3 N in the y-direction, Pythagoras theorem and the triangle explanation show what you need to do when calculating magnitude. Using *x* for the *x*-coordinate, *y* for the *y*-coordinate and *F* for the magnitude of the force, this can be expressed as:

In words, the resultant force is the square root of *x*2 plus *y*2. Using the example above:

So, 5 N is the magnitude of force.

Note that for three-component forces, you add the *z* component to the same formula. So:

## How To Find Net Force

Lets recap some of the steps of our previous example and try to generalize them so they apply in many other cases. The first thing we need to do to analyze any problem involving forces acting on a body is to place the origin of our coordinate system on the most convenient spot. A common place to do so is at the center of mass of the body being analyzed. Now, what direction should the y- and x-axes be pointing in?

Use the next image as an example. The origin coincides with the center of mass and we have decided to place the x-axis in the same direction as F1. This way, the other two force vectors form angles and with the x- and the negative y-axes, respectively. Actually, placing the x-axis in the same direction as F2 or F3 would be equivalent, since the remaining two forces would then form new angles with the axes of our coordinate system.;

**Tip 1: select a direction for the axes of your coordinate system that produces the least possible amount of angles between the forces and them.;**

Having done so, we can start breaking down the force vectors into their components, meaning their horizontal and vertical parts. For this, we need a convention for what is positive and negative. A very common one is that any vector or vector component pointing to the right or upwards is positive. Consequently, any vector or vector component pointing to the left or downwards will be negative.;

**Table 1: vector components summary**

Vector |

3,57 N | 11,01 N |

Fnet=Fnet-x2+Fnet-y2 |

## Newton’s Laws Of Motion

Newton came up with three laws of motion that explain the movement of all physical objects. They are the basics of all *classical mechanics*, which is also known as *Newtonian mechanics*.

**Newton’s first law of motion**

An object will remain at rest or continue to move in uniform motion unless acted upon by an external force.

**Newton’s second law of motion**

Force exerted by an object equals mass times acceleration of that object: F = m * a.

**Newton’s third law of motion**

When one body exerts a force on a second body, the second body exerts a force equal in magnitude and opposite in direction on the first body .

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## The Law Of Conservation Of Charge

The Law of conservation of charge states that the net charge of an isolated system remains constant.

If a system starts out with an equal number of positive and negative charges, there¹s nothing we can do to create an excess of one kind of charge in that system unless we bring in charge from outside the system . Likewise, if something starts out with a certain net charge, say +100 e, it will always have +100 e unless it is allowed to interact with something external to it.

Charge can be created and destroyed, but only in positive-negative pairs.

Table of elementary particle masses and charges:

## Why Is Static Electricity More Apparent In Winter

You notice static electricity much more in winter than in summer because the air is much drier in winter than summer. Dry air is a relatively good electrical insulator, so if something is charged the charge tends to stay. In more humid conditions, such as you find on a typical summer day, water molecules, which are polarized, can quickly remove charge from a charged object.

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## What Is Net Force

Newtons second law of motion relates the force applied to a body, F, and its resulting acceleration, a. It is expressed mathematically through the following equation, where the bodys mass, m, is the proportionality constant:;

F=ma |

Lets do a thought experiment to try and understand what this equation means. Imagine you are at the grocery shop and want to move a cart around to put your groceries in. If the cart was initially at rest, meaning it was not moving, and you push it, it will start to roll at a certain speed, lets say 1 m/s. In this case, the cart went from zero velocity to 1 m/s in a very short period of time.

Since there was a change in the carts velocity, we can say it was *accelerated*. If that change in velocity occurred, for example, in a timeframe of one second, we can say the acceleration was exactly 1 m/s2. Go ahead and read the section called How to measure acceleration to understand how we got this result. Now, according to equation 1, if there was an acceleration, there had to be also a force causing it, which is the one you applied when pushing the cart. The mass in the equation is, in this case, that of the cart, which is constant. This thought experiment is summarized by this image:

For all our calculations, the center of mass will have the same effect as the entire cart, and it will be represented by a gray circle. We can now draw all forces acting on this point, a.k.a. our grocery cart:

## How To Find Force

Let’s look at a few exercises so that nothing can surprise you in your physics class.

**1. Find the accelerating and retarding force:**

A cheetah has a mass of 50 kg. It accelerates from rest to 50 km/h in 3 seconds. Then it starts steadily slowing down and stops after 8 seconds.

Accelerating force:

50 km/h is equal to 13.89 m/s .

Acceleration is equal to difference in velocity over time:

a = / 3 s = 4.63 m/s2

Calculate accelerating force:

Fa = m * a = 50 kg * 4.63 m/s2 = 231.5 N

Retarding force:

a = / 8 s = -1.74 m/s2

Fr = 50 kg * -1.74 m/s2 = -87 N

Retarding force is negative, because it has an opposite direction to the accelerating force.

**2. How much force do you need to accelerate an object by 8 m/s2? What about when the object is three times heavier? How does it affect the force?**

F1 = 2 kg * 8 m/s2 = 16 N

F2 = 3 * 2 kg * 8 m/s2 = 48 N

If the mass is three times heavier, the force needs to be three times bigger.

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## Numerical Simulation Of The Coulomb Model

Despite being a simplified model of friction, the Coulomb model is useful in many numerical simulation applications such as multibody systems and granular material. Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently numerically integrate mechanical systems with Coulomb friction and bilateral or unilateral contact. Some quite nonlinear effects, such as the so-called , may be encountered with Coulomb friction.

## Can Net Force Be Negative

**Net force can be both positive and negative**. The net force is the sum of the vectors of all individual forces acting on an object. Forces are always positive in magnitude. But to make net force easier to calculate, we assume that forces aiming at opposite directions have different signs. Usually, we say that forces aiming to the right are positive, and to the left – negative. So, if you have two forces opposite in direction acting on an object and the net force aims to the left, you could say that the net force is negative.

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## Example: The Forces At The Top Of This Bridge Tower Are In Balance :

The cables pull **downwards** equally to the left and right, and that is balanced by the tower’s **upwards** push.

We can model the forces like this:

And when we put them **head-to-tail **we see they **close back on themselves**, meaning the net effect is zero:

The forces are in balance.

Forces in balance are said to be **in equilibrium**: there is also no change in motion.

## Resultant Force And Acceleration

If the resultant force is zero, a moving object will stay at the **same speed**. If there is no resultant force then a system is said to be in equilibrium.

If the resultant force is not zero, a moving object will speed up or slow down – depending on the direction of the resultant force:

- it will speed up if the resultant force is in the same direction as the object is moving
- it will slow down if the resultant force is in the opposite direction

Note that the object could also change direction, for example if the resultant force acts at an angle.

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## Weight And The Gravitational Force

When an object is dropped, it accelerates toward the center of Earth. Newtons second law states that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its * weight* w. Weight can be denoted as a vector w because it has a direction; *down* is, by definition, the direction of gravity, and hence weight is a downward force. The magnitude of weight is denoted as *w**. * Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration *g*. Using Galileos result and Newtons second law, we can derive an equation for weight.

Consider an object with mass *m* falling downward toward Earth. It experiences only the downward force of gravity, which has magnitude *w*. Newtons second law states that the magnitude of the net external force on an object is;*Fnet* = *ma*. Since the object experiences only the downward force of gravity, *F*net;=;*w*. We know that the acceleration of an object due to gravity is *g*, or *a;*=;*g*. Substituting these into Newtons second law gives

## Limitations Of The Coulomb Model

The Coulomb approximation follows from the assumptions that: surfaces are in atomically close contact only over a small fraction of their overall area; that this contact area is proportional to the normal force ; and that the frictional force is proportional to the applied normal force, independently of the contact area. The Coulomb approximation is fundamentally an empirical construct. It is a rule-of-thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility. Though the relationship between normal force and frictional force is not exactly linear , the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems.

When the surfaces are conjoined, Coulomb friction becomes a very poor approximation . In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive for this reason. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications.

#### “Negative” coefficient of friction

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## Newton Second Law Of Motion Calculator English Espaol

Newton’s Second Law states that the acceleration of an object produced by net force is directly proportional to magnitude of the net force in the same direction and inversely proportional to the mass of the object. The Newton’s 2nd law of motion explains the behavior of the object when an external force is applied. Use newton second law of motion calculator to calculate mass, acceleration, Net force. Enter the values in the Newton’s 2nd law calculator and hit calculate to find the results.

## 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.

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## Why Is Net Force Important

“Net force” is a central idea of dynamics. Here’s why:

Newton’s Laws are the big deal in dynamics. Newton’s First Law canbe stated:

If the on an object is zero, its acceleration will be zero.

You will soon find out that Newton’sSecond Law says:

where Fnet means “net force”.

In order to use Newton’s Laws, the first thing you need to know is”What is the net force”.

## Definition Of A Net Force

When we kick a soccer ball, then the ball takes off and moves through the air. Then, there is a net force acting on the ball. Again when the ball starts to come back to the ground and eventually stops, there is also a net force acting on the ball.

According to Newtons Second Law, when a net force is acting on an object, then that object must be accelerating. Therefore, its speed changes from second to second. Hence when we first kick the soccer ball, it accelerates, and when the soccer ball begins to slow down it is again accelerating.

Now, a net force is defined as the sum of all the forces acting on an object. The following equation is the sum of N forces acting on an object.

Where,

\ are the forces acting on a body.

When the body is at rest position then the net force formula is given by,

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## Example: Car On A Highway

What are the forces on a car cruising down the highway?

The engine is working hard, so why doesn’t the car continue to accelerate?

Because the driving force is balanced by:

- Air resistance ,
- Rolling resistance, also called rolling friction

Like this:

**W** is the car’s weight,

**R1** and **R2** are the rolling resistance of the tires,

**N1** and **N2** are the reaction forces .

*Note: steel wheels have less rolling resistance, but are way too slippery on the road!*

## Is Weight A Force

Weight is another term for gravitational force. In physics, weight and mass are not the same. Mass is an attribute of an object that resists any changes in motion. The weight force acting on the mass due to gravity. If its mass on the earth is 70 kilograms, then its weight is approximately 700 Newtons .

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## How To Calculate Net Force

**Draw all the forces acting on the body.**

**Locate the coordinate system in a way that produces the minimum number of angles with the forces.**

**Split each force in its horizontal and vertical components using its magnitude and the sine or cosine of each angle.**

**Assign the correct signs to the components depending on the selected convention.;**

**Add the horizontal and vertical components separately.**

**Calculate the net force magnitude and direction based on the net horizontal and vertical components.**

## Newtons Second Law Of Motion

The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In equation form, Newtons second law of motion is

}=\frac}}_}}\\.

This is often written in the more familiar form

**F***m***a**

When only the magnitude of force and acceleration are considered, this equation is simply

*Fnet = ma.*

Although these last two equations are really the same, the first gives more insight into what Newtons second law means. The law is a *cause and effect relationship* among three quantities that is not simply based on their definitions. The validity of the second law is completely based on experimental verification.

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## Is Force A Vector

Force is a vector. This means that it is determined by direction and size. Scalar quantities, such as length or mass, are determined only by size. Therefore, if you apply two forces to an object, you cannot add them as scalars. You must consider the direction and find the resultant force from the vector sum of the forces.

## How To Calculate Force

Force is the interaction with a system or object, which changes the motion of that object. Since there is no opposing force, this force also changes the speed of the system.

When the mass and acceleration are both known, just multiply them to calculate the force. However, acceleration is often not fully understood. Therefore, the position or velocity change used to calculate the acceleration. Contrary to acceleration and velocity, force is not the product of the derivative of time. This means that it is calculated at a specific time, rather than based on changes over time.

**Example 1:**

How to find force when the mass of a body is 4 kg and its acceleration is 5 meters per second square.

**Solution:**

The impact force calculator uses the force formula to determine the force:F=maF=4 kg5 \F=20 N

**Example 2:**

How to find net force, if the object is at rest position where the applied force is 15 Newton and Gravitational force is 50 Newton?

**Solution:**

The Net Force equation is:

n = a + g

now, net force calculator substitute all values in equation:

n = 15 + 50n = 65

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