## $$ F: S \leq \mu: F: $$

\ = force of static friction direction and magnitude change to keep acceleration zerobut only up to the maximum value

\ = normal force

\ = mu, coefficient of friction

Materials |
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**Example:****Example:**

Include both masses in the total mass.

**Example:**

Materials |
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0.2 |

First, draw a free body diagram. Then calculate the max static friction force on the 5 kg block.

Since the blocks aren’t moving, the opposing forces are equal. The friction force equals the tension force, which also equals the force of gravity for the right block. This means we can set the max static friction equal to the force of gravity for the right block.

Replace the force of gravity with “mg”, and solve for the mass.

Since the system isn’t moving the acceleration is zero. This means that opposing forces need to be equal. The friction force equals the tension force, which also equals the force of gravity on the right block.

## What Is The Difference Between Fg = Mg And Universal Gravitation

If an object of mass #m # is on the surface of earth of mass #M # and radius #R# then by the law of universal gravitation the force of gravity on the object is given by

#F_g= /R^2……#

is the universal gravitational constant.

Again acceleration due to gravity ## is the acceleration with which any object freely falls under the force of gravity. towards the center of the earth.

Now if the mass of the body be # m# then by *Newton’s laws* of motion the gravitational pull on the object will be given by

#F_g=”mass” xx “acceleration”=mxxg…….#

So origin of this equation is Newton’s laws of motion. Here only acceleration # # is originated from gravitational force.

Comparing equation and we can write

#mg= /R^2#

This equation shows how the acceleration due to gravity ## is related with universal gravitational constant ##

## When Does Normal Force Equal To $mg$

Can someone once and for all explain when does normal force equal to mg?

I know for sure that when there is no friction, normal force will be equal to mg.But, i encountered some questions when there is some mass on an incline with friction, and then the normal force was the y component of mg.

It does not make sense to me, because as i understood when there is friction, we cannot assume that mg will be equal to normal force.

Normal Force arises due to the Newton’s Third law. Normal Force will be always acting opposite to the force falling on the surface.Normal Force is a reaction force. Remember

Normal force is equal to mg only when the object is placed horizontally, and the force is acting in the direction of the gravitational field.

Now your second question

Here you will see that the weight of the body is passing through the Centre of gravity and acting in direction of the centre of the earth.

But the component of weight on the incline is not mg it is cos component.In order to satisfy the Newton’s third law Normal reaction to the object is the cos component$$N=Wg\cos \theta$$ even if friction is there or not there this will be the same

Normal force $F_N$ is just the force between two surfaces. It’s called “normal” because it acts perpendicular to the surfaces.

Gravitational force is completely unrelated. Gravity always acts with $F_g = -mg$. The minus sign indicates that the force points down.

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## Calculating The Force Of Gravity Between Two Objects

**Define the equation for the force of gravity that attracts an object,**XResearch source In order to properly calculate the gravitational force on an object, this equation takes into account the masses of both objects and how far apart the objects are from each other. The variables are defined below.

*Fgrav = /d2*.*Fgrav*is the force due to gravity

*G*is the universal gravitation constant 6.673 x 10-11 Nm2/kg2XResearch source

*m1*is the mass of the first object

*m2*is the mass of the second object

*d*is the distance between the centers of two objects

*r*instead of the letter

*d*. Both symbols represent the distance between the two objects.

**Use the proper metric units.**For this particular equation, you must use metric units. The masses of objects need to be in kilograms and the distance needs to be in meters . You must convert to these units before continuing with the calculation.

**Determine the mass of the object in question.**For smaller objects, you can weigh them on a scale or balance to determine their weight in grams. For larger objects, you will have to look-up the approximate mass in a table or online. In physics problems, the mass of the object will generally be provided to you.

**Measure the distance between the two objects.**If you are trying to calculate the force of gravity between an object and the earth, you need to determine how far away the object is from the center of the earth.XResearch source

*Fgrav = /d2*= /2

## How To Use The Gravity Formula

*You can enter this large number into the calculator by typing 5.972e24.*

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## How To Find Normal Force

wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 16 people, some anonymous, worked to edit and improve it over time.There are 11 references cited in this article, which can be found at the bottom of the page. This article has been viewed 722,570 times.Learn more…

Normal force is the amount of force required to counteract the other forces in any given scenario. The best way to go about finding it depends on the circumstances of the object and the variables you have data for. Keep reading to learn more.

## How To Calculate Force Of Gravity

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Gravity is one of the fundamental forces of physics. The most important aspect of gravity is that it is universal: all objects have a gravitational force that attracts other objects to them.XResearch source The force of gravity acting on any object is dependent upon the masses of both objects and the distance between them.XResearch source

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## How Do You Find And Solve A Composite Function

Composite functions can be thought of as ‘functions within functions’. For example, let’s suppose that

f = x3

defined for all real numbers.

**Q1) Solve the equation fg = 27**

Firstly, we must find the composite function fg in terms of x before we solve it. In order to do this, we can break down the function in the following way:

fg = f = f

As you can see, we have broken down fg into a function of g **within** a function of f. We can now replace ‘x’ in f = x3 with ‘x+5’:

fg = f = 3

We can now use the above function to rearrange and solve for fg = 27.

fg = 3 = 27

**A1) x = -2**

It is also possible to form a composite function by applying the same function twice. For example, if we apply the function f to f, we have ff or f 2.

f 2 = f

= x9

One thing to note when calculating composite functions is that **fg is unlikely to be the same as gf**. For instance, from using f and g from our example above, we can calculate gf below:

gf = g

This result is completely different from our result of fg = 3

Another point to consider when solving composite functions is the array of values for which the function holds i.e. the domain and range of the function. These values determine whether a composite function will solve for a particular value, and so it is important to find the domain and range. We will now use a different example from above to demonstrate this point.

Let f = x2 + 3

**Q2) Find fg and explain why fg = 1 has no real solution.**

Like in Q1) we must find the function fg before we solve it:

## What Is The Gravity Equation

Use the following formula to calculate the gravitational force between any two objects:

where:

- F stands for gravitational force. It is measured in newtons and is always positive. It means that two objects of a certain mass always attract each other
- M and m are the masses of two objects in question
- R is the distance between the centers of these two objects and
- G is the gravitational constant. It is equal to 6.674×10-11 N·m²/kg².

Did you notice that this equation is similar to the formula in Coulomb’s law? While Newton’s law of gravity deals with masses, Coulomb’s law describes the attractive or repulsive force between electric charges.

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## Normal Force And Friction

**Know the basic equation for kinetic friction.**Kinetic friction, or the friction of an object in motion, is equal to the coefficient of friction multiplied by the normal force of an object. In equation format, that looks like:

**f = * N**XResearch source

**f**stands for friction, refers to the coefficient of friction, and

**N**refers to the normal force of the object.

**Rearrange the equation to isolate the normal force.**If you have a value for the kinetic friction of an object, as well as that object’s coefficient of friction, you can calculate the normal force by using the formula:

**N = f /**XResearch source

*Example*: Find the normal force of a block when the coefficient of friction is 0.4 and the amount of kinetic friction itself is 40 N.

**Divide the kinetic friction by the coefficient of friction.**This is essentially all you need to do to find the value of the normal force.

*Example*: N = f / = 40 / 0.4 = 100

**Record your answer.**If desired, you can check your answer by plugging it back into the original equation for kinetic friction. Otherwise, you have completed the problem.

*Example*: The normal force is 100.0 N.

## Case : A Solid Uniform Sphere

The second situation we will examine is for a solid, uniform sphere of mass \text and radius \text, exerting a force on a body of mass \text at a radius \text *inside* of it . We can use the results and corollaries of the Shell Theorem to analyze this case. The contribution of all shells of the sphere at a radius greater than \text from the spheres center-of-mass can be ignored . Only the mass of the sphere within the desired radius \text_} is relevant, and can be considered as a point mass at the center of the sphere. So, the gravitational force acting upon point mass \text is:

\displaystyle \text=\frac_}}^2}

where it can be shown that \displaystyle \text_}=\frac\pi \text^3 \rho

Therefore, combining the above two equations we get:

\text=\frac \pi \text \rho \text

which shows that mass \text feels a force that is linearly proportional to its distance, \text, from the spheres center of mass.

As in the case of hollow spherical shells, the net gravitational force that a solid sphere of uniformly distributed mass \text exerts on a body *outside *of it, is the vector sum of the gravitational forces acted by each shell of the sphere on the outside object. The resulting net gravitational force acts as if mass \text is concentrated on a point at the center of the sphere, which is the center of mass, or COM . More generally, this result is true even if the mass \text is *not *uniformly distributed, but its density varies radially .

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## Acceleration Due To Gravity

The acceleration due to the force of gravity on Earth is designated by **g**. Its value is:

g =9.807 meters per second-squared in the metric or SI system of measurement

g =32.2 feet per second-squared in the English system of measurement

Note: Since most textbooks useg =9.8 m/s2 and 32 ft/s2, we will also use the rounded-off version in these lessons.

In the equation **F = mg**, you must use the same measurement system for mass, **m**, as you do for **g**.

Note:Some textbooks carelessly definegas theacceleration. That is incorrect and misleading, since gravity does not accelerate. The expression should beofgravitythe acceleration, which is correct description ofdue togravityg.Care must be taken in defining scientific terms.

## Calculating The Force Of Gravity On Earth

**Understand Newtonâs Second Law of Motion,**Newtonâs second law of motion states that any object will accelerate when acted upon by a net or unbalanced force.XResearch source In other words, if a force is acting upon an object that is greater than the forces acting in the opposite direction, the object will accelerate in the direction of the larger force.

*F = ma*.*F = ma*, where

*F*is the force,

*m*is the mass of the object, and

*a*is acceleration.

**Know the acceleration due to gravity on earth.**On earth, the force of gravity causes objects to accelerate at a rate of 9.8 m/s2. On the earthâs surface, we can use the simplified equation

*Fgrav = mg*to calculate the force of gravity.

*Fgrav = /d2*to determine force of gravity.

**Use the proper metric units.**For this particular equation, you must use metric units. The mass of the object needs to be in kilograms and the acceleration needs to be in meters per second squared . You must convert to these units before continuing with the calculation.

*Fgrav = mg*= 68*9.8 = 666 N.

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## You Feel Weightless If The Elevator Cable Breaks

The phenomenon of “weightlessness” occurs when there is no force of support on your body. When your body is effectively in “free fall”, accelerating downward at the acceleration of gravity, then you are not being supported. The sensation of apparent weight comes from the support that you feel from the floor, from a chair, etc. Different sensations of apparent weight can occur on an elevator since it is capable of zero or constant speed and can accelerate either upward or downward. If the elevator cable breaks then both you and the elevator are in free fall. The resultant experience of weightlessness might be exhilirating if it weren’t for the anticipation of the quick stop at the bottom.

## Normal Force With An External Downward Force

**Use the right equation.**To calculate the normal force of an object at rest when an outside force acts downward on that object, use the equation:

*N = m * g + F * sin’*XResearch source

**N**refers to the normal force,

**m**refers to the object’s mass,

**g**refers to the acceleration of gravity,

**F**refers to the outside force, and

**x**refers to the angle between the object and the direction of the outside force.

*Example*: Find the normal force of a block with a mass of 4.2 kg, when a person is pressing down on the block at a 30 degree angle with a force of 20.9 N.

**Find the object’s weight.**The weight of an object equals the mass of the object multiplied by the acceleration of gravity.XResearch source

**g = 9.8 m/s2**

*Example*: weight = m * g = 4.2 * 9.8 = 41.16

**Find the sine of the angle.**The sine of an angle is calculated by dividing the side of the triangle opposite the angle by the hypotenuse of the angle.

*Example*: sin = 0.5

**Multiply the sine by the outside force.**The outside force, in this instance, refers to the force acting downward on the object.

*Example*: 0.5 * 20.9 = 10.45

**Add this value to the weight.**Doing so will give you the normal force at work.

*Example*: 10.45 + 41.16 = 51.61

**Write your answer.**Note that for an object at rest being influenced by an external, downward force, the normal force will be greater than the weight of the object.

*Example*: The normal force is 51.61 N.

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