Articles by "moments"
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What is Equilibrium?
When a system is said to be in equilibrium this means it is in balance and is either moving at constant velocity motion or is at rest.

Situations that must exist for a system to be at equilibrium:

  1. The resultant force in any direction must be zero.
  2. The total moments of the system must be zero. Meaning:

Clockwise Moments = Anti- Clockwise Moments

How to calculate equilibrium?


Example 1
If the system below is in equilibrium find the unknown force “F”.

System in equilibrium


Step 1
In the question they stated that the system is in equilibrium, therefore you can go ahead and use the equation:
Clockwise Moments = Anti-Clockwise Moments

But remember that formula for moments is:
Force × Perpendicular distance from pivot


Therefore:
Clockwise Force × Perpendicular distance = Anti-clockwise Force × Perpendicular Distance


Step 2
Identify the forces in the system that are moving clockwise and anti-clockwise with their respective perpendicular distances, and then substitute those values in the above equation:


After substituting the values above into the formula you should get:

Clockwise Moments = Anti-Clockwise Moments
Clockwise Force × Perpendicular distance = Anti-clockwise Force × Perpendicular Distance
F × 8m = 120N × 6m

Step 3
After placing the values into the formula all that is left to do is transpose the formula to make “F” the subject then solve for “F”. The overall calculation would then be:

Calculating Equilibrium
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What is Moments?

By definition Moments, also known as torque, is the turning effect of a force. Moments can either be in a clockwise or anti-clockwise direction. The unit of moments is the Newton Meter (Nm).

Formula for Moments of a force:

      Moments (torque) = Force × Perpendicular distance from the pivot

How to calculate Moments?

Example 1
Find the total moments of the system below:

Diagram Showing Moments


Step 1

Identify which force in the system is moving in the clockwise direction and which is moving in an anticlockwise direction. The 50N force is the one moving in the clockwise direction (the same direction a clock’s pointer would move) while the 80N is moving in the opposite direction (anti-clockwise direction).

Showing Clockwise and Anti-clockwise Moments

Step 2

Use the formula given above to calculate the clockwise and anti-clockwise moments separately.

          Moments = Force × Perpendicular distance

          Clockwise Moments = Force × Perpendicular Distance
                                          = 50N × 6m
                                          = 300Nm

          Anti-Clockwise Moments = Force × Perpendicular Distance
                                                  = 80N × 4m
                                                  = 320Nm

Step 3

Now that you have calculated both clockwise and anti-clockwise moments you can now find the total moments of the system. This is found by subtracting the smaller moments from the larger, in this case the smaller of the two is the clockwise while the larger is the anti-clockwise.

         Total Moments = 320Nm – 300Nm
                                 = 20Nm in the anti-clockwise direction

 Note: Anti-clockwise direction is written at the end because it is larger.
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What is Impulse?
Impulse can be defined as the force per unit time or change in momentum. Momentum is changed whenever a force is applied to a body. From these definitions one can already see what formulas are in relation to impulse.

Formulas associated with Impulse:

                  Impulse = Force x Time
                                 Or
                  Impulse = Change in momentum = mV – mU

Where ‘m’ is Mass and V, U is final and initial velocity respectively.

Below are some calculations involving impulse. Here you’ll be using the formulas above to find the missing variable.

Example 1.
A force of 100 N is applied for 8 seconds. What is the impulse?

Answer:
Right away you can easily solve for impulse using the first formula above because all other variables are given.

       Therefore Impulse = Force x Time
                                   = 100N x 8sec
                                   = 800Ns

Example 2.
An impulse of 250Ns is applied for 10 seconds. What is the applied force?

Answer:
Again you can see that you have to use the first formula above, but in this case they gave values for impulse and time, therefore all you have to do is transpose the formula to make Force the subject and then solve for Force.


Example 3.

A body of 4kg is moving at 5m/s when it is given an impulse of 8Ns in the direction of the motion.

a) What is the Velocity of the body immediately after the impulse?
b) If the impulse acts for 0.02 seconds. What is the average value of the force exerted?

Answers:
a) Here they gave you mass (4kg), initial velocity (5m/s) and impulse (8Ns). Therefore all you need to do is transpose the second formula, which relates impulse to momentum, to make the final velocity(V) the subject of the formula and then solve.


b)All you need to do is transpose for force and then solve. When done transposing you should get:
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Difference Between Scalar and Vector

Scalars have magnitude only but Vectors have both magnitude and direction.

The table below displays some of the most popular scalar and vector quanities.


S.I Units

Mass --> Grams (g), or Kilograms(Kg)

Length --> Meter(m)

Time --> Seconds(s)
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A force can be defined as a push or a pull. Force can either cause an object to increase its speed or just move. Symbol of force is the newton(N). Force is a vector quantity.

Types of force:

  • Gravitational
  • Electric
  • Nuclear
  • Magnetic

Moments

The moment of a force is simply the product of the force and the perpendicular distance. The SI unit of moment is Newton metre(NM)

Formula for finding moments:

Moment = Force x perpendicular distance


Principle of Moments

The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the anti- clockwise moments about that point.



Centre of gravity

The centre of gravity of a body is defined as that point in the body at which all its weight acts.

Clockwise = Anticlockwise
W x d = W x d



Hook's Law

Hooke's law states that the force does not cause the material to remain permanently stretched then the extension (x) is proportional to the force applied.

F = Kx

where K is the force required to extend the material by one metre

elasticity refers to the stretching of objects(rubber band, springs) when pulled and returning to their original length when force is released.
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