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Forces - addition.

posted Jan 29, 2015, 1:55 AM by Ranmini Perera   [ updated Aug 15, 2019, 11:12 PM by Upali Salpadoru ]

    Fig 1  A sailing boat crossing a river.

   A sailing boat is crossing a river flowing fast. Imagine the force on the sail to be 800 N and the flowing river water to give a force of 600N.  

What is the total force? 
 If you use normal arithmetic of adding numerals you will get 1400 N. 
Is that correct?

Forces have directions.  The wind is forcing the boat to East while the current is taking it to North. 
So how can you add them? 

 The quantities that have a magnitude and direction are called ‘vectors’. These have to be added considering their direction. Let us consider a line diagram method to solve this problem .


Fig.2. A graph drawn to scale 100= i.

The red line represents the wind force while the force of the river water is shown in black.

The Green line, the diagonal gives the Resulting force. This can be eithr measured or calculated using the Pythagoras theorem.

How to get the direction?

The angle between the resultant and the x axis could be either measured or calculated using trignometry as shown below.

  Calculating the resultant and the direction.

       For the calculation we can easily use the Pythagoras  theorem.

R 2 = S 2  + N 2

R  =  √  42   +  32

R = 5

The angle may be calculated as follows using trigonometry.

Tan θ  = N / s

    = 3/ 4

    =  0.75

Therefore θ = 36.9 degrees.               

       For a detailed lesson click  Vectror- addition