FORCES

Measured in Newtons (N)

 

Combining (see also resultant below)

 

If F₁ = ai + bj and F₂ = ci + dj then

F₁ + F₂ = (a + c)i + (b + d)j ie, add together the i parts and add together the j parts.

 

Magnitude

 

If F₁ = ai + bj then,

Magnitude (length)  

 

Direction

 

If F₁ = ai + bj then,

 

 

Resultant

To find the resultant of two forces, add their i parts and their j parts.

 

If F₁ = ai + bj and F₂ = ci + dj then the resultant (R) is

R = F₁ + F₂

R = (a + c)i + (b + d)j

 

Eg If  = 2i + 3j and  = 5i  7j, then the resultant of AB and CD is:

 

R =  +     = 2i + 3j + 5i  7j

                        = 7i  4j

 

Equivalent Systems

 

If two systems are equivalent it means:

a)       their resultants are equal

b)       the sum of horizontal forces (i parts) will be the same for both systems.

the sum of vertical forces (j parts) will be the same for both systems.

 

Eg If  = 2i + 3j and  = 5i  7j are equivalent to xi + yj then

 

xi + yj   = 2i + 3j + 5i  7j

 

equating i (horizontal) and j (vertical) parts

 

xi         = 2i + 5i

            = 7i                  (ie. x = 7)

 

yj         = 3j  7j

            = - 4j                (ie. y = -4)