Case III Ө ≠0°≠180°

C. Combining Forces - Range of possible resultants

Ex) Forces of 100 N and 30. N force act on a body.  

Largest possible resultant =

Smallest possible resultant = ?

Concurrent Forces

All forces pass through
a common point

Not Concurrent

Ex) Which pair of concurrent forces may have a resultant of 20 nt?

a)  5 nt + 10 nt

b)  20 nt + 20 nt

 c)  20 nt + 50 nt

d)  30 nt + 5 nt  

Hint: Find the range of possible resultants for each choice

D. Finding resultants when angle between forces = 90°

Scale 1 N = 1 cm

Two Methods

Method One
 Graphical Method

(Draw It!!)

1. Draw vectors to scale (1 cm = 1 N)

2. Make parallelogram

3. Draw diagonal (resultant)

4. Find magnitude & direction of vector

Method Two

 - Trig. and Pythagorean
(More accurate)

1. Use a² + b² = c² (To find magnitude)

5.0 N²  + 12 N²  = R²

2.  Tanq =  Opp./Adj.

TanӨ = 5.0/12

Ө = ? 

Tan (5/12)

Inverse Tangent (5 /12)

13 N  22.6 ° N of W 

E. Equilibrant - Balancing Force

Resultants & Equilibrants
St. Mary's Physics

The Equilibrant is always equal in magnitude and opposite in direction to the resultant

If…

Equilibrant  = 5 N 53° S of E

Ex 2) Concurrent forces (acting together)
of 10. nt east and 10. nt south act on an object.

Resultant & Equilibrant using
Trig. & Pythagorean Theorem

1.  10 N² + 10 N² = c²

c = 14 nt

2.  R = 14 nt 45° S of E

Equilibrant  = 14 nt  45° N of W

Result.  Angle ≠ 90

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