Resultants - Graphical Method

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

Largest Possible Resultant =

Smallest Possible Resultant = ?

Largest Possible Resultant

= 130 N

Smallest Possible Resultant

= 70. N

Subtract

Smallest Resultant

Add

Largest 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

	Max	Min
a) 5 nt + 10 nt	15 nt	5 nt
b) 20 nt + 20 nt	40 nt	0 nt
c) 20 nt + 50 nt	70 nt	30 nt
d) 30 nt + 5 nt	35 nt	25 nt

D. Finding resultants when angle between forces = 90°

Ex 1 ) A 5.0 N force pulls an object north while a 12 N force is pulling the object west.

Find the resultant

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…

Resultant = 5 N 53° N of W

Then…

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