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 cm = 1 N???

 

 

 

 

Two Methods

 

Method One
 Graphical Method

(Draw It!!)

1. Draw vectors to scale (1 N = 1 cm)

 

 

 

2. Make a 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 

 

 

 

 

Name that direction

 

 

 

50 degrees N of E, 35 degrees N of W

65 degrees S of W, 80 degrees S of E

 

 

 

 

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

 

 

 

Let's go to the Videotape!

 

 

Result.  Angle ≠ 90

 

  

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