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Case III q ≠0°≠180°
C. Combining Forces - Range of possible resultants
Ex) Forces of 100N and 30N force act on a body.
Largest possible resultant =
Smallest possible resultant = ?
Ex) Which pair of concurrent forces may have a resultant of 20 nt?
a) 5 nt + 10 nt
Hint: Find the range of possible resultants for each choice
D. Finding resultants when angle between forces = 90°
Ex1) A 5N 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 - Use trig. and Pythagorean (More accurate)
1. Use a2 + b2 = c2 (To find magnitude) 5 N2 + 12 N2 = R2
2. Tanq = Opp./Adj. = 5/12 q = _________
13 N 22.6 ° N of W
E. Equilibrant - balancing force
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. Find resultant & equilibrant using the trig. & Pythagorean theorem
1. 10 N2 + 10 N2 = c2 c = 14 nt
2. R = 14 nt 45° S of E
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