Intro to Finding Resultants
Pre  Class Questions 1  3 Review – Finding
Resultants (F_{net})
Resultant  Single force that produces the same result as 2 or more forces
1. Angle between vectors below = 0 degrees (Same Direction) F_{net} = 9.0 N East F_{net} = 12 N Right
ADD Forces when angle = 0 deg
2. Angle between vectors below = 180 deg.
F_{net} = 40 N East (Subtract Forces)
3. Naming Direction with Angles The vector on the upper right is 50 degrees N of
E.
4. Angle between vectors = 90 degrees. Use TRIG to find the direction.
2. Make a parallelogram 3. Draw diagonal (resultant) 4. Find magnitude & direction of vector 1. Use a^{2} + b^{2} = c^{2} (To find magnitude)
5. 10. nt east and 10. nt south act on an object. Find F_{net} Finding F_{net} Using Components
Video Instruction showmethephysics.com
Find the resultants
Step 1. Find Components of all vectors (Use neg. and pos.)
Step 2. Add Components Find F_{y} and F_{x} of resultant F_{x} = 4.0 N  3.0 N= 1.0N F_{y} = 3.0 N  1.0 N= 2.0N Fx = 1.0 N Fy = 2.0 N
3. Use the pythagorean theorum to get the magnitude.
R = (1.0 N)^{2} + (2.0 N)^{2} = 2.2 N
4. Use tangent to get the direction Tangent(theta) = Fy/Fx = 2.0 N/1.0 N theta = 63 degrees R = 2.2 N 63 degrees N of E Ex) 5.0 N North & 3.0 N 30° S of E act concurrently (on a single point).
Find the F_{x} and F_{y}
1. Sketch Vectors Find F_{net} by adding components and using Tangent. Make a Table!
1. Combine F_{x} and F_{y} ΣF_{x} = 0 + 3Ncos30
ΣF_{x} = 2.6 N
ΣF_{y} = 5.0N  3.0Nsin30
ΣF_{y} = 3.5 N
Pyth. Theorem and Tangent (2.6 N)^{2} + (3.5 N)^{2} = R^{2}
tan(theta) = Fy/Fx = (3.5 N/2.6 N)
R = 4.5 N 53° N of E
E = 4.5 N 53° S of W
Quick Resultants Review 0 deg.  Same direction  ADD 180 deg.  Opp. Direction  Subtract 90 degrees  Pyth.
AP Question Hewitt Question
Ex) Relative to the ground, an airplane gains speed when it encounters wind from behind, and loses speed when it encounters wind head on.
When it encounters wind at a right angle to the direction it is pointing, its speed relative to the ground below A. increases. B. decreases. C. is the same as if there were no wind. D. Need more information.
Increases
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