Resultants when forces ≠ 90° - showmethephysics.com

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Intro to Finding Resultants

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Pre - Class Questions 1 - 3

Review – Finding Resultants (F_net)
0, 180., 90. degrees

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.
Name the rest of the directions.

35 degrees N of W
65 deg. S of W
80 deg. S 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 a² + b² = c² (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

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Find the resultants
of these 2 vectors

When theta is NOT 0, 90 or 180 it is more useful
to find F_net (Resultant)
by adding components

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

	X	Y
Vector B	4.0 N	3.0 N
Vector A	- 3.0 N	-1.0 N
F_net	1.0 N	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
of resultant in terms of theta

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

	X	Y
Vector 1	0	+5 N
Vector 2	2.6 N	-1.5 N
F_net	2.6 N	3.5 N

Pyth. Theorem and Tangent

(2.6 N)² + (3.5 N)² = R²

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.

Ranking Task

Rank the resultants from SMALLEST to LARGEST

Jan 2006

Monster Shoot Out Game

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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

1st Law AP