Forces

Resultants at 90°

Finding the Resultant & Equilibrant of Two Perpendicular Forces

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Do Now warm-up prompt

Two forces at 90° to each other combine like the legs of a right triangle

Angle = 90°

Ranking Task

Two forces act on a body. Rank the angles between the forces below, from largest resultants to smallest.

Ranking task diagram of angle pairs between two forces

Video Instruction

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D. Finding Resultants When the Angle Between Forces = 90°

Given

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!!)

Ruler

1. Draw vectors to scale (1 N = 1 cm)

Two vectors drawn to scale

2. Make a parallelogram

Parallelogram constructed from the two vectors

Protractor 101

Using a protractor to measure an angle
1. Use the Acute Angles Only   2. Use a ruler to get accurate measurements
Protractor measurement example
Protractor measurement example

3. Draw diagonal (resultant)

Diagonal of the parallelogram drawn as the resultant vector

4. Find magnitude & direction of vector

Tape measure Protractor

Parallelogram Method

Parallelogram method diagram

Method Two — Trig. and Pythagorean

(More accurate)

1. Use a² + b² = c² (to find magnitude)

Right triangle formed by the two forces and the resultant

5.0 N² + 12 N² = R²

2. Tan θ = Opp./Adj.

Tan θ = 5.0/12   →   θ = ?

Calculator 2nd function button
Tan (5/12) — Inverse Tangent (5 /12)
Compass rose showing N, S, E, W directions
Right triangle formed by the two forces and the resultant
↓

5.0 N² + 12 N² = R²     Tan θ = 5.0/12

R = 13 N, 22.6° N of W

Name That Direction

Four vectors drawn at various compass angles to name

50 degrees N of E, 35 degrees N of W

65 degrees S of W, 80 degrees S of E

Video Instruction

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E. Equilibrant — Balancing Force

Spider-Girl catching a falling man
Resultants and Equilibrants animation preview
Resultants & Equilibrants   [HTML5]
Show Me The Physics

Video Instruction

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The Equilibrant is always equal in magnitude and opposite in direction to the resultant.

[Flash]

Given

If the Resultant = 5 N, 53° N of W…

↓

Then the Equilibrant is equal in magnitude, opposite in direction:

Equilibrant = 5 N, 53° S of E

Video Instruction

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Ex 2

Given

Concurrent forces (acting together) of 10. nt east and 10. nt south act on an object.

Resultant & Equilibrant using Trig. & Pythagorean Theorem

Two concurrent force vectors, 10 N east and 10 N south
Right triangle diagram for the concurrent forces
↓

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!

Intermolecular bonds between water molecules are very strong

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Forces Not at 90° →