Forces

Resolution of Forces

Breaking a Single Force into Perpendicular x/y Components

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Do Now warm-up prompt

Resolving a force means breaking a single vector into perpendicular horizontal (Fx) and vertical (Fy) components

Figure calculating
Ranking Task Ranking task diagram of resultants at several angles

Rank the resultants from smallest to largest.
Hint: 0 degrees - Max R

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St. Mary's U. Astronomy and Physics Dept.

What crushed this can?

When the can is immersed in the water, the pressure inside the can is lower than the pressure outside

Review

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One of these things is not like the other!

One of these things is not like the other game
The idea for this game and graphic above come from a great high school physics teacher named Kelly O'Shea.
Rolling down animation
HaeLim (Emily) Wee, Class of 2017

Video Instruction

showmethephysics.com

Man pushing a refrigerator
Force on refrigerator acts in 2 directions
Force acting in two directions diagram
Force acts in 2 directions

H. Resolution of Forces

Breaking down a single vector into 2 or more vectors

Force components animation preview
[HTML5]
Show Me The Physics
Force resolved into perpendicular components diagram
Force resolved into perpendicular components diagram
Force resolved into perpendicular components diagram

Which component is responsible for making this cart move?

↓

Only horizontal part (Fx) of applied force

If the angle were increased, how would it change the size of the:

Vertical component?

↓

Increase

Horizontal component?

↓

Decrease

Video Instruction

showmethephysics.com

Ex 1

Given

A car is pulled with a force of 60. N at angle of 37° from the horizontal.
Find: the vertical and horizontal components of the applied force

Scale: 1 cm = 10 N

Force vector at an angle with a right triangle of components
Force vector diagram with angle and hypotenuse labeled
Force vector diagram with components labeled

Using Trigonometry

Right triangle showing SOHCAHTOA relationships for the force triangle
Sinθ = Opp = Fy
Hyp F

Cross Multiply

Fy = Fsinθ

Fx = Fcosθ

“One size fits all”

SOHCAHTOA reference card
Right triangle showing SOHCAHTOA relationships for the force triangle
↓

Fy = 60. N sin 37°

Fy = 36 N Up

Fx = 60. N cos 37°

Fx = 48 N Right

Check — a2 + b2 = c2

36 N2 + 48 N2 = 60. N2

Ex 2

Given

Weight of Cart = 80 N

Cart on an incline showing weight force

Horizontal Component of Weight Force?

↓

0 N

Vertical Component of Weight Force?

↓

80. N

Horizontal Component

0 N

Cart on an incline showing weight force

Vertical Component

80 N down

Ex 3

Given

A 50. N force at an angle of 80° has its angle changed to 10.°.
Find: How will the vertical and horizontal components change?

Angle and components animation preview
Angle & Components - Flash   [HTML5]
Show me The Physics Website
↓

Vertical component - smaller

Horizontal component - larger

Ranking Task

Rank the Vertical Components from least to greatest.

Ranking task diagram of vertical components
Explain your answers

Ex 4

Given

Parallel & perpendicular components

Box on a ramp components animation preview
[ Flash ]   [ HTML5]
Show Me The Physics
Box on ramp weight force diagram
F = 10. N (Weight)
Box on ramp weight force diagram with components
F = 10. N (Weight)
Box on ramp force diagram

Find the force holding the cart on the ramp and the force that acts down the ramp

↓

Force (down ramp) = Fapplied sinθ

= 5.0 N

Force (on ramp) = Fapplied cosθ

= 8.7 N

Ranking Task

Rank the parallel component from greatest to smallest.

Ranking task diagram of ramp components

Rank the perpendicular component from greatest to smallest.

Finding a horizontal component

Box on a Ramp

Show Me The Physics
YouTube Channel

Drag and Drop the forces on the center of the box

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