Free-body diagram

A free-body diagram is a diagram that shows, with arrows, all of the forces exerted on an object.

A free-body diagram is a representation of the object that simplifies a situation or problem

Free-body diagram

Method:1. Determine the body whose situation is to be analyzed

2. Represent the body with a point or square that corresponds to the object's centre

3. Show, with arrows, all of the forces acting on the body, making the origin of each arrow coincide with the point (square) drawn in the previous step; the length of the arrows must be proportional to the magnitude of the forces illustrated.(draw them to scale)

Free-body diagram

A box has a mass of 12kg Fg =9.8m/s2 x 12kg = 117.6N directed down

The table it sits on exerts a normal force up, equal to the force of gravity

A student pushes with a force of 40N to the right

The force of friction is 50N to the left

Free body diagram

1)Represent the body/object with a point that corresponds to the object's center2)Show with arrows, all of the forces acting on the body. The tail of the vector should start at the pointthe length of the vector is proportional to the magnitude of the vector (use a ruler)3)Set the origin of the Cartesian plane at the point, the y axis coincides with the normal(when applicable)

Page 289 Draw free body diagrams

Resultant Force

Remember that forces of vectors

If the vectors are at an angle we must decompose them (like we did with initial velocity)

CAREFUL: Is the angle from the horizontal (x axis)or the vertical (y axis). ?Adjust accordingly.

This vector is verticalNo need to decompose

This vector is at an angle

X component =

y component = 500

FT = 20N

Fg = 30N

FN = 30 N

This vector is verticalNo need to decompose

Example B page 291

Once all the forces are decomposed

Add up all the x components

Add up all the y components

Determine the resultant vector

Magnitude: Pythagoras

Angle: Trig

Force x component y component

drive

wind

current

Total FRx= FRy=

Find the magnitude of FR

Example B page 291

Once all the forces are decomposed

Add up all the x components

Add up all the y components

Determine the resultant vector

Magnitude: Pythagorus

Angle: Trig

Force x component y componentdrivewindcurrentTotal FRx= FRy=

Find the magnitude of FR

Equilibrium.

Determine the Resultant force acting on a body. (Add up all the vector components)

To put the body into equilibrium: add a new force equal in magnitude but opposite in direction (180o in a new direction)

F = 120N [E49oN]

To put the system in equlibriumAdd a Force that is 120N [W49oS]

Example C

If given a cartesian plane, use the graph paper to calculate the x and y coponents (easy)

Force X component

Y component

TotalFR=

θ

Example C

If given a cartesian plane, use the graph paper to calculate the x and y coponents (easy)

Force X component

Y component

-50 +70-60 +40-60 -70

Total -50 +40FR=

θ=tan-1 (40/50) = 39o

64N

-40

+5064

θ

The angle in trig angle method is 141o

So to put the system into equilibrium, I will add a vector of 64N at an angle of 141o + 180o = 321o

141

Section 13.2/ p. 292

Equilibrium

When FR = 0

When we add up all the x components they = 0When we add up all the y components they = 0

then we can say the body is in a state of equilibrium

Static Equilibrium: the object is stationary

Dynamic Equilibrium: the object is at a constant velocity(and FR = 0)

Types of questions:

Verify if the body is in equilibrium

What force can we add to put the body into equilibrium

Feq = -FR

FR = 0 N

we add up all the Forces (FR), the Force (Feq) required will be the same magnitude as FR but opposite direction