FREE BODY DIAGRAM FBD

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FORCES
NET FORCE
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FREE BODYDIAGRAMFBD
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From Simple to Complex

• 1) Horizontal plane
• 2) Inclined plane

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Drawing a FBD of forces on an object (on, not
by) 1. Choose the object to analyze. Draw it as
a dot. 2. What forces physically touch this
object? This object, not some other 3. What
action at a distance forces act on the
object? Gravity is the only one for this
PHYS2053 4. Draw these forces as arrows with
tails at the dot (object). 5. Forces only! No
accelerations, velocities, Get components of
Newtons 2nd Law Choose a convenient xy
coordinate system Find the x and y components of
each force in the FBD Add the x and y components
separately
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y
x positive y positive
x
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y
x negative y positive
x
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y
x
x negative y negative
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y
x
x positive y negative
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y
x positive y positive
x
??????
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y
q
x
q
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Horizontal plane

• 1) Horizontal force

Fa
A horizontal force Fa of 12 N is applied To a
block with mass m6kg, on a frictionless table.
The block was originally at rest when the force
was applied. Draw a FBD and find the acceleration
of the block and its velocity after it travels
0.4m from the origin
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FBD
y
Normal force mg 6kg 9.81 m/s2 (along
y) Weight -mg (along y) Applied force 12 N
along x
x
The net force F the y component is zero because
the normal Force and the weight cancel. The x
component is the applied Force. Hence Fx 12 N
and Fy 0 N
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The net force F the y component is zero because
the normal Force and the weight cancel. The x
component is the applied Force. Hence Fx 12 N
and Fy 0 N Applying the second Newton/s
law F m a Fx max
ax Fx/m ax 12N/6kg
ax 2 m/s2
Velocity after it travels 0.4 m from the
origin The block was originally at rest vx0
0m/s vx2 vx02 2ax(x-x0) vx v2ax(x-x0)
vx 1.26 m/s
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Horizontal plane

• 2) Force at an angle

q
A force Fa of 15 N making an angle of 35o from
the horizontal is applied to a block with mass
m6kg, on a frictionless table. The block was
originally at rest when the force was applied.
Draw a FBD and find the acceleration of the block
and its velocity after it travels for 5 seconds
from the origin
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FBD
Normal force
N
y
There is no motion in the y Direction (the block
does not jump !!!) Fy 0 N Hence Normal force N
wFsin(q) Motion along x Fa,x m ax ax
15N cos (35o)/6kg ax 2.05 m/s2 vx vo
axt vx 0m/s (2.05m/s2)(5s) vx 10.25 m/s
Fa,x
m
q
Fa,y
applied force
Fa
W
weight
x
Fx Fcos(q) Fy Fsin(q)
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Horizontal plane

• 3) Force at an angle friction

q
A force Fa of 15 N making an angle of 35o from
the horizontal is applied to a block with mass
m6kg, on a table with friction force Ff
opposing the motion of the block of 5.2 N
magnitude. The block was originally at rest when
the force was applied. Draw a FBD and find the
acceleration of the block and its position after
it travels for 5 seconds from the origin
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FBD
Normal force
N
y
There is no motion in the y Direction (the block
does not jump !!!) Fy 0 N Hence Normal force N
wFsin(q) Motion along x Fa,x Ff m
ax ax (15N cos (35o) -5.2N)/6kg ax 1.18
m/s2 x xo voxt (1/2) axt2 x
(1/2)(1.85m/s2)(5s)2 x 14.77 m
m
Fa,x
Ff
q
applied force
Fa,y
Fa
W
weight
x
Fx Fcos(q) Fy Fsin(q)
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y
q
x
q
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a 90o - ?
ß 90o - a ß 90o - (90o - ?)
ß ?
ß ???
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Inclined plane
1) Only gravitational force
d h/sin(q)
d
M 25 kg ? 25o h 2 m
Question What is the velocity of the block at
the bottom of the frictionless incline?
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FBD
Wx W sin ? Wy W cos ? N -Wy
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y-component of the net force is zero!
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A box with mass 45 kg is at rest when a force Fa
(20N)making an angle of 370 with the inclined
plane. The inclined plane makes an angle of 220
with the horizontal plane. When the box is
moving on the inclined Plane, there is a friction
force Ff of 5 N opposing the motion. The box
was Originally at a height h from the ground (h4
m). Draw the free body diagram for the box.
Determine the components x, y for all the forces
acting on the box. Find the net force and
acceleration Of the box.
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The conditions for a particle to be in equilibrium

• Necessary conditions for an object to settle into
  equilibrium
• SF 0
• SFx 0 and SFy 0

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• Both x and y forces must be considered separately.

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Homework from chapter 4

• 3, 9, 14, 20, 21, 23, 30, 34, 41, 52

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