Download Free Body Diagram

Newton’s 1st Law of Mechanics
A particle will continue is a straight line at constant
speed unless acted upon by a net push or pull (i.e.
force).
The property of a body to continue in a straight line at
constant speed is called Inertia.
Mass is the measure of a body’s inertia. Thus, a 2 kilogram object has twice the inertia of a 1 kilo-gram
object.
Newton’s 1st Law of Mechanics
Newton’s 1st Law tells us a couple of things:
1) The natural state of mater is a straight line at
constant speed.
2) If an object is not moving in a straight line and/or if
it is speeding up or slowing down then a net push
or pull must be acting upon the body.
Newton’s 2nd Law of Mechanics
The direction of the acceleration of a particle will be in
the direction of the net external force applied to the
particle. The magnitude of the particle’s acceleration
will be proportional to the magnitude of the net
external force applied to the particle and inversely
proportional to the mass of the particle.
F1
F2
A
F3
F1+F2+F3
Newton’s 2nd Law of Mechanics


 FExternal  m A
This is a vector equation. Each direction (x, y, and z)
can be solved independently!!
F  m A F  m A F  m A
x
x
y
y
z
z
Solving Newton’s 2nd Law
The mass of the particle is usually given or it can be
obtained using a scale. Thus, in theory all problems in
Newtonian Mechanics reduce to one of two types:
You have the acceleration and solve Newton II for
the forces.
1)
You have the forces and solve Newton II for the
particle’s acceleration.
2)
Free Body Diagrams
Solving Newton’s 2nd Law often requires us to identify
all of the forces acting upon a body.
Identifying the forces is not always obvious so
physicist have devised a graphical trick called a
Free Body Diagram to solve the left hand side of
Newton’s 2nd Law.
Drawing Free Body Diagrams
Step 1: Isolate the body
Step 2: Inventory the forces using WANTf
Step 3: Draw a coordinate axis
Step 4: Identify any critical angles or dimensions
(Our problems will generally have no angles or critical
dimensions!!)
Drawing Free Body Diagrams
Step 1: Isolate the body
Step 2: Inventory the forces using WANTf
Step 3: Draw a coordinate axis
Step 4: Identify any critical angles or dimensions
(Our problems will generally have no angles or critical
dimensions!!)
WANTf
Weight
Applied (springs, electric forces, etc.)
Normal (Force of contact)
Tension (strings or ropes)
Friction (sliding friction, air drag, etc.)
These are the only type of forces that exist in
mechanics!!!
Drawing Free Body Diagrams
Example: Draw the free body diagram for a ball falling
on the Earth with no air resistance.
Drawing Free Body Diagrams
Example: Draw the free body diagram for a ball falling
on the Earth with no air resistance.
Step 1: Isolate the body (Our body is a ball).
Drawing Free Body Diagrams
Example: Draw the free body diagram for a ball falling
on the Earth with no air resistance.
Step 1: Isolate the body (Our body is a ball)
Step 2: Inventory the forces
W
Drawing Free Body Diagrams
Example: Draw the free body diagram for a ball falling
on the Earth with no air resistance.
Step 1: Isolate the body (Our body is a ball)
Step 2: Inventory the forces
Step 3: Draw a coordinate axis
y
x
W
Drawing Free Body Diagrams
Example: Draw the free body diagram for a ball falling
on the Earth with no air resistance.
Step 1: Isolate the body (Our body is a ball)
Step 2: Inventory the forces
Step 3: Draw a coordinate axis
Step 4: Critical Angles & Dimensions (None)
y
x
W
Reading Your Free Body Diagrams
Example: Use your Free Body Diagram and your
knowledge of falling bodies to find a formula relating
weight and mass of an object.
Solution:
From reading our Free Body Diagram, we have
0  m Ax
- W  m Ay
We know that acceleration of a free falling object is
Ay   g
Reading Your Free Body Diagrams
Combining our results, we have
0  Ax
 W   mg
Thus, we have a relationship between the magnitude
of the weight of an object and the object’s mass:
W  m g  (10 m/s ) (mass in kilograms)
2
Weight VS Mass
As we learned earlier, mass is an intrinsic property of a
body that describes a bodies resistance to
acceleration.
Weight doesn’t belong to a body. It is a gravitational
force of attraction between the Earth and the body.
Without the Earth, the ball would have no weight, but it
still would have mass!!
Forces act upon bodies! They are not part of the body!
Drawing Weight Arrows
The arrow should start in the center of the body (this
point is called the “center of gravity”) and should point
straight downward toward the Earth.
Drawing Normal Force Arrows
A normal force is a force of contact between two
bodies. The force should be drawn on the free body at
the contact interface and in the direction that would
push the objects apart.
Problems
1) A TSU dorm has caught fire and a TSU student is
headed for safety by climbing down a rope. If the
students is climbing down the rope as shown below at
a decreasing speed
V
A.
B.
Draw the student’s Free Body Diagram
Determine if the student’s weight is greater or less
than the force the rope applies on the student
Problems
2) A bathroom scale actually reads the normal force
applied by the scale to you and not your weight. The
reading on the scale is sometimes called your
“apparent weight.
a) Describe a situation when the magnitude of your
apparent weight is more than the magnitude of your
actual weight.
b) Describe a situation when the magnitude of your
apparent weight is less than the magnitude of your
actual weight.
Problems
3) When a rock falls near the Earth its speed will
increase until it reaches some maximum value called
its terminal speed. After this time the air drag will
prevent the rock from gaining speed.
Draw a Free Body diagram for a rock that is falling
at its terminal speed.
a)
Determine the air drag if the rock has a mass of
2.5 kg.
b)
Problems
5) Use Newton’s 2nd Law to determine what the scale
will read in each of the problems below:
a)
2 kg
2 kg
b)
2 kg
Newton’s 3rd Law of Mechanics
If body A applies a force of some type upon body B
then body B must apply the same type of force upon
body A that is equal in magnitude and opposite in
direction.
FBA
Body A
FAB
Body B
Newton’s 3rd Law of Mechanics
Forces always come in pairs!!
If we take the entire universe as our system then the
sum of these forces always adds up to zero!!!
Thus, the total motion of the universe is always
conserved.
Physicists call this quantity related to motion the Linear
Momentum which is defined by the equation:


pmv
Conservation of Linear Momentum
The linear momentum of a system is conserved (i.e.
constant) if the system is isolated (i.e. there is no net
external force) or if the time in which any forces occur
is approximately zero (collisions, and explosions)!!




Δv m Δv  Δp
 F  m Δt  Δt  Δt


Δp   F t
 
Conservation of Linear Momentum
Example: A gun with a mass of two kilograms fires a
bullet of mass 0.005 kg with a speed of 180 m/s as
seen by an observer. What is the speed of the
recoiling gun as seen by the observer?
Solution: Considering the gun + bullet as the system,
the linear momentum just before and after the firing of
the gun is conserved.
y
x
Initially
Final
Conservation of Linear Momentum
Solution (continued):
The initial linear momentum in the x-direction is
px  2.0kg  0.005 kg( 0.0 m/s)  0.0 kg m/s
The final linear momentum is found by
p x  2.0 kg   v g  0.005 kg 180 m/s   0.0 kg m/s
y
x
Initially
Final
Conservation of Linear Momentum
Solution (continued):
2.0 kg   vg  0.005 kg 180 m/s 
vg

0.005 kg 180 m/s 

 0.45 m/s
2.0 kg