Forces
Forces
• Shows all forces as vectors acting on an object
• Push or pull on an object
• Causes acceleration
• Measured in Newtons N =
Contact Forces
Applied Force
Frictional Force
Tensional Force
Normal Force
Drag Force
Spring Force
Free Body Diagrams
• Vectors always point away from object
Kg m
s2
• Used to help find net force
Field Forces
Gravitational Force
Electrical Force
Magnetic Force
FN
Fpull
Ff
Fg
1
Find the unknown forces!!
Ex. 1
100 N
Ex. 2
2
Newton’s First Law
Law of Inertia – Resistance to change motion
FA
• Objects in motion stay in motion
75 N
• Objects at rest stay at rest
50 N
Fnet = ?
Fnet = 10 N Downward
Equilibrium – balanced forces, net force = 0
Fnet = 100N – 75 N
Fnet = FA – 50 N = ‐10 N
Net force – sum of all forces
Fnet = 25 N Upward
FA = 40 N
3
Newton’s Second Law
Drag Force
A net force will cause acceleration
• “friction” force from a fluid (gases and liquids)
mass
Terminal Velocity – constant velocity of falling
F = ma
force
Gravity force →
4
when Fdrag = Fg
acceleration
F = mg
Mass and weight are not the same!!!
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1
Forces
Newton’s Third Law
Solving Tips
• Each action has an opposite and equal reaction
FA on B = ‐ FB on A
1. Draw the problem and choose coordinates
• Interaction Pair – action / reaction forces
2. Determine known and unknown forces.
3. Create a free‐body diagram showing the net force.
4. Use Newton’s laws to link acceleration and net force.
5. Solve equations for the unknowns
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Combining Forces
Normal Force
+X
FN = mg
FN = mg + Fhand
FN = mg ‐ Fstring
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Friction Factor
Friction Force
• Always against motion
• Two branches of friction (3 Types)
– Kinetic (Moving)
• Sliding
• Rolling
– Static (Stationary)
• Friction of fluids is called viscosity
Kinetic Friction
Ff = k Fn
 = friction factor
Fn = Normal Force
Static Friction
Ff,static ≤ s Fn
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2
Forces
Static Friction
Fn
Fn
• The force of static friction is not constant!
Static FFriction
• The maximum static friction is equal
q to sFn
Ff,static,max ≥ Fapplied → stays still
Ff,k
Ff,s
Kinetic FFriction
• Static friction is equal to pulling force until the
object begins to move
Ff
Ff = sFn,
Ff,s,max
Ff = kFn,
Ff,static,max = Fapplied → constant speed, a=0
Ff,static,max ≤ Fapplied → accelerates
FApplied
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Static Friction and Motion
Thrust from Friction
What is the maximum acceleration a car can achieve if
the tires/road friction coefficient is equal to 0.7?
Fn
(ignore drag)
FDrag
Fnet,x = Fthrust ‐ Fdrag = ma
Fthrust
Fg
The
h maximum thrust
h
cannot exceed
d road
d friction
f
Fthrust = Ff,s,max = sFn= s mg
From Fnet,x
ma = s mg
a = s mg = (0.7)(9.8m/s2) = 6.9m/s2
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Static Equilibrium
Static Equilibrium
The most important rule:
ALWAYS FOLLOW THESE STEPS:
F = 0
This means that:
Fx = 0
and
1.
Draw a labeled free body diagram
2.
g
forces into components
p
Break angled
3.
Write net equations ( Fnet,x = … )
Fy = 0
Only use the components of angled forces!!
Fnet,x = 0 and Fnet,y = 0
4.
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Solve for unknowns one at a time
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3
Forces
Vector Direction ( 2 Common Ways)
Working with Forces at an Angle
• Labeled degrees north or south of x‐axis
• Degrees from east direction (0°).
80° N of East
45° S of East
O 80°
Or
30° N of West
O 315°
Or
O 150°
Or
When a force is at an angle:
•break into x and y components
–Do not use the original force again!!
•Add x and y components separately
•Find the new resultant force and its angle
80°
30°
45°
O
A
 = Tan‐1
F = Fx2+Fy2
Using the angle from the x‐axis:
X‐Component
y‐Component
Fx = F cos 
Fy = F sin 
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SOH
Right Triangle Help
O
A
A = H Cos θ
 = angle
Opposiite
 = Sin‐1
O = H Sin θ
 = Tan‐1
90°
Adjacent
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Forces at an Angle ‐ Breaking into components

FPy
m
FN
Find FP Components
FPx = FP Cos 
FPy = FP Sin 
Use components
for net equations
Fnetx = FPx
Fnety = FN + FPy ‐ Fg
CAH
TOA
A
O
Cos θ =
Tan θ =
H
A
A
O
= Cos‐1
= Tan‐1
H
A
O
Sin θ =
H
90° ‐ 
You will typically want to work
with the angle from the x‐axis.
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O
H
Adjacent
Opposite
O = H Sin θ
A = H Cos θ
O = A Tan θ
A=
O = H2 ‐ A2
O
Tan θ
A = H2 ‐ O2
Hypotenuse
O
H=
Sin θ
A
H=
Cos θ
H = A2+O2
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Forces on a Ramp ‐ Breaking into components
Find Fg Components
Fgx = Fg Cos (90‐)
Fgy = Fg Sin (90‐)
FP

FPx

Or just use SOH CAH TOA
Fgx = Fg Sin 
Fgy = Fg Cos 
Fg = mg
FN should not equal Fg !!
FN = Fg ‐ Fpy if ay = 0
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Use components
for net equations
Fnetx = ‐Fgx
Fnety = FN ‐ Fgy

Fg = mg
FN should not equal Fg !!
Many cases, FN will equal Fgy
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4
Forces
Free Body Diagrams
Tension Force
Spring Force
Drag Force
1