ch4 Newton's Laws NOTES.notebook 1 December 02, 2013 F ree B ody D iagram s Common Forces: • Gravity (F G ) • Normal (F N ) • Friction (F F ) • Tension (F T ) • Spring (F S ) Always points down. Always away from surface. Opposes motion. Rope, chain, string, cable, etc. away from object. Away or towards object.
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ch4 Newton's Laws NOTES.notebook
1
December 02, 2013
Free Body Diagrams Common Forces:
• Gravity (FG)
• Normal (FN)
• Friction (FF)
• Tension (FT)
• Spring (FS)
Always points down.
Always away from surface.
Opposes motion.
Rope, chain, string, cable, etc. away from object.
Away or towards object.
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December 02, 2013
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December 02, 2013
Chapter 4 Newton's Laws (Forces)
Every object continues at a state of rest or constant velocity unless acted upon by an unbalanced force.
Inertia
Acceleration is inversely proportional to mass.
F = ma
F = ma
F = ma
Newton's First Law
Newton's Second Law
frictionless
F10 kg
a = 3.5 m/s2
The 20 kg crate accelerates to the right at 0.1 m/s2. What is the force F?
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December 02, 2013
Newton's Third Law
Forces come in pairs...action and reaction
not on the same object.....
Air pushed down
Helicopter pushed up
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December 02, 2013
NSL Problems
30 N10 N4 kg
40 N
30 Nm
a = ?
10 N
a = 2 m/s2
a = 1.45 m/s28 kg
90 N
m = ?
F = ?
F
10,000 N
9,800 N
500 N200 N
m = 1000 kg
FNET= ?
a = ?
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December 02, 2013
Normal
Weight & Normal
11 kg
8 kg
11 kgThe Moon
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December 02, 2013
FNET = ΣF = maΣFx = max
Multiple Forces
ΣFy = may
7.5 kgF = 150 Nf = 70 N
T = ?
a = 0.85 m/s2
75 kg
4 kg
[1.23 m/s2 at 4.1o]
sumup
6 kg
a = 2.5 m/s2
F = 20 N
What must be the friction force?
[5 N]
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December 02, 2013
Vertical Motion (Elevators & Pulleys)
SCALE READS THE NORMAL FORCE
scale
mgirl = 43 kg
Scale reads 370 N
a = ?
Find F if:
at rest.....
a = 0.8 m/s2
12 kg
F
What will the scale read if...
accelerates up at 1.2 m/s2
accelerates down at 4.5 m/s2m = 70 kg
What is the force of motor A and motor B?
[1.2 m/s2]
[14.7 N]
[13.5 N]
[770 N]
[371 N]
[A: 49 N]
[B: 98 N]
20 kg
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December 02, 2013
Friction
FF = μFN μ = coefficient of friction(mu)
• Opposes motion• 2 Types (static & kinetic)
A 17 kg rubber tire is at rest on wet concrete• What force is required to move it?
at rest
moving
FBD
FBD
(wet)
(wet)
• What force is required to accelerate it 3.0 m/s2 to the right?
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December 02, 2013
Solving Problems• Draw FBD (calculate F's)• Forces Cancel?• Set ΣF = ma• Solve
Curlingv0 = 4 m/s
What will be the acceleration of the stone?
How far will it travel?
μK = 0.04
[0.39 m/s2]
[20 m]
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December 02, 2013
T = 60 N8 kg
μk=0.25
What will be the acceleration?
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December 02, 2013
Inclines
F||
F Τ
θ
w = mg
θ
N
Starts at rest...how long to reach the bottom if frictionless?
1.7 m
How long to reach the bottom if μK = 0.22?
25o
[0.91 s]
[1.25 s]
If μS=0.38 what is the maximum angle it can be so it won't slip?
θ
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December 02, 2013
Multiple Objects• Draw FBD (Calculate Forces)• Forces Cancel?• Ignore Tensions...at first.• FNET = ma (which way is a?)• Solve......bubble to get tensions..
Atwood's Machine...Find the acceleration and tension in the rope.
2 kg
a = 4.2 m/s2T = 28 N
3 kg
Find the a, then the T...
Find the a and T...
6 kg 13 kg
4 kg
5 kg
a = 1.4 m/s2T = 34 N
a = 3.6 m/s2T = 81 N
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December 02, 2013
Calculate a and T if it is frictionless.
T3.5 kg
2 kg
a = 3.56 m/s2T = 12.5 N
Calculate a and T if μK = 0.33
T
2 kg
3.5 kg
a = 1.51 m/s2T = 16.6 N
Find m.....
m
4 kg
a = 2 m/s2
m = 1.28 kg
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December 02, 2013
Calculate a, T1, and T2 if frictionless.
Calculate a, T1, and T2 if μK = 0.3
T1
T2
T2T1
Calculate a, T1, and T2 if μK = 0.2
T1
T2
μK = 0.19
friction
less
a = 1.37 m/s2T1 = 88.2 NT2 = 32.3 N
a = 3 43 m/s2T1 = 6 37 NT2 = 19 1 N
a = 4 9 m/s2T1 = 4 9 NT2 = 14 7 N
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December 02, 2013
Find a, T1, and T2. No friction...
3 kg
10 kg
7 kg
T1T2
Find a, T1, and T2, μK = 0.35
4 kg
T2 6 kgT1
9.5 kg
a = 1.96 m/s2T1 = 55 NT2 = 35 N
a = 1.71 m/s2T1 = 46 NT2 = 77 N
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December 02, 2013
100 N5 kg
8 kg
Find the acceleration and the tension....
μK = 0.1
μK = 0.2
Stacked Problems.....
3 kg
μ = 0.1
μ = 0.2T
Acceleration of the 5 kg?
Find T
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December 02, 2013
24o
mB = 3.5 kgmA = 0.5 kg
μAB = 0.2
μincline = 0.045
Find the acceleration....
a = 2.14 m/s2
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