“how physical forces affect human performance.” -video
TRANSCRIPT
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“How physical forces affect human performance.”
-video
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Sir Isaac Newton
• 1642-1727
• Physicist, mathematician, astronomer, natural philosopher, alchemist and theologian
• “The most influential person in all of human history.”
• Laid the basis for modern physics
•BIOMECHANICS
• Nothing more important than his 3 LAWS OF MOTION
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3 Laws of Motion
2 assumptions: EQUILIBRIUM and CONSERVATION OF ENERGY
Sum of all forces equals zero
Energy can never be created or destroyed only converted between forms
Law 1: INERTIA
-Every object in a state of uniform motion tends to remains in that state of motion unless an external force is applied to it.
-ex downhill skier
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Law 2: ACCELERATION
-a force applied to a body causes an acceleration of that body of a magnitude proportional to the force, in the direction of the force.
-Ex: throwing a baseball
- F = ma
- units: Newton (N)
Law 3: REACTION
-for every action there is an equal and opposite reaction
-Ex: jumping to block a spike in volleyball
**complete the handout on Newton’s three laws**
-video
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Types of Motion• Linear
• Rotational
-movement in a direction
-force through centre of mass
-Sometimes in a straight line sprinter running down track
-Sometimes change in direction “juking” in football
-F = ma, v = d/t
-movement around an axis
-force “off-centre” of mass = rotation
-gymnast flip or skater spin
-T = F(FA), I = mr2, H = Iω, ω = ΔΘ/t
Conservation of MomentumThe total momentum of any group of objects remains the same unless outside forces act on the objects
p = mv, m = mass Units: kgm/s
v = velocity
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Example 1 – Conservation of Linear Momentum
A 90 kg hockey player travelling with a velocity of 6 m/s collides with an 80 kg hockey player moving at 7 m/s. What is the resultant velocity when the two players collide?
(Since momentum is always conserved, the sum of the momentum before the collision must equal the sum of the momentum after the collision)
m1v1 + m2v2 = mtotalvresultant
(90)(6) + (80)(-7) = (90 + 80)vresultant
-20 = 170v
-0.12 m/s = v
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Rotational Motion-remember this is motion around an axis
-rotate, turn, spin, etc
Linear Motion Rotational Motion
Displacement Angular displacement ΔΘ
Velocity Angular Velocity ω
Acceleration Angular acceleration
Force Torque τ / Μ
Mass Moment of Inertia I
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Example 2 -Analyzing a figure skater spin
Part 1: How does the skater start the spin?
Outside Force
Torque = tendency of a force to rotate an object
M = force x force arm
= N x m
= Nm
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Fulcrum
Force = 100 N
Force arm = distance from force to fulcrum = 0.25 m
Torque = M = F(FA)
M = (100N) (.25m)
= 25 Nm
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So how can you manipulate this equation to increase torque?
1. Increase the amount of force
M = F(FA)
= (200)(.25)
= 50 Nm
2. Increase/Decrease force arm
M = F(FA) M = F(FA)
= (100)(.50) = (100)(.10m)
= 50 Nm = 10 Nm
This explains why you grab a LONGER wrench the tougher the bolt
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Example 2 -Analyzing a figure skater spin
Part 1: How does the skater start the spin?
Outside Force
Torque = tendency of a force to rotate an object
M = force x force arm
= N x m
= Nm
Inertia of Object
Moment of inertia = rotational inertia
I = sum of the masses x radius of gyration
= Σmr2
= kg x m x m
= kgm2
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Let’s determine the moment of inertia our figure skaters would produce doing a jump or spin.
Meghan Dwyer Kristy Bell
Now what do we need?
Mass:
Radius of gyration (ie arm length):
I = Σmr2
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Part 2 –How does the skater produce angular momentum
H = IωH = angular momentum
I = rotational inertia
ω = angular velocity
ω = Δθ/t
Units = Nm/sLet’s assume both girls have equal angular velocities of 5 radians/second
What are their angular momentums?
H = Iω
H = I(5 rad/s)
H = ? Nm/s
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Part 3 –Conservation of angular momentum
Let’s play with this equation a little bit by looking at the variables during each phase of the jump/spin
Phase 1: Entry
Remember: Momentum must stay the same
H = Iω-arms straight out; determines momentum
Phase 2: Rotation
H = Iω-arms brought tight to body
Phase 3: Exit
Angular velocity increases turn faster
-stop spin; decrease angular velocityH = Iω
Increase rotational inertia stick out arms
-video
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Example #3
A gymnast has planned to finish off her balance beam routine with a stationary front flip as a dismount. The gymnast has a mass of 40 kg and the distance from her hips to the tips of her fingers is 85 cm. Calculate her angular momentum if during her flip she is able to reach an angular velocity of 3.5 radians per second?