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Kinetics are the CauseKinetics are the Cause

• Kinetics cause Kinematics (not vice versa)Kinetics cause Kinematics (not vice versa)• Kinematics such as velocity describe the Kinematics such as velocity describe the

motion.motion.• Kinetics such as force, tell us what Kinetics such as force, tell us what

produced the motion.produced the motion.• E.g., A force acting on a mass produces E.g., A force acting on a mass produces

an acceleration, which results in a change an acceleration, which results in a change in velocity, and thus a change in in velocity, and thus a change in displacement.displacement.

04/21/23 Dr. Sasho MacKenzie - HK 376 2

Newton’s Second Law Newton’s Second Law ExploredExplored

The acceleration of an object is The acceleration of an object is proportional to the net force proportional to the net force acting on it. The acceleration is acting on it. The acceleration is also in the same direction as the also in the same direction as the force.force.

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F = maF = ma

• All the external forces acting on an All the external forces acting on an object are summed using vector object are summed using vector addition to give you a net force which addition to give you a net force which has both a magnitude and direction.has both a magnitude and direction.

• This net force will accelerate the This net force will accelerate the object in the direction of the net object in the direction of the net force, and with a magnitude inversely force, and with a magnitude inversely proportional to the object’s mass.proportional to the object’s mass.

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What’s the acceleration of What’s the acceleration of the mass?the mass?

F1

F3

F2

F4

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Finding Net ForceFinding Net Force

F1F4F2

F3Net Force: F F1F3

F2

F4

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Representing Net ForceRepresenting Net Force

The net external force will accelerate the object’s center of mass (CM).

CM5 kg a = 50 N = 10 m/s/s

5 kgNet Force: F

50 N

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Vector AdditionVector Addition

5 kg

10 N

30 N

30 N

10 N

Net Force or Resultant: FR

FR = (302 + 102) = 31.6 N

Tan = Opposite = 10 N = 0.33 Adjacent 30 N

= Arctan (0.33) = 18.4

a = Net Force/Massa = 31.6 N / 5 kg = 6.3 m/s/s

18.4

a = 6.3 m/s/s

y

x

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Resolving Vectors into Resolving Vectors into ComponentsComponents

5 kg

3050 N

50 N

30

Fx

Fy

Cos (30) = Adj = Fx Hyp 50 NFx = Cos (30)*50 N = 43.3 N

Sin (30) = Opp = Fy Hyp 50 NFy = Sin (30)*50 N = 25.0 N

Force Components

ax = Fx/m = 43.3 / 5 = 8.7 m/s/s

ay = Fy/m = 25.0 / 5 = 5.0 m/s/s

Acceleration Components

y

x

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F = ma not always F = ma not always usefuluseful

F = ma, tells us the instantaneous F = ma, tells us the instantaneous acceleration when the net force acts.acceleration when the net force acts.

• For most practical situations in For most practical situations in biomechanics, velocity has more biomechanics, velocity has more meaning than acceleration.meaning than acceleration.

• Further, practitioners such as coaches Further, practitioners such as coaches are usually interested in the velocity are usually interested in the velocity after a net force has acted.after a net force has acted.

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ImpulseImpulse

• To determine the speed of a baseball pitch, To determine the speed of a baseball pitch, or how high someone will jump, we are or how high someone will jump, we are interested in the average force exerted while interested in the average force exerted while the hand is in contact with the ball or the the hand is in contact with the ball or the feet are in contact with the ground.feet are in contact with the ground.

• The product of the average force and the The product of the average force and the time that it acts is called time that it acts is called impulseimpulse..

tFImpulse • A net force of 100 N acting for 2 s A net force of 100 N acting for 2 s

generates 200 Ns of impulse.generates 200 Ns of impulse.

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Change in MomentumChange in Momentum

• The momentum of an object is the The momentum of an object is the product of its mass and velocity.product of its mass and velocity.

mvMomentum• Conveniently for biomechanists, the Conveniently for biomechanists, the

Impulse-MomentumImpulse-Momentum relationship relationship states that a net impulse equals a states that a net impulse equals a changechange in momentum. in momentum.

• This relationship is really just a revised This relationship is really just a revised (actually original) form of the 2(actually original) form of the 2ndnd Law. Law.

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Newton’s 2Newton’s 2ndnd Law Revised Law Revised

vmtF

maF Multiply both side by t

Since v = at

Impulse Change in momentum

tmatF

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Impulse = Impulse = FFt = t = FFddtt

• Impulse is the area under the force time Impulse is the area under the force time curve.curve.

• It is the sum of all the infinitely small areasIt is the sum of all the infinitely small areas

• It is equal to the It is equal to the changechange of momentum of an of momentum of an object. Momentum = mass x velocity.object. Momentum = mass x velocity.

• If the object’s mass remains constant, If the object’s mass remains constant, impulse changes the velocity of an object.impulse changes the velocity of an object.

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Impulse: Force vs. Time GraphImpulse: Force vs. Time Graph

Force (N)

Time (s)

•Impulse = Fdt = F1t1 + F2t2 + F3 t3 + …… = mv

Instantaneous Force Infinitely small time period

How fast is the pitch?How fast is the pitch?A pitcher wears a special glove which allows the force between his hand and the ball to be calculated at every instant during the delivery. From the force/time graph below, we can calculate the speed of a 0.2 kg ball.

Force (N)

Time (s) 0.5

20

Area under curve = 7 NsΣFΔt= ImpulseImpulse = 7 Ns

Impulse = m (Vf – Vi), Since Vi was zero,

Vf =Impulse / m = 7 / 0.2 = 35 m/s = 78.8 mph 15Dr. Sasho MacKenzie

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Ball ExampleBall ExampleF = 490.5 N

50 kg

A 490.5 N net force acts vertically downward on a 50 kg wrecking ball for 2 s.

1. What is the acceleration of the ball?

2. If the ball was initially at rest, what is the final velocity of the ball?

These questions can be answered with both forms of Newton’s 2nd Law