Transcript 008 Newton`s Second Law Explored

Kinetics are the Cause
• Kinetics cause Kinematics (not vice versa)
• Kinematics such as velocity describe the
motion.
• Kinetics such as force, tell us what
produced the motion.
• E.g., A force acting on a mass produces
an acceleration, which results in a change
in velocity, and thus a change in
displacement.
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Newton’s Second Law
Explored
The acceleration of an object is
proportional to the net force acting
on it. The acceleration is also in
the same direction as the force.
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F = ma
• All the external forces acting on an
object are summed using vector
addition to give you a net force which
has both a magnitude and direction.
• This net force will accelerate the
object in the direction of the net force,
and with a magnitude inversely
proportional to the object’s mass.
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What’s the acceleration of
the mass?
F2
F1
F3
F4
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Finding Net Force
F2
Net Force: F
F3
F3
F4
F1
F2
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F1
F4
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Representing Net Force
5 kg
Net Force: F
50 N
CM
a = 50 N = 10 m/s/s
5 kg
The net external force will accelerate the object’s center
of mass (CM).
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Vector Addition
y
Net Force or Resultant: FR
30 N
5 kg
x
10 N
30 N
10 N
FR =  (302 + 102) = 31.6 N
Tan  = Opposite = 10 N = 0.33
Adjacent
30 N
 = Arctan (0.33) = 18.4
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a = Net Force/Mass
a = 31.6 N / 5 kg = 6.3 m/s/s
a = 6.3 m/s/s
18.4
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Resolving Vectors into
y
Components
5 kg
30
30
50 N
x
50 N
Fy
Fx
Force Components
Cos (30) = Adj = Fx
Hyp
50 N
Fx = Cos (30)*50 N = 43.3 N
ax = Fx/m = 43.3 / 5 = 8.7 m/s/s
Sin (30) = Opp = Fy
Hyp
50 N
Fy = Sin (30)*50 N = 25.0 N
ay = Fy/m = 25.0 / 5 = 5.0 m/s/s
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Acceleration Components
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F = ma not always useful
• F = ma, tells us the instantaneous
acceleration when the net force acts.
• For most practical situations in
biomechanics, velocity has more
meaning than acceleration.
• Further, practitioners such as coaches
are usually interested in the velocity
after a net force has acted.
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Impulse
• To determine the speed of a baseball pitch,
or how high someone will jump, we are
interested in the average force exerted
while the hand is in contact with the ball or
the feet are in contact with the ground.
• The product of the average force and the
time that it acts is called impulse.
Impulse   F  t
• A net force of 100 N acting for 2 s generates
200 Ns of impulse.
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Change in Momentum
• The momentum of an object is the
product of its mass and velocity.
Momentum  mv
• Conveniently for biomechanists, the
Impulse-Momentum relationship states
that a net impulse equals a change in
momentum.
• This relationship is really just a revised
(actually original) form of the 2nd Law.
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Newton’s
nd
2
Law Revised
 F  ma
Multiply both side by t
 Ft  mat
Since v = at
 Ft  mv
Impulse
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Change in momentum
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Impulse = Ft = Fdt
• Impulse is the area under the force time
curve.
• It is the sum of all the infinitely small areas
• It is equal to the change of momentum of
an object. Momentum = mass x velocity.
• If the object’s mass remains constant,
impulse changes the velocity of an object.
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Impulse: Force vs. Time Graph
Force (N)
Time (s)
•Impulse = Fdt = F1t1 + F2t2 + F3 t3 + …… = mv
Instantaneous Force
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Infinitely small time period
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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. Area under curve = 7 Ns
ΣFΔt= Impulse
Impulse = 7 Ns
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Force
(N)
Time (s)
0.5
Impulse = m (Vf – Vi), Since Vi was zero,
Vf =Impulse / m =
7 / 0.2 = 35 m/s = 78.8 mph
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Ball Example
F = 490.5 N
A 490.5 N net force acts vertically
downward on a 50 kg wrecking
ball for 2 s.
50 kg
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
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