Chapter 12

1
Chapter 12 Linear Kinetics
2

• Force
• The push or pull acting on the body measured in
  Newtons (N)
• The relationship between the forces which affect
  a body, and the state of motion of that body, can
  be summarized by Newtons three Laws of Motion
• 1. Law of Inertia
• A body will continue in its state of rest or
  motion in a straight line, unless a force (i.e.,
  a net or unbalanced force) acts on it
• 2. Law of Acceleration
• If net force acting in a body is not zero, the
  body will experience acceleration proportional to
  the force applied
• S F m a Units 1N (1 kg) (1 m/s2)
• 3. Law of Action/Reaction
• For every action, there is and equal and
  opposite reaction.

3
Sprinting example
Free Body Diagram
4
Ground Reaction Force
SF m . acg (GRFv - W) m .
acg where GRFv vertical ground reaction
force W weight m body mass acg is the
vertical acceleration of the center of gravity
(CG)
GRFv
If GRFv W, then SF 0 (no net force) and
acg 0 If GRFv gt W, then SF gt 0 (net force
upwards) and acg gt 0 (positive) If GRFv lt
W, then lt 0 (net force downwards) and acg lt 0
(negative)
5

• If GRFv W, then SF 0 (no net force) and
  acg 0
• 1. CG Motionless
• 2. CG moving with a constant velocity
• If GRFvgt W, then SF gt 0 (net force upwards) and
  acg gt0 (positive)
• 1. the speed of the CG is increasing as it
  moves upward ( dir)
• 2. the speed of the CG is decreasing as it
  moves downward (- dir)
• If GRFv lt W, then lt 0 (net force downwards) and
  acglt 0 (negative)
• 1. the speed of the CG is decreasing as it
  moves upward ( dir)
• 2. the speed of the CG is increasing as it
  moves downward (- dir)
• Rapid Squat force trace.

6

• Ground reaction force examples
• 1. A person whose mass is 75 kg exerts a
  vertical force of 1500N against the ground. What
  is the individuals acceleration in the vertical
  direction? (Remember to state whether the
  acceleration is positive or negative

Weight mg 75 kg x ( 9.81 ms-2) - 736N SF
ma 1500 736 75 a a (1500 736)/75
10.2 ms-2
736 N
1500 N
7

• 2. If the same person then reduces the vertical
  force to 500 N, what acceleration does the
  persons CG now have?

SF ma 500 736 75 a a (500 736)/75 -
3.15 ms-2
736 N
500 N
8
A 90 kg sprinter pushes against the blocks with a
force of 2000 N at an angle of 30o to the
horizontal. Neglecting air resistance, what is
the acceleration of the sprinters CG in both the
horizontal and vertical directions? What is the
resultant acceleration?

• 1. Apply SF ma in the horizontal
• direction
• 2000 (cos 30o) 90 x ah
• ah (2000 (cos 30o))/90
• ah 1732.1/90 19.25 ms-2
• 2. Apply SF ma in the vertical
• direction
• 2000 (sin 30o) - 882.9 90av
• av (1000 882.9)/90
• av 1.3 ms-2

9N
3.
R
1.3 ms-2
19.25 ms-2
Resultant acceleration R2 1.32 19.252 R
19.29 ms-2
9
Momentum

• Quantity of motion that a body possesses
• Product of mass and velocity M mv
• In the absence of external forces, the total
• momentum of a given system remains constant
• Conservation of Linear Momentum
• Total momentum before Total momentum after

10
V 5 m/s
Example
Total momentum before Total momentum after ML
MR MBoth mLvL mRvR mBothvBoth (130 kg)
(5 m/s) (85 kg) (-6 m/s) (130 kg 85 kg)
(vBoth) 650 kg m/s 510 kg m/s (215 kg)
(vBoth) vBoth (650 kg m/s 510 kg
m/s)/215 kg 0.65 m/s
11
Impulse Momentum Relationship

• MBefore SF (?t) MAfter
• where SF (?t) impulse
• Example 90 kg person lands from a jump. Just
• before impact, vertical velocity v - 5 m/s.
  What
• would be the mean net ground reaction force if it
• takes 0.1 s to reach zero velocity?
• MBefore SF (?t) MAfter
• (90 kg) (- 5 m/s) SF (0.1 s) 90 kg (0 m/s)
• SF (90 kg) (5 m/s)/ 0.1 s 4500 N 5 times
  body weight
• What if it took 0.25 s to reach zero velocity?
• SF (90 kg) (5 m/s)/ 0.25 s 1800 N 2 times
  body weight

12
Impulse in a javelin throw. Elite athletes are
able to apply a force over a longer time frame by
leaning back and pulling the javelin from behind
the body and releasing it far out in front.
13
Impulse in the high jump. Elite jumpers lean back
prior to take-off which allows them to spend more
time applying force to the ground.