1. Basic Biomechanics, (5th edition) by Susan J. Hall, Ph.D.
Chapter 12
Linear Kinetics of Human Movement

2. 1st Newton’s Laws What is the law of inertia?
A body will maintain a state of rest or constant velocity unless acted on by an external force that changes the state.

3. 2nd Newton’s Laws What is the law of acceleration?
A force applied to a body causes acceleration of that body
of a magnitude proportional to the force
in the direction of the force
and inversely proportional to the body’s mass
F = ma

4. 3rd Newton’s Laws What is the law of reaction?
For every action, there is an equal and opposite reaction.
When one body exerts a force on a second, the second body exerts a reaction force that is equal in magnitude and opposite in direction on the first body.

5. Newton’s Laws
The weight of a box sitting on a table generates a reaction force by the table that is equal in magnitude and opposite in direction to the weight. wt R

6. Mechanical Behavior of Bodies in Contact
What is friction?
A force acting over the area of contact between two surfaces
direction is opposite of motion or motion tendency
magnitude is the product of the coefficient of friction () and the normal reaction force (R); F = R

7. Mechanical Behavior of Bodies in Contact
Static
Fm = sR
Dynamic
Fk = kR
Applied external force
Friction
For static bodies, friction is equal to the applied force. For bodies in motion, friction is constant and less than maximum static friction.

8. Example:
The coefficient of static friction between a sled and the snow is 0.18, with a coefficient of kinetic friction of A 250 N boy sits on the 200 N sled. How much force directed parallel to the horizontal surface is required to start the sled in motion. How much force is required to keep the sled in motion?

9. Mechanical Behavior of Bodies in Contact
Pushing a desk
Pulling a desk
R = wt + Pv
R = wt - Pv wt
Is it easier to push or pull a desk across a room?

10. Example:
If μs between a basketball shoe and a court is 0.56, and the normal reaction force acting on the shoe is 350 N, how much horizontal force is required to cause the shoe to slide?

11. Solution: μs = 0.56, R = 350 N Fm = μsR = 0.56(350)
= 196 N (greater than)

12. Mechanical Behavior of Bodies in Contact
What is momentum?
quantity of motion possessed by a body
measured as the product of a body’s mass and its velocity; M = mv

13. Mechanical Behavior of Bodies in Contact
What is the principle of conservation of momentum?
In the absence of external forces, the total momentum of a given system remains constant.
M1 = M2
(mv)1 = (mv)2

14. Example:
Two skaters gliding on ice run into each other head-on. If the two skaters hold onto each other and continue to move as a unit after the collision, what will be their resultant velocity? Skater A has a velocity of 5 m/s and a mass of 65 kg. Skater B has a velocity of 6 m/s and a mass of 60 kg.

15. Solution: ma = 65 kg, va = 5 m/s, mb = 60 kg, vb = -6 m/s
m1v1 + m2v2 = (m1 + m2)v
65(5) + 60(-6) = ( )v
v = -35/125
v = 0.28 m/s B pushing A

16. Mechanical Behavior of Bodies in Contact
What causes momentum?
impulse: the product of a force and the time interval over which the force acts

17. Mechanical Behavior of Bodies in Contact
What is the relationship between impulse and momentum?
Ft = M
Ft = (mv)2 - (mv)1

18. Mechanical Behavior of Bodies in Contact
What does the area under the curve represent? 3 2 1
Time (ms) A B
Force (Body Weight)
Force-time graphs from a force platform for high (A) and low (B) vertical jumps by the same performer.

19. Example:
A baseball with an initial velocity of 20 ms-1 is hit by a player and then moving in the opposite direction. After the ball is hit, it moves with a velocity of 36 ms-1. The ball has a mass of 0.16 kg and the time of impact is 8.0 x 10-3 s.
Calculate:
The impulse applied to the ball
The impulse force exerted on the ball by the bat

20. Mechanical Behavior of Bodies in Contact
What is impact?
a collision characterized by:
the exchange of a large force
during a small time interval

21. Mechanical Behavior of Bodies in Contact
What happens following an impact?
This depends on:
the momentum present in the system
the nature of the impact

22. Mechanical Behavior of Bodies in Contact
What is the nature of impact?
It is described by the coefficient of restitution, a number that serves as an index of elasticity for colliding bodies; represented as e.

23. Mechanical Behavior of Bodies in Contact
What does the coefficient of restitution describe?
relative velocity after impact
-e = relative velocity before impact
v1 - v2
-e = u1 - u2

24. Mechanical Behavior of Bodies in Contact
Ball velocities before impact
Ball velocities after impact
u u2
v v2
v1 - v2 = -e ( u1 - u2)
The differences in two balls’ velocities before impact is proportional to the difference in their velocities after impact. The factor of proportionality is the coefficient of restitution.

25. Mechanical Behavior of Bodies in Contact
The coefficient of restitution between a ball and a flat, stationary surface onto which the ball is dropped may be approximated using the following formula:
e = √(hb/hd)
hb = the height to which the ball bounces
hd = the height from which the ball is dropped

26. Example:
A ball dropped on a surface from a 2 m height bounces to a height of 0.98 m. What is the coefficient of restitution between ball and surface?

27. Solution:
e = √(hb/hd)
e = √(0.98/2)
e = 0.7

28. Mechanical Behavior of Bodies in Contact
What kinds of impact are there?
perfectly elastic impact - in which the velocity of the system is conserved; (e = 1)
perfectly plastic impact - in which there is a total loss of system velocity;
(e = 0)
(Most impacts fall in between perfectly elastic and perfectly plastic.)

29. Work, Power, and Energy Relationships
What is mechanical work?
the product of a force applied against a resistance and the displacement of the resistance in the direction of the force
W = Fd
units of work are Joules (J)

30. Work, Power, and Energy Relationships
What is mechanical power?
the rate of work production
calculated as work divided by the time over which the work was done W t
units of work are Watts (W)
P =

31. Example:
A set of 20 stairs, each of 20 cm height, is ascended by a 700 N man in a period of 1.25 seconds. Calculate the mechanical work, power, and change in potential energy during the ascent.

32. Solution: W = Fd, P = W/t, PE = wt(h) F = 700 N
d or h = 20 X 20 cm = 400 cm = 4m
t = 1.25 s
W = 700(400) = 2800 Nm = 2800 J
P = 2800/1.25 = 2240 J/s = 2240 W
PE = 700(4) = 2800 J

33. Work, Power, and Energy Relationships
What is mechanical energy?
the capacity to do work
units of energy are Joules (J)
there are three forms energy:
kinetic energy
potential energy
thermal energy

34. Work, Power, and Energy Relationships
What is kinetic energy?
energy of motion
KE = ½mv2
What is potential energy?
energy by virtue of a body’s position or configuration
PE = (wt)(h)

35. Work, Power, and Energy Relationships
What is the law of conservation of mechanical energy?
When gravity is the only acting external force, a body’s mechanical energy remains constant.
KE + PE = C
(where C is a constant - a number that remains unchanged)

36. Work, Power, and Energy Relationships
29.4
24.5
19.6
14.7
9.8
3.1
4.4
5.4
6.3
4.9
3.0
2.5
2.0
1.5
1.0
Ht(m) PE(J) V(m/s) KE(J)
Time
Height, velocity, potential energy, and kinetic energy changes for a tossed ball. Note: PE + KE = C

37. Example:
Using the principle of conservation of mechanical energy, calculate the maximum height achieved by a 7 N ball tossed vertically upward with an initial velocity of 10 m/s.

38. Work, Power, and Energy Relationships
What is the principle of work and energy?
The work of a force is equal to the change in energy that it produces in the object acted upon.
W = KE + PE + TE
(where TE is thermal energy)

39. Linear Kinetics of Human Movement
Chapter 12
Linear Kinetics of Human Movement