1. Linear Kinetics Objectives
Identify Newton’s laws of motion and gravitation and describe practical illustrations of the laws
Explain what factors affect friction and discuss the role of friction in daily activities and sports
Define impulse and momentum and explain the relationship between them
Explain what factors govern the outcome of a collision between two bodies
Discuss the interrelationship among mechanical work, power, and energy
Solve quantitative problems related to kinetic concepts

2. Linear Kinetics Outline - The Relationship between force and motion
Read Chapter 12 in text
Classification of forces
Types of forces encountered by humans
Force and motion relationships – three ways to look at it:
Instantaneous effect – Newton’s law of acceleration (F=ma)
Force applied through time (Impulse-momentum)(Ft = mv)
Conservation of Momentum
Force applied through distance (work-energy) (Fd = 1/2mv2)
Conservation of Energy
Self-study problems
Sample problems: #2 p 392; #3 p 396, #4 p 397, #5 p 402, #6 p 405, #7 p 408
Introductory problems, p 411: 1,3,5,7,8,10
Homework problems (Due Thursday, April 20)
Additional problems, p 412: 6,8,9

3. Effect of forces on the system (can be total human body, or a part of the body)
Action vs reaction
Internal vs external
Motive vs resistive
Force resolution – horizontal and vertical components
Simultaneous application of forces – determining the net force through vector summation

4. External forces commonly encountered by humans
Gravitational force (weight = mg)
Ground Reaction Force (GRF)(Figure 12-4, p 386)
Vertical
Horizontal (frictional)
Frictional force (coefficient of friction) (pp )
Elastic force (coefficient of restitution) (pp )
Free body diagram - force graph (p 63)

5. Force Plates – Measurement of ground reaction forces

6. Coefficient of friction, resistance to sliding:
Cfr = Frf /Nof
Sample Prob
# 2, p 392

7. Coefficient of Restitution (COR)
COR is a measure of the liveliness of an object
When 2 objects collide:
When one object is stationary,
this reduces to:
An alternative way to measure COR
is to drop a ball and measure the ht
bounced compared to ht dropped:

8. Coefficient of Restitution (COR)
COR of balls dropped or thrown at a rigid wooden surface is shown here.
COR increases
directly with
temperature and
inversely with
impact velocity.

9. Coefficient of Restitution (liveliness or bounciness)

10. Free body diagrams:

11. Instantaneous Effect of Force on an Object
Remember the concept of net force?
Need to combine, or add forces, to determine net force
Newton’s third law of motion (F = ma)
Inverse dynamics – estimating net forces from the acceleration of an object
Illustrations from Kreighbaum: Figures F.4, F.5, and F.6 (pp )

15. Force Applied Through a Time: Impulse-Momentum Relationship (pp 295-399)
Impulse - the area under the force-time curve
Momentum - total amount of movement (mass x velocity)
An impulse applied to an object will cause a change in its momentum (Ft = mv)
Conservation of momentum (collisions, or impacts)
in a closed system, momentum will not change
what is a closed system?
It is a system where net forces are zero
Example – horizontal movement of airborne objects, or where frictional forces are negligible
Example: Sample problem #3, p . 396
Second example – slide # 19 (football player jumping and catching a ball)

16. Sample problem #4, p 397 Impulse: area under force- time curve
Net impulse (Ft) produces
a change in
momentum (mV)
Sample problem
#4, p 397

17. Vertical
impulse
While
Running:
Area under
Force-time
curve

18. Anterioposterior
(frictional)
component
of GRF: impulse
Is area under
Force-time curve
Positive and
Negative impulse
Are equal if
Horizontal comp
Of velocity is
constant

19. Conservation of momentum: when net impulse is zero
(i.e. the system is closed), momentum does not change
Also, sample prob #3, p 396

20. Force Applied Through a Distance: Work, Power, Energy (pp 403-409)
Work - force X distance (Newton-meters, or Joules)
On a bicycle: Work = F (2r X N)
Running up stairs: Work = Weightd (slide 21)
On a treadmill: Work = Weightd X per cent grade (slide 22)
Power - work rate, or combination of strength and speed (Newton-meters/second, or watts)
On a treadmill: P = Weightd X per cent grade/ time
On a bicycle: P = F (2r X N) / time
Running up stairs: P = Weightd /time (See next slide)
Energy - capacity to do work
kinetic, the energy by virtue of movement (KE = 1/2 mv2 )
gravitational potential, energy of position (PE = weight x height)
elastic potential, or strain, energy of condition (PE = Fd)

21. Power running up stairs:
Sample prob
#6, p 405
Power running up stairs:
Work rate = (weight X vertical dist) ÷ time

22. Work while running on treadmill:
Note that vertical distance equals the product of running speed, time, and %grade.

23. Calculating Power on a Treadmill
Problem: What is workload (power) of a 100 kg man running on a treadmill at 10% grade at 4 m/s?
Solution:
Power = force x velocity
Force is simply body weight, or 100 x 9.8 = 980 N
Velocity is vertical velocity, or rate of climbing
Rate of climbing = treadmill speed x percent grade = 4 m/s x .1 = .4 m/s
Workload, workrate, or power = 980N X .4 m/s = 392 Watts
Note: 4 m/s = 9 mph, or a 6 min, 40 sec mile
Calculate your workload if you are running on a treadmill set at 5% grade and 5 m/s.
Answer for 200 lb wt (91 kg) is: 223 Watts

24. Conservation of Energy
In some situations, total amount of mechanical energy (potential + kinetic) does not change
Stored elastic energy converted to kinetic energy
diving board
bow (archery)
bending of pole in pole vault
landing on an elastic object (trampoline)
Gravitational potential energy converted to kinetic energy
Falling objects
Videodisk on pole vault

25. Energy conservation – Case I : elastic potential (strain) and kinetic
Potential energy (FD) +
Kinetic energy (1/2mv2)
remains constant

26. Energy conservation – Case II : gravitational potential and kinetic
Potential energy
(Wh) + kinetic
energy (1/2mv2)
remains constant

27. Conservation of energy: gravitational potential and kinetic
Sample problem
#7, p 408

28. Falling objects and work-energy relationship
Problem:
If a 2 kg object is dropped from a height of 1.5 meters, what will be its velocity and kinetic energy when it hits the ground?
Solution:
Kinetic energy at impact (mgh)
equals the potential energy at drop
height (½ mv2)
Potential energy at drop(mgh)
= Nm
Kinetic energy at impact
= Nm; v = 5.42 m/s

29. Three ways to minimize impact force of 2 colliding objects
Force-time, or impulse-momentum relationship (Ft = mv)
Increase time through which force is applied
Force-distance, or work-energy relationship (FD = ½ mv2)
Increase distance through which force is applied
Force-area, or pressure concept (P = F/a)
Increase area over which force is applied

30. Revisiting the problem from week 1 regarding man falling from ledge
A man fell from the railing of a walkway on a second-story apartment building. He was found lying unconscious on his back with his center of mass located 5 feet horizontally from a second story walkway and railing. The top of the railing was 21.6 ft above the ground. His blood alcohol content was found to be .30 (inebriated) and he has no memory of how he fell. In order to appraise liability for the accident, we need to determine if the victim walked into the railing or if he was sitting on the railing and fell off. Can this be done from the information given? How?
(Hint: First, find time of flight, then find horizontal velocity, then try to figure out what forces were required to obtain this velocity by using Newton’s law of acceleration (F = ma)

31. Linear Kinetics Formulae