1. Classification of Forces
Action vs reaction
Internal vs external
Motive vs resistive
Force resolution – horizontal and vertical components
Simultaneous application of forces - vector summation

2. Types of external forces encountered by humans
Gravitational force (weight = mg)
Ground Reaction Force (GRF)
Vertical
Horizontal (frictional)
Frictional force (coefficient of friction)
Elastic force (coefficient of restitution)
Centripetal force (mv2/r)
Buoyant force
Free body diagram - force graph

3. Force Plates – Measurement of ground reaction forces

4. While walking

5. Cfr = Frf /Nof

6. Coefficient of restitution – Relative
velocity before and after impact:

7. Coefficient of restitution – drop test

9. Centripetal &
Centrifugal forces
Cf = mv2/r

10. Buoyant Force = weight of water displaced by a
body. If weight of water displaced by your body
is more than your body, then you will float. Your
body will only sink down to the point where Wt = Bf

11. Buoyant force = wt
of water displaced
Will this person float?
Rotate?
How can you tell?

12. Free body diagrams:

13. Free body diagrams

14. Force and Motion Relationships
Instantaneous Effect of force on motion is to accelerate the object: F=ma
Force applied through a distance: work-energy relationship
Force applied through a time: impulse-momentum relationship

15. 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 )

16. Vector Resolution Problems
Projectile motion situations
Find horizontal velocity
Find vertical velocity
Friction problems
Find horizontal force component (Friction)
Find vertical component (Normal)
First step in adding, or combining vectors
When more than one force is acting on an object
When adding velocity vectors

17. Vector resolution: Vert comp = F•sin•Θ Horiz comp = F•cos•Θ Θ Θd Θ
Turning comp = F•d•sinΘ
Radial comp = F•d•cosΘ
(d = d•sinθ)

18. Vector Addition Problems
Combining forces
Net effect of two forces applied to any object
What is maximum safe speed for a curve?
Centrifugal force, frictional force, & gravity
What makes a spitball work?
Wind force and weight
Combining velocities
In crossing a river, what direction is best?
Velocity of water and swimmer
In aviation, correcting for wind
air speed and ground speed

19. Sum of two forces: Sum of two velocities:

20. (May be deleted if your calculator provides
resultant angle in a deg system)

25. Force Applied Through a Time: Impulse-Momentum Relationship
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?

26. Impulse: area
under force-
time curve
Impulse produces
a change in
momentum (mV)

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

28. 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

29. Conservation of momentum: when net impulse is zero
(i.e. the system is closed), momentum does not change

30. Conservation of momentum: is this a closed system?

31. Force Applied Through a Distance: Work, Power, Energy
Work - force X distance (Newton-meters, or Joules)
On a bicycle: Work = F (2r X N)
On a treadmill: Work = Weightd X per cent grade
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
What about kilogram-meters/min?
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)

32. Work while pedaling on bicycle:
From McArdle and Katch.
Exercise Physiology

33. Work while running on treadmill:
From McArdle and Katch. Exercise Physiology
Note that %grade = tan θ X 100,
and tan θ and sin θ are very
similar below 20% grade

34. 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
Problem: Calculate your workload if you are running on a treadmill set at 5% grade and 5 m/s.
Answer for 200 lb wt is: 223 Watts

35. Power running up stairs:
Work rate = (weight X vertical dist) ÷ time

36. 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

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

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

39. Linear Kinetics Formulae