Chapter 12
Linear Kinetics of Human
Movement – Part 3
Basic Biomechanics, 4th edition
Susan J. Hall
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
WORK
Work done on a body by a force is equal to the
product of its magnitude and the distance the body
moves in the direction of the force.
Work = Force magnitude x Distance moved W = Fd
• Positive work: motion in same direction as applied
force (concentric)
• Negative work: motion in opposite direction as
applied force (eccentric)
• Common units: joule (J) J = Nm = .7376 ft∙lb
Mechanical work  caloric expenditure
This is a jewel
Sample Work Problem
• A weight lifter performs a two-hand snatch, a lift
in which a barbell is raised overhead in one
continuous motion. If he lifts 60 kg upward, 2
meters, what amount of work did he perform?
60 kg x 9.81 m/s2 = 589 N (F = ma)
589 N x 2 m = 1178 Nm or Joules
•The weight lifter holds the 60 kg barbell overhead.
How much work does he perform?
589 N x 0 m = 0 Nm or Joules
Sample Work Problem
• Adrian has a body mass of 76 kg and
has an arm length of 61 cm (distance from chin
to bar). If he performs 10 pull-ups, what amount
of work did he perform?
76 kg x 9.81 m/s2 = 745.5 N
745.5 N x 0.61 m = 454.8 Nm or J
• How much work does Adrian perform on his
descent?
Eccentric contraction is negative work.
POWER
Power: rate at which mechanical work is performed
Power =
Work
=
W
change in time
t
Power = force x distance =
Fd
change in time
t
Since v = d / t,
Power = Fv
Units: watts (W) 1 W = 1 J/s
English Units: horsepower 1 hp = 550 ft·lb/s
Sample Power Problem
• Brianna bounded up the six steps covering
1.05 meters in 0.75 seconds. She weighs 598 N
(61 kg). How much mechanical power does she
generate?
• W = Fd
61 kg x 9.81 m/s2 x 1.05 m
627.9 Nm or J
• P = W/t
627.9 J / 0.75 s = 837.2 J/s or Watts
ENERGY
Energy: the capacity to do work
Forms: mechanical, chemical, nuclear, heat, etc.
Mechanical energy is capacity to do mechanical work.
Units are the same as work: joules
ENERGY
Kinetic energy (KE): energy of motion
• KE = ½ mv2 = ½ kg ∙ (m2/s2) = ½ kg ∙ m/s2 ∙ m
= ½ mass ∙a∙ distance
• KE = ½ Force ∙ distance (N ∙ m or J)
Potential energy (PE): energy by virtue of a body’s
position or configuration
• PE = (wt)(h) = N ∙ m (J) or lb ∙ ft
• PE = magh
Potential Energy
Energy due to position or composition.
Stored Energy.
Potential Energy
• Which has more potential energy?
Gas has chemical
Climber is high up,
potential energy.
so she has potential
energy
•
Boulder has nowhere to
go so no potential energy
A gallon of gas can move a car 30 miles, but a rock climber landing on a car
won’t really move it much at all.
Sample Potential Energy
Problem
• What is the potential energy of a 75 kg barbell
lifted and held at a height of 2 m?
• PE = magh
PE = 75 kg x
9.81 m/s2 x
2 m =1471 Nm
Strain Energy
Strain energy (SE):
capacity to do work by
virtue of a deformed
body’s return to its
original shape
A form of potential energy
• SE = 1/2 kx2
k=constant
x = distance over which
the material is
deformed
Kinetic Energy
• Kinetic energy is the energy of things in motion:
• Kinetic energy = 1/2 mass x velocity2
• Which has more kinetic energy?
Velocity is 1800 km/hour
mass is 10 grams
10 times more energy
than the baseball
Not moving
no kinetic energy
140 km/hour
145 grams
Sample Kinetic Energy
Problem
• What is the kinetic energy of an 8 kg bowling ball
rolling with a velocity of 4 m/s?
•
•
•
•
KE = ½(m)(v2)
KE =.5 x 8 x 42
KE = 64 kg ∙ m2/s2
KE = 64 Nm or J
Conservation of Mechanical Energy
• Consider a ball tossed vertically into the air
Law of conservation of mechanical energy:
• When gravity is the only acting external force, a
body’s mechanical energy remain constant
• (PE + KE) = C
– C is a constant indicating the total amount of
energy in a system when gravity is the only
external force acting on the system
– As PE increases, KE decreases and vice-versa
Sample Problem
• A 10 kg pumpkin is dropped off a building’s roof
from a height of 18 m. What is the velocity
immediately before impact with the sidewalk?
• PE + KE = C
• PE = (wt)(ht)
and
KE = ½mv2
• OR… (v2)2 = (v1)2 + 2ad
Principle of Work & Energy
• The work of a force is equal to the change in
energy that it produces on the object acted on
• W = KE + PE + TE TE = Thermal Energy
Mechanical work  caloric expenditure
• ~25% of energy consumed by muscle is converted
into work, thus ~75% is thermal energy or used in
chemical processes.
Sample Problem
• How much mechanical work is required to catch a
0.7 kg hockey puck shot traveling at a velocity of
45 m/s?
•
•
Δ
Δ
W = Δ KE = KE2 – KE1
KE = ½(mv2)
KE = 0 – (.5 x .7 x 452)
KE = 708.75 Nm
Summary
• Mechanical work is the product of force and the distance
through which the force acts
• Mechanical power is the mechanical work done over a
time interval
• Mechanical energy has two forms: kinetic and potential
• When gravity is the only acting external force, the sum of
the kinetic and potential energies possessed by a given
body remains constant
• Changes in a body’s energy are equal to the mechanical
work done by an external force