Linear Kinetics
Work, power & energy
Today
 Continue the discussion of collisions
 Discuss the relationships among
mechanical work, power and energy
 Define center of gravity and explain
the significance of center of gravity
location in the body
Impact
 Type of collision characterized by
exchange of a large force over a
small time
 Post impact behavior depends on
collective momentum & nature of
impact
1.Perfectly elastic impact
2.Perfectly plastic impact
Elastic vs plastic
 Perfectly elastic
 Velocities after impact are same as
velocities before
 Perfectly plastic
 One of the bodies does not regain
original shape & bodies do not separate
Coefficient of restitution
 Describes relative elasticity of an
impact
 Unitless number between 0 and 1
 Between two moving bodies
 Between balls and surface
Two moving bodies
 “…the difference in their velocities immediately after
impact is proportional to the difference in their velocities
immediately before impact..”
-e = relative velocity after impact
relative velocity before impact
OR
-e = v1 – v2
u1 – u2
 Tennis: ball & racket, ball & court
 Influencing factors: grip, racket size &
weight, string type, tension, swing
kinematics, ball condition
Moving body & stationary one
 Describes the interaction between
two bodies during an impact
e=
rebound height
drop height
 Increased by
temperature
impact velocity &
Lab exercise……
Work, Power & Energy
Relationships
Work: from a mechanical standpoint
 Force applied against a resistance X
the distance the resistance is moved
W = Fd
W = F X d X cos
ex: 20N
moves 5 m in direction of F
W = 100 Nm or 100 J
 No movement --- no mechanical work*
Muscles perform work
 Positive work: muscle torque &
direction of angular motion in same
direction
 Negative: muscle torque & direction of
angular motion opposite
 Units: N • m = J
 Is isometric exercise mechanical work?
Work examples
1. Lifting a weight from the ground to a
shelf
2. Bringing the weight from another
room????
3. Driving up hill
4. Driving down hill?????
Work is energy that has been used!
Example problems
W = (100 N) * (5 m)* cos(0 degrees) = 500 J
W = (100 N) * (5 m) * cos(30 degrees) = 433 J
W = (100 N) * (5 m) * cos(0 degrees) = 500 J
Work problem
 580 N person runs up a flight of 30
stairs in 15 s
 Each stair = 25 cm height
 How much work is done?
Known: wt (F) = 580 N
h = 30 X 25 cm
t = 15 s
Power
 Rate of work production
P=W
t
P = Fv
• Units: watts
or
P = fd
t
W = 1J/s
Amanda and Shelley, are in the weight room. Amanda
lifts the 100-pound barbell over her head 10 times in one
minute; Shelley lifts the 100-pound barbell over her head
10 times in 10 seconds.
Who does the most work?
Who delivers the most power?
Power problem
 580 N person runs up a flight of 30 stairs
in 15 s
 Each stair = 25 cm height
 How much mechanical power is generated?
Known: wt (F) = 580 N
h = 30 X 25 cm
t = 15 s
W = 4350 J
Power
 Applications
 Throwing, jumping,
weight lifting, sprinting
 Force & velocity critical
to performance
 Power experiment
Energy
 “…the capacity to do work…”
 “how long we can sustain the output of
power”
 “how much work we can do”
 Mechanical energy  mechanical work
 Two forms
 Kinetic energy
 Potential energy
 Strain energy
Kinetic energy
 Energy of motion
KE = ½ mv2
 KE = 0 when motionless
 Increases dramatically as v increases
2kg
2kg
1 m/s 
3 m/s 
Kinetic energy
 Increases dramatically as v increases*
2kg
2kg
1 m/s 
3 m/s 
KE = ½ mv2
KE = (0.5) (2 kg) (1 m/s)2
= (1 kg) (1m2/s2)
=1J
* exponential increase
KE = (0.5) (2kg)(3m/s)2
= (1kg)(9m2/s2)
=9J
Potential energy
 “..energy stored because of position….”
 wt of a body X ht above reference surface
 Stored energy
PE = wt • h
PE = magh
 Example:
50 kg
1m
Strain energy
 Elastic energy
 Capacity to do work due to a deformed
body’s return to original shape
SE = ½ kx2
 K = spring constant
 X = distance deformed
 Muscles store strain energy when stretched
 Other examples
Conservation of mechanical energy
 Tossing ball into air
 As ball gains height
 gains PE
 Loses KE (losing velocity)
 At apex
 Height & PE at max value
 Velocity & KE = 0
 As ball falls
 Gains KE
 Loses PE
Conservation of mechanical energy
 “..when gravity is the only external
force, a body’s mechanical energy
remains constant...”
(PE + KE) = C
2kg
1.5 m
What is the velocity just
before impact with the floor?