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 impact2. 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

Tennis: ball & racket, ball & court

Influencing factors: grip, racket size & weight, string type, tension, swing kinematics, ball condition

OR -e = v1 – v2

u1 – u2

Moving body & stationary one

Describes the interaction between two bodies during an impact

e = rebound height

drop height

Increased by impact velocity & temperature

Lab exercise……

Work, Power & Energy Relationships

Work: from a mechanical standpoint

Force applied against a resistance X the distance the resistance is moved

W = FdW = 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 hill4. 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 cmt = 15 s

Power

Rate of work production

P = W or P = fd t t

P = Fv• Units: watts 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 Nh = 30 X 25 cm

t = 15 sW = 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 motionKE = ½ mv2

KE = 0 when motionless Increases dramatically as v increases

2kg

1 m/s

2kg

3 m/s

Kinetic energy Increases dramatically as v increases*

KE = ½ mv2

* exponential increase

2kg 2kg

1 m/s 3 m/s

KE = (0.5) (2 kg) (1 m/s)2

= (1 kg) (1m2/s2) = 1 J

KE = (0.5) (2kg)(3m/s)2

= (1kg)(9m2/s2) = 9 J

Potential energy

“..energy stored because of position….” wt of a body X ht above reference surface Stored energy

PE = wt • hPE = magh

Example: 1 m50 kg

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

What is the velocity justbefore impact with the floor?

2kg

1.5 m