# Linear Kinetics Work, power & energy. Today  Continue the discussion of collisions  Discuss the relationships among mechanical work, power and energy.

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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  Tennis: ball & racket, ball & court  Influencing factors: grip, racket size & weight, string type, tension, swing kinematics, ball condition OR -e = v 1 – v 2 u 1 – u 2

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 = 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 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 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 mv 2  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 mv 2 * exponential increase 2kg 1 m/s  3 m/s  KE = (0.5) (2 kg) (1 m/s) 2 = (1 kg) (1m 2 /s 2 ) = 1 J KE = (0.5) (2kg)(3m/s) 2 = (1kg)(9m 2 /s 2 ) = 9 J

Potential energy  “..energy stored because of position….”  wt of a body X ht above reference surface  Stored energy PE = wt h PE = ma g h  Example: 1 m 50 kg

Strain energy  Elastic energy  Capacity to do work due to a deformed body’s return to original shape SE = ½ kx 2 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 just before impact with the floor? 2kg 1.5 m

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