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Linear Kinetics Work, power & energy

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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

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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

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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

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Coefficient of restitution Describes relative elasticity of an impact Unitless number between 0 and 1 Between two moving bodies Between balls and surface

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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

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Moving body & stationary one Describes the interaction between two bodies during an impact e = rebound height drop height Increased by impact velocity & temperature

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Lab exercise……

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Work, Power & Energy Relationships

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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*

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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?

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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!

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Example problems W = (100 N) * (5 m)* cos(0 degrees) = 500 J

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W = (100 N) * (5 m) * cos(30 degrees) = 433 J

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W = (100 N) * (5 m) * cos(0 degrees) = 500 J

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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

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Power Rate of work production P = W or P = fd t t P = Fv Units: watts W = 1J/s

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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?

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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

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Power Applications Throwing, jumping, weight lifting, sprinting Force & velocity critical to performance Power experiment

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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

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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

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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

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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

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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

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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

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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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