Work, Power & Energy Work, Power & Energy Explaining the Causes of Motion in a Different Way

Work lThe product of force and the amount of displacement along the line of action of that force. Units: Newtonmeter (Joule) ft. lbs (horsepower)

Work = F x d To calculate work done on an object, we need: The Force ¬The average magnitude of the force ­The direction of the force The Displacement ¬The magnitude of the change of position ­The direction of the change of position

Calculate Work lDuring the ascent phase of a rep of the bench press, the lifter exerts an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m upward lHow much work did the lifter do to the barbell?

Calculate Work Table of Variables: Force = N Displacement = +0.8 m Force is positive due to pushing upward Displacement is positive due to moving upward

Calculate Work Table of Variables: Force = N Displacement = +0.8 m Select the equation and solve:

- & + Work lPositive work is performed when the direction of the force and the direction of motion are the same l ascent phase of the bench press l Throwing a ball l push off (upward) phase of a jump

Calculate Work lDuring the descent phase of a rep of the bench press, the lifter exerts an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m downward

Calculate Work Table of Variables Force = N Displacement = -0.8 m Force is positive due to pushing upward Displacement is negative due to movement downward

Calculate Work Table of Variables Force = N Displacement = -0.8 m Select the equation and solve:

- & + Work lPositive work lNegative work is performed when the direction of the force and the direction of motion are the opposite l descent phase of the bench press l catching l landing phase of a jump

Work performed climbing stairs lWork = Fd lForce l Subject weight lFrom mass, ie 65 kg lDisplacement l Height of each step lTypical 8 inches (20cm) lWork per step l 650N x 0.2 m = Nm lMultiply by the number of steps

Work on a stair stepper lWork = Fd lForce l Push on the step l???? lDisplacement l Step Height l8 inches l“Work” per step l ???N x.203 m = ???Nm

Work on a cycle ergometer lWork = Fd lForce l belt friction on the flywheel lmass (eg 3 kg) lDisplacement l revolution of the pedals lMonark: 6 m l“Work” per revolution

Work on a cycle ergometer lWork = Fd lForce l belt friction on the flywheel lmass (eg 3 kg) lDisplacement l revolution of the pedals lMonark: 6 m l“Work” per revolution l 3kg x 6 m = 18 kgm

Similar principle for wheelchair

…and for handcycling ergometer

Power lThe rate of doing work l Work = Fd Units: Fd/s = J/s = watt

Calculate & compare power lDuring the ascent phase of a rep of the bench press, two lifters each exert an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m upward lLifter A: 0.50 seconds lLifter B: 0.75 seconds

Calculate & compare power Lifter A Table of Variables F = 1000 N d = 0.8 m t = 0.50 s Lifter B’s time would be.75 sec instead of.5 sec

Energy lEnergy (E) is defined as the capacity to do work (scalar)Energy l Many forms l No more created, only converted l chemical, sound, heat, nuclear, mechanical lKinetic Energy (KE): l energy due to motion lPotential Energy (PE): l energy due to position or deformation

Kinetic Energy Energy due to motion reflects l the mass l the velocity of the object KE = 1/2 mv 2

Calculate Kinetic Energy How much KE in a 5 ounce baseball (145 g) thrown at 80 miles/hr (35.8 m/s)?

Calculate Kinetic Energy Table of Variables Mass = 145 g  kg Velocity = 35.8 m/s

Calculate Kinetic Energy Table of Variables Mass = 145 g  kg Velocity = 35.8 m/s Select the equation and solve: KE = ½ m v 2 KE = ½ (0.145 kg)(35.8 m/s) 2 KE = ½ (0.145 kg)( m/s/s) KE = ½ (185.8 kg m/s/s) KE = 92.9 kg m/s/s, or 92.9 Nm, or 92.9J

Calculate Kinetic Energy How much KE possessed by a 68.1 kg female volleyball player moving downward at 3.2 m/s after a block?

Calculate Kinetic Energy Table of Variables l68.18 kg of mass l-3.2 m/s Select the equation and solve: KE = ½ m v 2 lKE = ½ (68.18 kg)(-3.2 m/s) 2 lKE = ½ (68.18 kg)(10.24 m/s/s) lKE = ½ ( kg m/s/s) lKE = Nm or J

Calculate Kinetic Energy Calculate Kinetic Energy Compare KE possessed by: l a 220 pound (100 kg) running back moving forward at 4.0 m/s l a 385 pound (175 kg) lineman moving forward at 3.75 m/s

Calculate Kinetic Energy Calculate Kinetic Energy Table of Variables m = 100 Kg v = 4.0 m/s Select the equation and solve: KE = ½ m v 2 KE = ½ (100 kg)(4.0 m/s) 2 KE = 800 Nm or J Table of Variables m = 175 kg v = 3.75 m/s Select the equation and solve: KE = ½ m v 2 KE = ½ (175)(3.75) 2 KE = 1230 Nm or J

Potential Energy Two forms of PE: lGravitational PE: l energy due to an object’s position relative to the earth lStrain PE: l due to the deformation of an object

Gravitational PE lAffected by the object’s l weight lmg l elevation (height) above reference point l ground or some other surface lh GPE = mgh

Calculate GPE How much gravitational potential energy in a 45 kg gymnast when she is 4m above the mat of the trampoline? Trampoline mat is 1.25 m above the ground

Calculate GPE GPE relative to mat Table of Variables m = 45 kg g = 10 m/s/s h = 4 m PE = mgh PE = 45kg * m/s/s * 4 m PE = J GPE relative to ground Table of Variables m = 45 kg g = 10m/s/s h = 5.25 m PE = mgh PE = 45kg * m/s/s * 5.25 m PE = J

Conversion of KE to GPE and GPE to KE and KE to GPE and …

Strain Energy lWhen a fiberglass vaulting pole bends, strain energy is stored in the bent pole lBungee jumping lWhen a tendon/ligament/muscle is stretched, strain energy is stored in the elongated elastin fibers.

Work - Energy Relationship lThe work done by an external force acting on an object causes a change in the mechanical energy of the object