Work, Power & Energy
Work The product of force and the amount of displacement along the line of action of that force. Units: ft . lbs (horsepower) Newton•meter (Joule) e
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 During 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 How much work did the lifter do to the barbell?
Calculate Work Table of Variables: Force = +1000 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 = +1000 N Displacement = +0.8 m Select the equation and solve:
- & + Work Positive work is performed when the direction of the force and the direction of motion are the same ascent phase of the bench press Throwing a ball push off (upward) phase of a jump
Calculate Work During 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 = +1000 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 = +1000 N Displacement = -0.8 m Select the equation and solve:
- & + Work Positive work Negative work is performed when the direction of the force and the direction of motion are the opposite
Energy Energy (E) is defined as the capacity to do work (scalar) Many forms No more created, only converted chemical, sound, heat, nuclear, mechanical Kinetic Energy (KE): energy due to motion Potential Energy (PE): energy due to position or deformation
KE = 1/2 mv2 Kinetic Energy Energy due to motion reflects the mass the velocity of the object KE = 1/2 mv2
Kinetic Energy Units: reflect the units of mass * v2 Units KE = Units work
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 0.145 kg Velocity = 35.8 m/s
Calculate Kinetic Energy Table of Variables Mass = 145 g 0.145 kg Velocity = 35.8 m/s Select the equation and solve: KE = ½ m v2 KE = ½ (0.145 kg)(35.8 m/s)2 KE = ½ (0.145 kg)(1281.54 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 150 pound female volleyball player moving downward at 3.2 m/s after a block?
Calculate Kinetic Energy Table of Variables 150 lbs = 68.18 kg of mass -3.2 m/s Select the equation and solve: KE = ½ m v2 KE = ½ (68.18 kg)(-3.2 m/s)2 KE = ½ (68.18 kg)(10.24 m/s/s) KE = ½ (698.16 kg m/s/s) KE = 349.08 Nm or J
Calculate Kinetic Energy Compare KE possessed by: a 220 pound (100 kg) running back moving forward at 4.0 m/s a 385 pound (175 kg) lineman moving forward at 3.75 m/s Bonus: calculate the momentum of each player
Calculate Kinetic Energy Table of Variables m = 100 Kg v = 4.0 m/s Select the equation and solve: KE = ½ m v2 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 v2 KE = ½ (175)(3.75)2 KE = 1230 Nm or J
Calculate Momentum Momentum = mass times velocity Player 1 = 100 kg * 4.0 m/s Player 1 = 400 kg m/s Player 2 = 175 * 3.75 m/s Player 2 = 656.25
Potential Energy Two forms of PE: Gravitational PE: Strain PE: energy due to an object’s position relative to the earth Strain PE: due to the deformation of an object
Gravitational PE Affected by the object’s GPE = mgh weight mg elevation (height) above reference point ground or some other surface h GPE = mgh Units = Nm or J (why?)
Take a look at the energetics of a roller coaster Calculate GPE How much gravitational potential energy in a 45 kg gymnast when she is 4m above the mat of the trampoline? Take a look at the energetics of a roller coaster
Calculate GPE Trampoline mat is 1.25 m above the ground 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 More on this GPE relative to mat Table of Variables m = 45 kg g = -9.81 m/s/s h = 4 m PE = mgh PE = 45kg * -9.81 m/s/s * 4 m PE = - 1765.8 J GPE relative to ground Table of Variables m = 45 kg g = -9.81 m/s/s h = 5.25 m PE = mgh PE = 45m * -9.81 m/s/s * 5.25 m PE = 2317.6 J
Strain PE Affected by the object’s amount of deformation stiffness greater deformation = greater SE x2 = change in length or deformation of the object from its undeformed position stiffness resistance to being deformed k = stiffness or spring constant of material SE = 1/2 kx2
Strain Energy When a fiberglass vaulting pole bends, strain energy is stored in the bent pole Pole vault explosion
Strain Energy Plyometrics When a fiberglass vaulting pole bends, strain energy is stored in the bent pole Bungee jumping When a tendon/ligament/muscle is stretched, strain energy is stored in the elongated elastin fibers (Fukunaga et al, 2001, ref#5332) k = 10000 n /m x = 0.007 m (7 mm), Achilles tendon in walking When a floor/shoe sole is deformed, energy is stored in the material . Plyometrics
Work - Energy Relationship The work done by an external force acting on an object causes a change in the mechanical energy of the object
Work - Energy Relationship The work done by an external force acting on an object causes a change in the mechanical energy of the object Bench press ascent phase initial position = 0.75 m; velocity = 0 final position = 1.50 m; velocity = 0 m = 100 kg g = -10 m/s/s What work was performed on the bar by lifter? What is GPE at the start & end of the press?
Work - Energy Relationship What work was performed on the bar by lifter? Fd = KE + PE Fd = ½ m(vf –vi)2 + mgh Fd = 100kg * - 10 m/s/s * 0.75 m Fd = 750 J W = Fd W = 100 kg * .75m W = 75 kg m W = 75 kg m (10) = 750 J
Work - Energy Relationship What is GPE at the start & end of the press? End (ascent) PE = mgh PE = 100 kg * -10 m/s/s * 1.50 m PE = 1500 J Start (ascent) PE = 100 kg * -10 m/s/s * 0.75m PE = 750 J
Work - Energy Relationship Of critical importance Sport and exercise = velocity increasing and decreasing kinetic energy of a body similar to the impulse-momentum relationship Ft = m (vf-vi)
Power The rate of doing work Work = Fd Units: Fd/s = J/s = watt
Newton’s Laws of Motion 1st Law – An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force. 2nd Law – Force equals mass times acceleration. 3rd Law – For every action there is an equal and opposite reaction.
1st Law of Motion (Law of Inertia) An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.
1st Law Inertia is the tendency of an object to resist changes in its velocity: whether in motion or motionless. These pumpkins will not move unless acted on by an unbalanced force.
Friction! There are four main types of friction: What is this unbalanced force that acts on an object in motion? Friction! There are four main types of friction: Sliding friction: ice skating Rolling friction: bowling Fluid friction (air or liquid): air or water resistance Static friction: initial friction when moving an object
2nd Law The net force of an object is equal to the product of its mass and acceleration, or F=ma.
2nd Law When mass is in kilograms and acceleration is in m/s/s, the unit of force is in newtons (N). One newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.
For every action, there is an equal and opposite reaction. 3rd Law For every action, there is an equal and opposite reaction.
3rd Law According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.