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

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 performed climbing stairs Work = Fd Force Subject weight From mass, ie 65 kg Displacement Height of each step Typical 8 inches (20cm) Work per step 650N x 0.2 m = 130.0 Nm Multiply by the number of steps

Simple machines and work-- Forces involved: Input Force FI Force applied to a machine Output Force FO Force applied by a machine

Two forces, thus two types of work Work Input work done on a machine =Input force x the distance through which that force acts (input distance) Work Output Work done by a machine =Output force x the distance through which the resistance moves (output distance)

Mechanical Advantage (MA) – expressed in a ratio WITH NO UNITS!! The number of times a machine multiplies the input force. MA = output force/input force

Efficiency Efficiency can never be greater than 100 %. Why? Some work is always needed to overcome friction. A percentage comparison of work output to work input. work output (WO) / work input (WI)

Mechanical advantage of levers. Ideal = input arm length/output arm length input arm = distance from input force to the fulcrum output arm = distance from output force to the fulcrum

2. The Wheel and Axle A lever that rotates in a circle. A combination of two wheels of different sizes. Smaller wheel is termed the axle. IMA = radius of wheel/radius of axle.

3. The Inclined Plane A slanted surface used to raise an object. Examples: ramps, stairs, ladders IMA = length of ramp/height of ramp Can never be less than one.

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

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

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)

Work - Energy Relationship If more work is done, greater energy greater average force greater displacement Ex. Shot put technique (121-122). If displacement is restricted, average force is __________ ? (increased/decreased) “giving” with the ball landing hard vs soft

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

Calculate & compare power During 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 Lifter A: 0.50 seconds Lifter 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