Work, Power and Energy RelationshipsDr. Claire Egret

IntroductionWork Force application over a distancePower Amount of mechanical work performed in a given timeEnergyThe capacity to do work or sustain power

Work, Power, and Energy RelationshipsWhat is mechanical work? the product of a force applied against a resistance and the displacement of the resistance in the direction of the forceW = Fd units of work are Joules (J)

WorkWhen the muscles of the human body produce tension resulting in the motion of a body segment, the muscles perform work on the body segment.

Example : Athlete bench presses mass of 40kg over distance of 0.3m (up phase), Calculate the work.

WorkThe mechanical work performed may be characterized as either positive or negative work.When both the net torque and the direction of the motion are in the same direction, the work done by the muscles is said to be positive.Performing positive mechanical work typically requires greater caloric expenditure than performing the same amount of negative mechanical work.

Work, Power, and Energy RelationshipsWhat is mechanical power? the rate of work production calculated as work divided by the time over which the work was done WP = t units of work are Watts (W)

ProblemA 580N person runs up a flight of 30 stairs of rise (height) of 25cm during a 15s period.How much mechanical work is done?How much mechanical power is generated?

Measurement of Work and Power

The term ergometry refers to the measurement of work output.Ergometer refers to the apparatus or device used to measure a specific type of work.One of the earliest ergometers used to measure work capacity in humans was the bench step.

Measurement of Work and PowerBench StepWork = force x distance= mg x distance = 70 x 10 x (0.5 x 30 x 10)= 105000 joules= 105 kilojoulesPower = work minutes = 105000 / (10 x 60) = 175 W

Suppose a 70kg man steps up and down on a 50cm bench during 10 minutes at a rate of 30 steps per minute. Calculate the work and the power.

Measurement of Work and PowerCycle ErgometerSuppose a 70 kg man performed cycle ergometer exercise during 10 minutes and applied 20N on the pedals. If you know that:- distance traveled per pedal revolution = 6m- pedaling speed = 60 revolutions per minutes

Calculate the work and the power developed by this man.

ExampleWork = force (kg) x distance (m)= 20 x (6 x 60 x 10)= 20 x 3600= 72000 Joules or 72 kilojoules

Power = work minutes= 72000 / (10 x 60)= 120 W

Measurement of Work and PowerTreadmill Incline of the treadmill is expressed in percent gradePercent grade is the amount of vertical rise per 100 units of belt travelFor example, a subject walking on a treadmill at a 5% grade travels 5 meters vertically for every 100 meters of the belt travel.

Vertical displacement = % grade x Distance

Determination of Percent Grade on a Treadmill

Work, Power, and Energy RelationshipsWhat is mechanical energy? the capacity to do work units of energy are Joules (J)

there are two forms energy: kinetic energy potential energy

Work, Power, and Energy RelationshipsWhat is kinetic energy? energy of motionKE = mv2 and KE = I2 What is potential energy? energy by virtue of a bodys position or configurationPE = (wt)(ht)

Work, Power, and Energy RelationshipsWhat is the law of conservation of mechanical energy?When gravity is the only acting external force, a bodys mechanical energy remains constant.KE + PE = C(where C is a constant - a number that remains unchanged)

Work, Power, and Energy RelationshipsHeight, velocity, potential energy, and kinetic energy changes for a tossed ball. Note: PE + KE = C

ProblemA 2kg ball is dropped from a height of 1.5m. What is its velocity immediately before impact with the floor?

Work, Power, and Energy RelationshipsWhat is the principle of work and energy?The work of a force is equal to the change in energy that it produces in the object acted upon.W = KE + PE + TE(where TE is thermal energy)

ProblemHow much mechanical work is required to catch a 1.3kg ball traveling at a velocity of 40m/s?

ExampleThe work-energy relationship is evident during movements of the human body.The arches in runners feet act as a mechanical spring to store and subsequently return, strain energy as they cyclically deform and then regain their resting shapes.Two-joint muscles in the human body also serve to transfer mechanical energy from one joint to another, thereby reducing the mechanical work required of the muscles crossing the second joint during a given movement.

ConclusionApproximately 25% of the energy consumed by the muscles is converted into work, with the remainder changed to heat or used in the bodys chemical processes