LINEAR KINETICS (PART 2): WORK, ENERGY, AND POWER Readings: McGinnis Chapter 4

Transcription

1 LINEAR KINETICS (PART 2): WORK, ENERGY, AND POWER Readings: McGinnis Chapter 4 1 WORK: Another way of expressing the effect of a force. Mechanically, work is done on an object when a force causes a change in position. The work done on a body by a force is equal to the product of its magnitude and the distance the body moves in the direction of the force while the force is being applied to it. [so d actually stands for the component of displacement parallel to the force.] Units of measurement: N m 1 N m of work = 1 joule (J) Simple examples: 1. Weight lifting: Lifting a 750 N barbell 0.4 m from the floor...

2 Average force applied to the barbell? Will the force be constant? 2 Distance through which the force is applied? W = (750 N)(0.4 m) = = 2. Walking up a flight of stairs... Effectively raising body weight some vertical distance d represented by the height of the stairs. e.g., A person weighing 700 N climbs a flight of stairs containing twenty (20) 25 cm steps. Average force needed to raise body weight? Total vertical distance? d = (20)(25 cm) = = W = (700 N)(5 m) = =

3 3. An aerobic step routine N aerobics instructor 15 cm steps (6 inches or 0.15 m) 600 steps (e.g., 60 steps per minute for 10 minutes) Total distance body cg raised = (600 steps)(0.15 m/step) = W = We ve focused on the positive work (lifting the body). What about lowering the body? Is there work done moving down? Yes, gravity does work on the body as the muscles resist the effort (i.e., eccentric muscle activity). During eccentric activities, muscles are doing negative work.

4 From a human performance perspective, negative work by muscles is important: a) it costs energy to do negative work b) eccentric muscle activity is a major contributor to 4. Isometric muscle activity: e.g., weightlifter applies 800 N force to barbell but is unsuccessful in lifting it... How much work is done? Must be displacement in the direction of the force in order for there to be measurable work done by the force. Thus far, no mention of time required for work to be done... e.g., previous stair climbing example: 700 N person, vertical rise = 5 m Slowly (e.g., 20 s) vs. rapidly (e.g., 5 s)? 4

5 Work done in each case? 5 W = (700 N)(5 m) = 3500 J Same for both regardless of time (i.e., regardless of task intensity). The rate at which work is being done (i.e., an indicator of task intensity) = Power. POWER (or power output): : P = W / ( t) Power best mechanical indicator of the intensity of physical task. Analogous to VO 2 from physiology. Metric unit for power: watt (W) U.S. or English unit: horsepower (hp) 1 hp = 746 W Previous stair climbing example... W = 3500 J Case 1: t = 20 s, Case 2: t = 5 s

6 Average Power? 6 Case 1: P = (3500 J)/(20 s) = = Case 2: P = (3500 J)/(5 s) = = Realistic power output values for the human body? Power capabilities of the human body? Wingate anaerobic power task? Well-trained distance cyclist?

7 Ability to sustain power varies dramatically with the duration of the task Power (hp) 1.5 (1492 W) (746 W) 1.0 Sprinting: ~ hp Distance running: ~0.5 hp Duration of run (min) Other engines: 75 cc motorcycle: 5 hp 250 cc motor: hp kitchen mixer: 0.1 hp Human body... not a powerful machine, but versatile. Power can be applied in many ways for many tasks.

8 Components of human power production: 8 Strength (force producing ability combined with speed (or velocity)... P = W /( t) = (F d)/( t) since d/( t) = avg. velocity P = F v (average power) Powerful P = F v (instantaneous power) e.g., Automobile - main advantage of high hp engine is not so much in producing a high top speed but rather in generating high acceleration (e.g., 0-60 mph in short time) e.g., Human sprinter - high power output capability is especially important to success...tied to ability to accelerate to top speed. Capability of producing high muscle forces with relatively high speeds of muscle shortening

9 Link to metabolic energy cost... 9 Stair climbing: Twenty 25 cm steps in 20 seconds by a 700 N person... W = (700 N) (20)(25 cm) = (700 N)(5 m) = P = 3500 J / (20 s) = = This represents a low to moderate intensity for a physically active, young adult. Since 1 calorie (i.e., Kcal) = J (or 1 J = cal), the power output of the stepping task can be converted to other units of measurement: P = (175 J/s)(.239 cal/j) = 41.8 cal/s = Kcal/s = 2.51 Kcal/min = Kcal/hr Remember, this is the mechanical power output.

10 If the body is 25% efficient in converting metabolic energy to mechanical energy, the metabolic energy cost of the task would be 4 times greater than the mechanical power generated... (150.5 Kcal/hr) (4) = 602 Kcal/hr This is our estimate of the rate of metabolic energy consumption. Stated differently, if a candy bar contains 300 Kcal, it would require about 30 minutes to burn off that candy bar, or almost 6 hours to expend 3500 Kcal (1 lb. of fat). Challenge of the day: Estimate the rate of energy consumption for the aerobics instructor in example 3. 10

11 ENERGY: Broadly defined as the capacity to do work. 11 Three forms of mechanical energy... An object has energy by virtue of its motion (kinetic energy), position (potential energy), and/or state of deformation (strain energy): 1. Kinetic energy (KE) energy of... KE = ½ mv 2 i.e., any body in motion will possess kinetic energy e.g., a 60 kg sprinter traveling at 10 m/s KE = (½)(60 kg)(10 m/s) 2 = 3000 kg m 2 /s 2 = 2. Potential energy (PE) energy associated with an object's vertical position with respect to some arbitrary reference height, usually the ground... PE = Wh = mgh

12 12 where W is weight (which = mg) and h is height. e.g., the mechanical energy of a 1.3 N (0.13 kg) baseball thrown vertically at 10 m/s... At instant of release (h=0), PE = = KE = = At peak height (5 m), PE = = KE = = Upon returning to release position, PE = = KE = = Note the direct exchange between PE and KE PE is greatest when ball is at its highest vertical position, and when gravity is the only external force acting on an object, its mechanical energy is. (Gravity is said to be a Conservative Force.)

13 Work-Energy Theorem: 13 Because work and energy have the same units (J), you would suspect that there is a relationship between the two. This relationship is very similar to Newton s Second Law (and derived from it). The Work-Energy Theorem states that the work done by the resultant force acting on a body equals the change in of the body. Example:

14 One final mechanical energy form of interest: Strain energy (SE)... Whenever an object has the ability to return to its original shape after being deformed... (e.g., tennis ball during impact, rubber band being stretched) it is said to possess strain energy when deformed. e.g., an archery bow has the capacity to do work on an arrow (i.e., strain energy) when deformed by drawing the string back. A useful concept when considering impacts/collisions... e.g., a bouncing ball During each impact, KE from ball s fall is converted to SE during deformation. SE is then converted back to KE during restitution (during return to original shape). Because collisions are not perfectly elastic, some mechanical energy is lost as heat (bounce height gradually decreases).