(Premier Login aceputt) Forum Owner Posted Apr 29, 2009 11:25 AM
Dear BigNose,
Sorry, your description is not Newtonian. Ask any high school physics teacher. F=ma means "no acceleration, no force". If a=0, F=0. Simple.
The "force" is spoken of correctly as "what causes the acceleration". A "force" that produces 1g of acceleration from the motors of a rocket ship "accelerates" the rocket ship with a constant rate of increasing velocity, but the "acceleration" rate is CONSTANT and not increasing. A constant acceleration makes the rocket ship go faster and faster and faster and faster and faster and faster .... etc.
A ball with ZERO velocity (at Time 1) is "accelerated" with a FORCE from zero to velocity X (at Time 2) in so many seconds (Time 2 - Time 1), so the RATE of acceleration over this time is fixed and not increasing. There was ZERO acceleration before Time 1, and the Force applied accelerated the ball to Velocity X. There is no INCREASE of acceleration; there is the application of a Force to the ball of a certain magnitude that produced the change in velocity in a given amount of time.
It is of course possible to apply unequal forces over a given time span, and this causes changing rates of acceleration. A downswing with an increasing rate of acceleration versus a natural pendular pattern of downward acceleration will result in "faster" putter head velocity at the bottom of the stroke. But one can arrive at this identical velocity with a variety of acceleration patterns and timings.
The SAME force will accelerate the same two masses with exactly the same rate of acceleration. Force X1.03 will accelerate these two objects from 10 mph to 20 mph in one second, so the RATE of acceleration is 10 mph/s ("Acceleration 1"). Later, when Force X1.03 is AGAIN applied to both objects, both objects will increase AGAIN at the SAME rate of acceleration (10 mph/s) and at the end of one second both will have increased speed from 20 mph to 30 mph ("Acceleration 2") . Now if there is a third object of the identical mass in this world that is currently traveling at 5 mph, and the SAME Force X1.03 is again applied this time to all three objects, after one second the third object has accelerated at the rate of 10 mph/s from 5 mph to 15 mph, and the other two have accelerated at the SAME rate of 10 mph/s from 30 mph to now 40 mph ("Acceleration 3"). The same force applied identical times results in three identical accelerations, not one acceleration and then an INCREASED acceleration and then another INCREASED acceleration. It's the same with accelerating a car three times: the same force applied three times equally will accelerate the car from speed 1 then to speed 2 then to speed 3, and the rate of acceleration all three times is the same, not getting bigger each step up in velocity.
A car that is going at a constant velocity has NO FORCE making it go faster (or slower). Forgetting friction and air resistance, any object in constant motion is undergoing NO FORCE. No force, no acceleration; no acceleration, no change in velocity. No change in velocity, no force and no acceleration.
Your example of the car changing velocity is not an INCREASE of acceleration, since a car at any steady velocity has NO ACCELERATION AT ALL. There is no acceleration to increase. Acceleration does not "hang around" after the force has been applied. And the force does not either.
Even though you oppose the force of the engine against the force of drag, when the two forces are equal, there is NO ACCELERATION and merely a steady velocity. So far as the object is concerned, when two forces equally oppose one another, the object experiences NO FORCE. No force, no acceleration. "Newton's Second Law [F=ma] applies to a wide range of physical phenomena, but it is not a fundamental principle like the Conservation Laws. It is applicable only if the force is the net external force." No "net" force, no change in velocity.
Again, the REAL problem here is twofold: faulty conceptualization and faulty language to embody the faulty conceptualization. If you can't say it, you don't know it; and if you can't say it correctly, you don't correctly know it.
In your case, here again is your language:
"So many students (A & B included) don't connect the concept that you make your car go faster by increasing its acceleration (hence, the correct name of that pedal, the accelerator). Or that when you pedal your bike faster, you are increasing the acceleration on the bike. They don't get that the new increased speed is the result of a rebalance of the new acceleration and drag forces. They memorize F=ma, but don't actually know what it means. It is one of the toughest things to overcome -- learning that your instincts are wrong. This is true in the physics classroom, and this is true in golf. Higher speed is the result of increased acceleration, and longer drives are the rest of not using your hands, etc. You have to fight to overcome your first instincts of how position, velocity, and acceleration are related in physics and your first hit instincts in golf."
The faulty conceptualization is the notion that there IS an acceleration at Time 1 and then an increase in (this existing) acceleration to get to a faster speed at Time 2. There is not. At Time 1, when the speed is steady, there is NO FORCE and NO ACCELERATION. A "balance" of forces means there is "no net force" in any specific direction and therefore no acceleration and no change in velocity. That's the case at Time 1 for anything moving at a steady velocity -- no "net force". That's the problem in your first two sentences above.
The sentence "They don't get that the new increased speed is the result of a rebalance of the new acceleration and drag forces." implies that the acceleration is still hanging around. It's not. If there were still a Force causing any change in velocity, the velocity will continue changing as long as the force persists. That's why 1g force applied to a rocket ship will eventually accelerate the rocket ship to the speed of light.
t = [v(final) - v(initial)] / g
How long does it take a rocket ship experiencing 1g to increase velocity from zero to the speed of light? The speed of light is 186,282.397 miles per second, which is 983,307,056.16 feet per second (ft/sec). The "force" of gravity on earth gives any and all masses (1g) acceleration for free-fall at the rate of 32 feet per second each second (32 ft/sec^2). So the equation above becomes:
This number of seconds is 355.65 days. So applying 1g "force" to the back of a rocket ship in space will accelerate the rocket ship from 0 miles per hour to the speed of light 186,282.397 miles per second (or 670,616,629.2 miles per hour) so long as the force is applied and the acceleration rate stays CONSTANT for nearly a year. How much "force" is exactly needed depends upon the "mass" of the rocket ship. F=ma. To get a = 1g for a 1-ton rocket ship (2,000 lbs or 907.18474 kg of mass), F = 907.18474 kg * 9.8 m/s^2 = 8,890.4 Newtons of "force". This is the same as 1,998.5 pounds, about like the "force" that a 2,000 pound ball of iron exerts on a person's toe when it rolls on top of their foot. That much "force" applied for nearly a year will accelerate a 1-ton rocket ship to the speed of light in empty space. (I know that in Special Relativity, this description is not accurate, since a mass at a velocity near the speed of light grows "more massive", and this requires greater and greater "force" to approach closer and closer to the limit speed of light, but in "our world" the description is accurate enough for describing how 'force" and "acceleration" work together on objects.)
If you STOP or REMOVE the force early at any specific time during that 355 days, the rocket ship simply STAYS at whatever velocity it then has attained. For example, if the force at the back of the rocket ceases after 30 days or 2,592,000 seconds, the velocity of the rocket ship at that time is v = gt, or v = 32 ft/sec^2 * 2,592,000 sec, or v = 82,944,000 ft/sec (same as 15,709.09 miles/sec or 56,552,727.27 miles per hour). But for all time thereafter, the rocket ship will REMAIN at this velocity forever so long as it moves thru empty space. No change in velocity means no acceleration. So once the force ceases, the acceleration disappears (becomes zero).
Your most recent language still has this faulty conceptualization of the acceleration hanging around with a given velocity. It doesn't. Any steady velocity has ZERO acceleration. You write, however:
"And, now that we know the force the engine has to be generating, and recalling that F=ma, we find the new acceleration the engine must be producing to achieve the newer speed. The acceleration needed to achieve v_2>v_1 is greater than the previous acceleration a_2>a_1."
Your term "producing" implies the acceleration stays around or else the "new [constant] speed" will drop off. That's not a correct way to conceive the physics. You also incorrectly think that the acceleration that got the car to velocity 1 must be SMALLER than the acceleration that increases the speed from velocity 1 to the faster velocity 2. Not true. An astronaut floating in outer space with a can of aerosol hair spray will accelerate from floating "motionless" beside the rocket ship to floating away at 1 mph after a single two-second blast of the hair spray. Then he will float away at 1 mph forever. One week later, while floating deeper into space at 1 mph, the astronaut gives a second blast of hair spray for another two-second pulse and he speeds up from 1 mph to 2 mph, and then floats away forever thereafter at 2 mph. The acceleration RATES are the same going from 0 to 1 mph and from 1 mph to the greater velocity of 2 mph. The acceleration used to get from 1 to 2 mph is NOT GREATER THAN the acceleration used to get from 0 to 1 mph. Now, going 2 mph, the astronaut gives merely a ONE-second blast of hair spray. He now increases speed from 2 mph to 2.5 mph. He went from a lesser speed to a greater speed but he did so with LESS acceleration than he used to get to 2 mph. In your view, ANY acceleration that gets a moving object from velocity 1 to a faster velocity 2 must ALWAYS BE GREATER than the acceleration that sped up the object from velocity 0 to velocity 1. That's simply "wrong", as in "not really the case anywhere in the known universe."
You write: "Thusly, my statement is correct -- in order to achieve a higher velocity, you have to increase the acceleration of the car, because the increased acceleration is the increase in force the engine puts out which determines the velocity that balances the new engine force with the drag force."
Your concept is that acceleration 1 "goes with" (stays with, exists alongside of, simultaneously accompanies and is necessary to, is an essential ingredient or component of) velocity 1 and to get the car to velocity 2, you simply INCREASE acceleration 1 to acceleration 2. But the truth is that when the car is going velocity 1, there is NO ACCELERATION. Your balancing concept of engine force versus drag force is a perfect example of "naive physics" getting it wrong.
Aristotle's view that heavy objects inherently tend to come to rest and that once a force ceases, the object will stop moving, is based on the premise that "every motion has a cause", but this was eventually modified by medieval thinkers to the notion of "impulse" by which an agent of force "impresses" into an object a magnitude of force that persists therein until resistance wears the impulse down. Most people blend the Aristotelian and medieval notions:
"For some students, the effect of a force may not appear at the instant it is applied, or the effect may be self-consuming or dissipated by external
resistances:
"The force does act only after...it overcomes the initial velocity."
"This force cannot stay forever...Nothing stays forever."
"The cannon has enough force to take [a cannonball] only that far."
"The force decreases...because of the pull of gravity in that [opposite]
direction."
Your discussion uses "drag" and "balancing" with these implicit misconceptions about the nature of force and the acceleration it causes -- a blend of the notion that with the engine off the car will "naturally" stop and that only with the engine pressing acceleration steadily into the car can the car maintain a steady velocity. Velocity in itself is NOT caused by anything. In physics, an object moving at 10 mph is not different in kind from an object moving at 30 mph or at rest, but IS different in kind from an object that is undergoing a FORCE that accelerates its velocity. But once the force is no longer active, the velocity does not change any more. Nothing "causes" a moving object to "maintain" its current velocity -- that's the "weird" thing in physics that humans just don't seem to accept when they try to "cipher" it all out.
Aristotle made the same mistake with his ideas of resistance:
"Aristotle discussed the resistance of a medium in detail and inferred that the speed is inversely proportional to the resistance R, which depends on the size and shape of the body as well as the density of the medium. Thus in an appropriate system of units (which Aristotle never discusses), Aristotle's law of falling bodies can be written as v = W/R." (From I. Halloun and D. Hestenes, Common Sense Concepts about Motion, Am. J. Phys. 53, 1056-1065 (1985), accessed 04/29/09. ) That's the same thing you are doing with "drag": the car velocity depends on the "balance" or ratio of engine "force" to drag "force". (You also confuse the concepts of "work" and "force" -- the engine performs mechanical "work" by moving a mass against drag a certain distance, and the engine expresses "power" by doing X amount of "work" in a certain amount of time. For example, a horsepower is equal to 550 ft lb/s, so to move a 2,000 lb car at 35 mph or 51.5 ft/s requires 187 horsepower to shove a motionless car 51.5 feet in just one second (102,900 ft lbs/s). A "horsepower" will move one pound 550 feet in one second or, the same, will move 550 pounds just 1 foot in one second.)
NASCAR teams test the aerodynamic designs of their car (to reduce oppositional "drag") at the GM and DaimlerChrysler proving facilities in Arizona, using a "straight-line" test as follows:
"In general a proving grounds site will cover several thousand secured acres, with multiple asphalt layouts and test tracks. The GM Desert Proving Grounds, for example, covers nearly 5,000 acres, while the DaimlerChrysler Arizona Proving Grounds is approximately 5,400 acres.
The GM and Ford facilities both contain 5-mile, banked ovals with long straightaways and wide, sweeping turns. DaimlerChrysler's site has 10 major facilities, including a 4.2-mile oval, a 2.4-mile straightaway, and an 18-acre skid pad at the site's Vehicle Dynamics Facility (VDF).
Teams typically use the straightaways to perform straight-line tests, which are either coast-down tests or downforce tests. In a coast-down test, the test driver will get the car to a certain speed-200 mph, for example-then clutch the car or take it out of gear. With the car coasting, engineers will measure the time and distance it takes for the car to get to another predetermined speed-50 mph, for example. Drag is then calculated using the measurements obtained."
(Jerry Boone, Stock Car Aerodynamics - Bad Air?, StockCarRacing.com, p3, accessed 04/29/09.) This is the same as "cutting the engine off" to see the effect of drag. Once drag is removed entirely (as in outer space), cutting the engine off results in NO DECREASE IN VELOCITY. The velocity at the moment the engine is cut off simply CONTINUES FOREVER, and there is no "cause" required to "keep" the speed up, ever. Ever.
"Drag is the major obstacle to acceleration and racing speed. A passenger car driving on the highway spends an estimated 60 percent of its energy overcoming air drag, a far greater percentage than tire friction and the energy needs of the drive train itself."
"For highway driving conditions, it is estimated that driveline uses about 15% of the total energy to required to push your vehicle down the highway, tire rolling resistance represents about 25%, and air drag is about 60%!"
Perhaps a better example to help clarify the "common sense" earth-bound figuring out of all this is to consider how a fan aimed straight up gives a stream of vertical wind that keeps a ping pong ball steady at a given height against the CONSTANTLY APPLIED downward force of gravity. The wind also has to be CONSTANTLY APPLIED, but when the opposing forces "balance", there is "no net force" and hence the ball stays in one place (has zero velocity and zero acceleration). There is NO DRAG either, since the ball has to be moving to experience drag, and it's not moving. INCREASING the "force" of the wind a notch by turning up the fan will do what?
a) move the ball at a steady velocity to a higher height where it again stops;
b) move the ball with changing velocity to a higher height where it again stops;
c) start the ball rising at a steady velocity without ever stopping;
d) start the ball accelerating upward faster and faster without ever stopping.
What actually happens is that as the ball gets farther from the fan, the speed of the wind on the back of the ball diminishes (the stream is opposed by other motionless air in the way) and hence the FORCE of the wind against the ball diminishes, so the ball rises and slows, and as it moves drag also comes into the picture, so the ball rises with changing velocity but again stops at a higher height. Okay, so let's put the fan on the back of the ball like a propeller. Now what happens when you turn the velocity of the propeller up? The added FORCE from the increased propeller velocity will:
a) move the ball at a steady velocity to a higher height where it again stops;
b) move the ball with changing velocity to a higher height where it again stops;
c) start the ball rising at a steady velocity without ever stopping;
d) start the ball accelerating upward faster and faster without ever stopping.
In this case, the ball will not do either of the above, but will start accelerating from motionless to faster velocity but drag will also start to increase, so eventually the ball will settle down to a TOP velocity but will keep moving so long as the propeller stays turning at this same velocity. A skydiver free-falling from 10,000 feet will not accelerate steadily faster and faster until he hits the ground, because DRAG will result in the free-fall stalling out at a "terminal velocity" that is plenty fast, but the skydiver won't get going faster than this as he continues to fall. This terminal velocity is about 200 km/h or 124 mph. (Speed of a Skydiver (Terminal Velocity), The Physics Factbook, Hypertextbook.com.)
"A free-falling object achieves its terminal velocity when the downward force of gravity (Fg) equals the upward force of drag (Fd). This causes the net force on the object to be zero, resulting in an acceleration of zero." (Terminal Velocity, Wikipedia.com, accessed 04/29/09.) In the other direction, moving against air resistance along a highway, the drag opposes the forward motion, and, as you say, INCREASES with increasing velocity. But it is NOT "Force" from the engine that overcomes the drag; instead, it is POWER (force performing a given amount of work in a given amount of time, or the rate of doing work).
"The power needed to push an object through a fluid [or the gas of air] increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power." (Drag, Wikipedia.com, accessed 04/29/09.)
All of this "drag" business obscures and confuses the reality of the physics of force, mass and acceleration. This confusion is why Galileo and Newton both had to conceive the physics WITHOUT the drag or wind resistance or friction on earth mucking up the clarity of the physics, and this INABILITY of most humans to think like that generates "naive physics" of faulty conceptualizations of what is happening in reality.
What difference does it make in golf? It usually means the golfer "thinks" about "how hard to hit the ball" or "how fast to hit the ball" or that he needs to "increase the acceleration" of the putter thru impact to "avoid deceleration. Golfers typical misunderstand the difference between "force" and "momentum". Almost everyone does NOT get the difference between "mass" and "weight". Nearly everyone believes that the heavier object falls "faster" and therefore arrives at the bottom of a pendulum swing going "faster" than a lighter object swinging on the same radius. Nearly everyone thinks that a larger backstroke takes longer to cover the distance down to the bottom of the pendular arc than a shorter backstroke with the putter head beginning "closer" to the bottom. Golfers very nearly ALWAYS misconceive the relative influences of air resistance, green surface friction, and gravity sideways torquing of a putted ball rolling across a contoured green. Golfers have very faulty concepts of what "true roll" means, how to generate it, and what difference it makes for putts, putters, and stroke motions. Golfers and indeed supposed golf "scientists" usually confuse the relationship between potential and kinetic energy in a pendular stroke with the "force" that results from the "momentum" of the putter head impacting the ball and mistakenly believe that the energy cannot possibly be sufficient to roll a ball very far, since the putter height at the top of the backstroke is not high enough to correspond to much energy. This in turn leads these supposed experts to state that increasing acceleration and TORQUING the stroke MUST be required to get the desired level of energy, and that a natural pendular stroke CANNOT POSSIBLY generate enough force for usual putts -- all of which is incorrect. It sometimes results in golfers thinking there is a magic spot in a breaking putt where "gravity will take over and move the ball downhill the rest of the way to the hole so all the golfer needs to do is get the ball to that spot" and other nonsense like that. (What was gravity doing before that magic point -- waiting secretly in the bushes?) The basic idea that putts always travel uphill before "breaking downhill" back to the hole is incorrect in itself -- breaking putts travel "away" from a straight line between ball and hole and then travel back "towards" this line and the hole at the end of this line, but many breaking putts never result in the ball being "uphill" with the hole "downhill" beneath it -- the hole is "uphill" above the ball all the way until the ball drops over the lip. Plenty of putts are "downhill all the way", so the ball at address is presumably already at that magic point, so just tapping the ball to get it moving the least sped possible is all that should be required, but it usually isn't and this only works when the slope and green speed combine so that NO BALL WILL STOP ONCE STARTED. So that's all a very limited and limiting way to approach the issue. The misconceptions in the physics of body motion are too numerous to catalog. These misconceptions pop up all the time in golfers' thinking about what is going on and what they need to do to make things work out.
What do you think happens in a pendulum putting swing? Do you think the putter head has increasing acceleration into impact? If you think it is accelerating, that is correct, but if you think the acceleration is increasing, that is incorrect. And if you also think that the acceleration is at least NOT decreasing, that also is incorrect. The acceleration in a clock's pendulum DISAPPEARS completely right at the bottom of the stroke. Right at the bottom, the acceleration is ZERO. Before the bottom, the acceleration is DECREASING (but still positive). After the bottom, the acceleration goes from ZERO into negative, and gets more and more negative as the swing continues. If you think at the start of the downstroke from the top of the backstroke that the acceleration is INCREASING, that is incorrect. The acceleration at that point is maximum but immediately starts to diminish.
In general, people get very confused when they try to conceptualize velocity and acceleration, as you exhibit. Velocity is change of position over time and acceleration is the RATE of CHANGE (increase or decrease) of the velocity. No change in velocity, no acceleration; no acceleration, no force; any steady velocity has ZERO net force and ZERO acceleration. Any application of force to a steady velocity object imparts an acceleration from velocity X to velocity Y, but neither the force nor the acceleration need "hang around" and neither becomes "welded into" the velocity and neither is required to keep being applied to keep the velocity at the same level, as long as nothing opposes the motion of the object to slow it down.
In your drag versus engine "balancing", you confuse velocity and acceleration and also have vague and confused times that are being talked about. The drag you talk about is a CONSTANTLY APPLIED FORCE in opposition, and so must be met by the CONSTANT APPLICATION of the countering engine force. If these forces were visualized as opposing diminoes walking straight at each other meeting at a scrimmage line, one domino per slice of time, there is one white drag domino met by one black engine domino and then there is a second black engine domino like a halfback following a blocker. At each moment, the second force does its thing and disappears and the acceleration gets the car from zero to 35 mph. The acceleration RATE is not an increase over a preexisting acceleration, since there wasn't one until the halfback domino made it past the scrimmage line. Once the second black domino force has been applied, the force disappears. Then a second slice of time occurs with three other dominoes. And this keeps the car at 35 mph. That's all complicated but its not a good way to think about physics so that the reality becomes clear.
Surely you've seen the space movies where the space-walking astronauts accidentally "drops" the screwdriver and it floats away forever. If the astronaut shoved the screwdriver away towards the SUN, the screwdriver would speed up to velocity X (say, 10 mph) and then continue coasting along at this "cruise speed" forever or until it actually hit the SUN. No change in velocity once the force stops acting. At 10 mph for the rest of the trip of the screwdriver, there is no force and zero acceleration.
Steady velocity with no CHANGE in velocity, no acceleration. NO acceleration, no force. No force, no change in velocity. No change in velocity, no force.
Basically, if you depress a gas pedal 2 inches and then keep it depressed at that level, the car will get faster and faster and faster and faster and faster etc. Ignoring drag, if you get the car to 60 mph on a flat road without weight and friction and air resistance and drag, and then cut the engine off, the car will STAY at 60 mph indefinitely.
Naive physics are born out of a "common sense" wrestling to speak about what happens on earth, and this is the problem. Physics has to be conceptualized without the colored lenses of the earth-only experiences in order to get the concept correct. And then the language is not goofy.
Once the concepts get corrected, and the language goofiness subsides, THEN the person can actually learn and think and understand. But don't for a second think your explanations are free of naive physics misconceptions and goofy language. It's just human nature to do what you do. But it's not a good thing -- it's just a workable solution MOST of the time, but unfortunately not usually a workable approach for understanding sports movements and teaching and learning them.
Golf instructors who either a) cannot explain how a body skill works in terms of accurate cause and effect, or b) use odd language with embedded misconceptions of naive physics or weird anatomical or biomechanical notions as if this doesn't matter and as if clarity of understanding and teaching is not really required are not helpful in the long run. In the long run, this is a major problem that needs fixing in golf.