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Subject:
Mechanics; relationship between speed on an inclined plane and gravity
Category: Science > Physics Asked by: duepflischiesser-ga List Price: $5.00 |
Posted:
13 Mar 2003 04:42 PST
Expires: 12 Apr 2003 05:42 PDT Question ID: 175574 |
Wasn't it Galileo that dropped a feather and a cannonball on a vacuumy day from the tower at Pisa and found that they fall at the same speed? So gravity acts on all objects the same, regardless of their mass. When flying a glider one presumes that the only force moving the airplane forward is gravity; the airplane "falls" towards earth, but on an inclined plane so to speak due to its geometry. All glider pilots know that a heavier glider falls faster, i.e. travels forward faster at the same sink ratio, and that's why they have water tanks in their wings that can be filled when more speed is desired. But if mass and descent rates are independent, why is this? It doesn't have anything to do with gliders, because when skiing or bicycling with my much lighter wife, the same principle clearly applies. |
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Subject:
Re: Mechanics; relationship between speed on an inclined plane and gravity
Answered By: hedgie-ga on 13 Mar 2003 19:26 PST |
duepflischiesse The comments below provided useful information but your question " If mass and descent rates are independent, why is this? " can be addresses in a more specific manner. You are right that this behavior is universal and I will try to explain why in some cases the descent rate does and in same cases in does not depend on mass. I will describe an equation which covers both cases. I could paraphrase that equation in words if you would prefer and request that in 'clarification of the answer.' The equation describes the 'balance of forces' and is usually presented in a quite a confusing manner: http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1d.html By writing the equation down will help us to avoid semantic ambiguities which contribute to the confusion. The exact form of equation depends on specific situation. For example, here is the form which applies to a glider which is not accelerating (meaning, it's speed vector is not changing): http://www.grc.nasa.gov/WWW/K-12/airplane/glidvec.html In situation where there is acceleration, gravity and some friction the balance of forces can be written thus: Force_of_Friction + Force_of_gravity = Force_of_Inertia or Ff + Fg = Fi Lets examine these forces, the terms in this equation: Force of Inertia is Proportional to (inertial) mass: Fi = Mass* acceleration Force of Gravity (Weight) is proportional to (gravitational) mass Fg = Mass * g (g is intensity of gravitational field) Force of friction depends on many things (size, shape, speed, friction or drag coefficient d) but not on Mass: Ff = speed* d (speed of the object with respect to the medium). Thanks for bearing with us. Here is Your answer: When Ff is small (or absent) e.g. in the outer space, the equation is reduced to Fg = Fi Mass can be canceled and motion is then independent of the mass. When Ff is not negligeable, then acceleration depends on mass. DEMONSTRATION The 'evacuated cylinders' with feather and heavier object (penny) http://www.pha.jhu.edu/facilities/pir/lecdemo/M-c2a.html are built to demonstrate this: As you remove the medium (air) frictional force Ff tends to zero and both object hit at the same time - showing motion is independent of mass. Science museums, Boston, Exploratorium have a larger version of this experiment. http://www.exploratorium.edu/snacks/falling_feather.html The story of Galielo and Tower of Pisa is believed to be apocryphal; He did experiments which clarified interplay of inertia and gravity. but since he could not have 'removed the air' from Pisa., the cannon ball, penny and feather would not hit at the same time. SEARCH TERMS balance of forces (This should be used with some 'physics term' such as 'mass' or 'inertia' to weed out all metaphorical uses in other fields, such as politics) evacuated cylinder, free-fall IN CONCLUSION Thanks for asking this questions. This topic is confusing to many, partly because the 'balance of forces' is often explained in a confusing way in schools. Please feel free for ask for clarification of any term or step in this reasoning. hedgie | |
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Subject:
Re: Mechanics; relationship between speed on an inclined plane and gravity
From: dmooredotcom-ga on 13 Mar 2003 09:59 PST |
I think it was two cannon balls of different weight.. and that story is disputed. |
Subject:
Re: Mechanics; relationship between speed on an inclined plane and gravity
From: flajason-ga on 13 Mar 2003 11:15 PST |
Galileo's experiment was to actually roll two balls of different weights but same porportions down an inclined plane. Unfortunately, Galieleo lacked the precision instruments we have today to measure two balls dropped simultaneously with any accuracy. What you are asking is true to an extent, but the situations also deal with fluid mechanics, friction, and momentum. Consider a large fully weighted semi truck and a small compact car. Place them on top of a hill with a steep incline and let them roll (in nuetral) to the bottom where it levels out flat. The semi will take longer to get up to speed than the compact, but it will have more momentum when it reaches the bottom and will travel much further when it reaches the flat stretch. When skiing with your wife, you'll probably find that she gets off to a bit of a head start, but with your larger mass, once you get up to speed, it takes less effort for you to maintain your speed than it does for her. The same principle applies to the heavier glider. Hope this helps! fla-jason |
Subject:
Re: Mechanics; relationship between speed on an inclined plane and gravity
From: xarqi-ga on 13 Mar 2003 11:28 PST |
Dave Scott, during the Apollo 15 mission, dropped a hammer and a falcon feather while on the moon - they hit the surface at the same time. As for your glider, see: http://www.patprojects.org/glider/aovt/weight.htm |
Subject:
Re: Mechanics; relationship between speed on an inclined plane and gravity
From: thenextguy-ga on 14 Mar 2003 13:19 PST |
I don't believe the comment about the truck vs. car on the hill is correct. First, the speed (in the airless, frictionless case) of each will be the same. It's found by conservation of energy to be the square root of 2*g*(height difference). The same mass appears in both kinetic & potential energies. True, this does ignore some small effects - neither vehicle will reach the speed above because some of that potential energy will go into rotational kinetic energy of the wheels, and the wheels on cars & trucks are generally not the same diameter or mass. When they get to the bottom, friction will eventually stop them. The force of friction (rolling friction in this case) depends on the weight of the object (more specifically, the normal force, but they're the same magnitude on flat ground). The truck has a larger mass for friction to decelerate, but the frictional force between the truck's tires & the road is also larger because of that larger mass. When air is involved, the real point is that, at the moment something is dropped, it will accelerate towards the Earth at "g" or 9.8 m/s^2. Air resistance is proportional to the object's velocity (or v^2, sometimes) and therefore provides an opposing force which rises as the object gains speed. The gravitational force stays constant, but the force of air resistance grows until the two perfectly balance (terminal velocity). With no further acceleration, the object falls at constant velocity until it hits. So, without air, mass doesn't really affect the speed of a falling or sliding object. With it, mass & surface area & shape all become important. |
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