Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: weeman on 16/03/2004 06:33:47
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This question is to be considered in space away from any effecting masses. I am trying to find a formula to figure out the loss of energy when an object weighing x amount traveling at an x amount of speed in one starting direction makes a gradual turn of 90 degrees. What is the force applied to its opposition and what speed is lost? Imagine a track in space and an object was traveling down this track at a set speed. When the object reached the curve, how fast would the track want to start moving and how much will the object want to slow down? For ease of formula imagine the track can only travel in the objects original direction, so the object would want to turn and the track would go straight.
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Issac Newton answered this question:
F=ma
where F is the force, m is the mass of the object, and a is the acceleration.
In the case you describe, there is no energy lost (assuming "perfect" interactions that don't generate heat). As for the track, I don't really understand the configuration. How much it actually moves depends on how massive it is. The total momentum ( mV )of the system will remain the same, with kinetic energy being transferred from the object to the track. Since you say the track is constrained to move only in one direction, you are assuming that there is some sort of outside force being applied to the track.
If the track is curved but constrained not to rotate or move "sideways" to the original motion of the object, then the initial momentum of the object is M1=m1v1 where v1 is the velocity of the object. In this interaction, this momentum will be transferred to the system of the object and the track M1=M2=m2v2 where m2 and v2 are the mass and velocity of the object and track. The direction of travel will be in the original direction.
I hope this helps, but I don't think I'm understanding the problem correctly.
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John - The Eternal Pessimist.
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Yes, to amplify that a bit... If you are asking how much energy is lost during a 90 degree turn of an object initially in rectilinear motion, the answer is zero, unless there is some other lossy interaction. Newtons second law, F=mA, is a vector relationship, and in performing this 90 degree turn, the force applied to the moving mass, m, is at 90 degrees to the path of the mass at all times. The energy expended is described by a vector "dot product", which is always zero when the angle between the two factors is 90 degrees. The speed of the mass is the same after the turn, although the velocity of the mass has turned by 90 degrees.
Look for a college physics textbook in your local library, and go find "uniform circular motion" for a complete explanation.
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I thought the dot product was the scalar product (and that the cross product was the vector product)?
Anyways...
I would try to help on this issue, but i really can't quite understand the question. Surely there would be absolutely no energy loss but rather an energy gain, as the force is applied perpendicular to the direction of travel and never in the opposite direction to which it is travelling?
"I have great faith in fools; self-confidence my friends call it."
-Edgar Allan Poe
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The dot product is the scalar product and the cross product is the vector product. In this case, energy is expended to accelerate the object to the new direction. However, the object will have the same kinetic energy after the turn as before because it is going the same speed. Kinetic energy is not a vector, and thus is not dependent on direction. As gsmollin says, look up "uniform circular motion" in a physics text for all the details.
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John - The Eternal Pessimist.