MasterColg

Elaborate.

The energy has to come from somewhere. In the example of the pitch it was chemical energy converted by muscle cells into kinetic. Do you honestly expect me to believe that our pitcher burns more calories in one frame of reference than another in a single pitch?

It doesn’t hold true in the light of empirical evidence. The Pitcher is at rest in reference to the train. If the observer on the train records a velocity of 10mps forward and the train is moving at 10mps forward, then the observer at the rail bed must record a velocity of 20mps vis-a-vis the Galilean transformations. The supposition that a pitcher must exert two separate levels of force in a single pitch to satisfy the requirements of separate frames of reference is patently absurd. The supposition that a pitcher on a train must exert more force, i.e. impart more energy to the ball to achieve 10mps in a forward throw than a rearward throw is likewise patently absurd. -------------------------------------------------------------------------- The rocket is moving at 10,000mps with respect to buoy A after burning 1g of fuel. It releases buoy B and is now at rest in reference to it. Both the rocket and buoy B are now moving at 10,000mps in reference to buoy A. The Rocket now burns 1g of fuel along the original vector and is now moving (as you have already stated) at a velocity of 10,000mps in reference to buoy B. Again this is simple addition of velocity. If Buoy A is stationary, Buoy B is moving at 10,000mps relative to it, and the rocket is moving 10,000mps faster than Buoy B along the same vector, then the rocket must be moving at a velocity of 20,000mps relative to buoy A.

You have one Throw and two observers: Observer A is standing next to the pitcher on the train. He records a speed of 10mps or 50J Observer B is standing next to the rail bed beside the train. He records a speed of 20mps or 200J Trace the origin of the balls kinetic energy for both frames of reference. --------------------------------------------------------------------------- The rocket is moving at 10,000mps with respect to buoy A after burning 1g of fuel. It releases buoy B and is now at rest in reference to it. It burns its remaining gram of fuel along what ever vector you like. What is its speed now in reference to buoy B?

Ill begin by addressing your reply in reverse order: Chemical energy in my arm is translated into Kinetic energy in the ball, which is then translated into thermal energy in the glove. Kinetic energy is not conserved but energy in general is. It is true that I did not take the trains reaction of my throw into account. It would have been minute and there are a lot of other things that I didn’t take into account, Wind resistance and gravity just to name two. None of these things are relevant to the question and I ignored them for simplicity’s sake. The calculation of an objects kinetic energy is completely dependant on frame of reference. However the statement that I imparted 50J of energy to the ball is not. It is based on the referential frame of the thrower and no one in an external frame will observe differently. The scenario works fine if we adhere to a single frame of reference, that of the catcher: As we stand together by the tracks he will observe the ball approach him at 10mps and he can calculate the Kt to be 50j. As the train passes and the ball is dropped to him he will observe it to be traveling at 10mps and he can again calculate the Kt to be 50j. Again the train passes and the ball is thrown, he observes the ball approach him at 20mps (disregarding external influence) He can then calculate the Kt to be 200j. Here the question arises. He knows the limit of my arm is 10mps or 50j. He knows that the speed of the train is constant and that any reaction of it to my throw would have had a negative affect on the speed and energy of the ball therefore it’s contribution could only have been 10mps or 50j. He knows that energy can be converted from one form to another, but it cannot be created or destroyed and he wonders where the extra 100j came from… I constructed the scenario with frames of reference as an aid to understanding. The formula implies that it requires 4 times as much energy to accelerate an object to 100mps as it does to accelerate it to 50mps. Here is another illustration: Take a rocket in deep space. You place a buoy (A) to provide a frame of reference and burn half of your fuel in acceleration. (Assume that this fuel is energy dense so that the loss of its mass will not unduly affect the next phase, say the ships mass is 1,000,000Kg, it contains 2grams of fuel and it burns 1g in the first phase) Your buoy’s beacon now indicates that it is receding at a rate of 10000mps. You place a second buoy (B) and burn the remaining fuel along the same vector. The signal from B indicates a velocity of 10000mps and the signal from A indicates a velocity of 20000mps, all is well except that according to the formula you should have burned 4 times as much fuel to reach 20000mps as you did to reach 10000mps.

E = .5*m*v^2 I have a problem with this formula. To illustrate lets play some mental catch with a friend. Assume I have a ball weighing 1 Kg and that I can throw it 10mps. When my friend catches it he will absorb the 50joules of transitional kinetic energy that my arm had imparted to the ball. My arm gets tired and I board a train and my friend remains by the track. (Didn’t I mention that we were playing catch next to a railroad track that goes in a big circle? Well we are…) The train is traveling at 10mps and as I pass my friend I drop the ball so he can catch it. Again when my friend catches it he will absorb the 50joules imparted to the ball by the train. My arm is feeling better now so I throw the ball to my friend as the train passes him. The train is going 10 mps and I throw at 10mps giving the ball a combined speed of 20mps. This time when my friend catches the ball he must according to the formula absorb 200joules of energy imparted to the ball by the train and my arm. The question is, if I imparted 50joules and the train imparted 50joules, where did the other 100 joules come from? Can anyone help me out here?