How to derive the law of conservation of mechanical energy

AI Thread Summary
The discussion focuses on deriving the Law of Conservation of Mechanical Energy from the Work-Energy Theorem, specifically aiming to arrive at the equation 0 = ΔU + ΔK. Participants express uncertainty about where to begin the derivation and seek guidance on assumptions that should be stated. The context involves a lab experiment with a cart being pulled by a hanging mass, utilizing a force sensor for tension measurement and a position sensor. Clarification on the relationship between work done, potential energy (U), and kinetic energy (K) is emphasized as crucial for the derivation. Overall, the thread highlights the need for foundational understanding of energy transformations in mechanical systems.
Chase R
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Homework Statement



Derive the Law of Conservation of Mechanical Energy starting from the Work-Energy Theorem. State any assumptions.

Homework Equations



I'm not really sure where to start with this. Basically how to end up with the equation 0=\DeltaU+\DeltaK

The Attempt at a Solution

 
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Anyone? It's for a lab that's due tomorrow morning. Any little info on where I should start with this would be great! By the way, if it helps, the procedure for this lab was a cart that it is getting pulled forward by a hanging mass. There was a force sensor to measure the tension in the string and a position sensor.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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