Yes! If a and a0 are in the same direction, and we assumed that they are opposite in direction one of them would come out to be negative and correct us. Just put in the signs of the forces correctly.
Well, whatever force we apply on the spring to contract it is stored in the spring as its potential energy. So the work done in compressing the spring is F.x. Where x is the compression in the spring. As the force varies with the compression(kx) here we calculate the work done for elemenal...
Try to derive it yourself. Ill give you a hint. Restoring force applied by a spring is directly proportional to its contraction/expansion in the direction to attain natural length. F=-Kx, also work done is F. dx. Try getting an answer
Here we have just assumed a>a0. If our assumption is wrong, the acceleration will become negative and tell us that our assumption is opposite to what actually is happening. You can assume m3 to be accelerating upwards, you will get the same answer but with different signs.
Every engine has a working fluid inside it which is responsible for all the things the engine does. It is the fluid which absorbs heat from the hot reservoir and also the one to reject heat into the cold reservoir. Let's talk about the basic heat engine, A Steam engine.
Water here is the...
Okay, so isn't the heat taken by the engine equal to the heat rejected by the reservoir?
Consider your attached file, is their any other way that the heat is being dissipated or lost other than being absorbed by the engine?
Your professor is absolutely correct. See, how a heat engine works is that it absorbs heat from the hot reservoir, uses part of it to do some work and rejects the remaining heat to the cold reservoir...
By Qc = 500 you imply that the Work done by the engine is 0. I can't see it being right.
Can you show how you got it to be 500?
P. S The wording seems more than fine to me