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I have a question about certain conditions in Newtonian mechanics...

Let's say you had an incline, with a pulley at the edge of the top, frictionless, let's keep the string & pulley masses negligible, and there's a light string connecting an object hanging, and an object on the incline...

I know that all of our assumptions that tension is equal is true, but how is the tension equal throughought? Isn't it accelerating a different value on both sides? I know I'm probably asking a stupid question, but if the two masses are different (one is 3kg, one is 9kg, for instance) the acceleration on one due to the tension will be more than the other, wouldn't it? Or would it not?

Can someone explain this to me with proof behind the explanation? (Again, apologize if this is a stupid question)

Also, let's say a projectile was thrown with some initial velocity. At its highest point, when we consider its potential energy, (Let's say it has a constant horizontal velocity, i.e. it was given that initial velocity at an angle in the first place) do we consider it by considering both the horizontal potential and kinetic energy as well as the vertical potential and kinetic energy, (by using vector addition and the like) or do we consider them to be two different things and ignore the horizontal direction?

Can someone explain this with proof and perhaps an example?

Thanks a lot for any responses.

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# Two questions concerning mechanics

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