Recent content by JJ__

I'm using the notation T* to indicate the adjoint of T. I got as far as to say that if T is injective, then T* is surjective. But I don't know how to show that T*T is invertible. Showing that T*T is surjective or injective would imply invertibility, but I'm not sure how to do that either. I...

I can't think of a counterexample.

How far will the spring extend, given that the block is not attached? Will it extend beyond its natural length? How to calculate at what point the box comes off the spring?

This is just a conceptual question. I get that when a car is turning on an unbanked curve, the friction provides the centripetal force. I don't understand why this is though. I thought friction is supposed to oppose the direction of motion. But that would imply that the direction...

Ooh okay got it! That makes sense. Is it possible to solve for the tension forces? (If so I will try it)

Yes that's what I was assuming. Is that not correct? What exactly are the forces that are acting on the pulley and causing it to rotate?

Why would this be the case? What are the forces exerted on the pulley?

The problem is attached in the photo. The correct answer, according to the teacher's solution, was obtained using conservation of energy. Initially I tried using Newton's law/kinematics and got the wrong answer. Why didn't this work? Can you ever use Newton's law/kinematics to solve pulley...