In which context did this question come up? Have you studied the variational principle?TheDispStud said:Homework Statement:: A particle of mass m moving with velocity v1, leaves a half-space in which the potential is a constant U1 and enters the other half-space, where the potential energy is a different constant U2.
Relevant Equations:: Determine the change in the direction of motion of the particle.
Unfortunately, I have no idea about a possible solution.
Does this question look similar to the refraction of light?TheDispStud said:Yes, we discussed about the Hamilton variational principle.
What would Hamilton say in this case?TheDispStud said:This is an exercise of Analytical Mechanics :-)
I've given you two ideas: refraction and Hamilton's principle. It's up to you to show us something based on those ideas.TheDispStud said:I really have no idea :(.. I mean I studied the theory but i do not see how to solve this problem!
A change in the direction of motion of a particle can occur due to a force acting on the particle, such as gravity or a collision with another object. This force causes the particle to accelerate in a different direction, resulting in a change in its motion.
No, according to Newton's first law of motion, an object at rest or in motion will remain in its state of motion unless acted upon by an external force. Therefore, a particle cannot change direction without an external force acting on it.
The mass of a particle does not directly affect its change in direction. However, a particle with a larger mass will require a greater force to change its direction compared to a particle with a smaller mass.
A change in direction refers to a change in the path or trajectory of a particle, while a change in velocity refers to a change in the speed or magnitude of the particle's motion. A change in direction can occur without a change in velocity if the speed remains constant, and vice versa.
Friction is a force that opposes motion and can cause a change in direction for a particle. For example, if a particle is moving on a surface with friction, the frictional force will act in the opposite direction of the particle's motion, causing it to change direction or slow down.