Solving Oscillating Particle Homework: Max Speed of 1.90g Particle

[jmm]

Homework Statement

What is the maximum speed of a 1.90g particle that oscillates between x=2mm and x=8mm in the figure?

Homework Equations

?

The Attempt at a Solution

I don't have the foggiest idea how to do this problem. If someone could point me in the right direction I'd really appreciate it. Thanks!

 

[Matterwave]

If the particle oscillates there, how much potential energy is lost when it gets to the lowest point? Where does this potential energy go (since energy can't be created or destroyed)?

 

[Torquescrew]

Currently trying to sort this kinda' stuff out myself.

I don't really know how to explain it, but I think that the point at which the particle has the greatest speed will be the part at which it is neither accelerating or decelerating.
Unless I'm totally wrong.

 

[Matterwave]

You're half right. The point of greatest speed will correspond to no more acceleration (no faster!), but not to no more deceleration (it can obviously get slower).

 

[jmm]

The potential energy is converted to kinetic energy so it would be moving fastest at x=4mm. I know that Total Energy = Potential Energy + Kinetic Energy but how do I know what the total energy is? Since it's oscillating, would the total energy of the system be entirely in the form of potential energy at x=2,8mm? If so, total energy would be 5J and its kinetic energy at x=4mm would be 4J. So v=sqrt(2E/m)=64.9m/s Does that sound right?

 

[Torquescrew]

You're half right. The point of greatest speed will correspond to no more acceleration (no faster!), but not to no more deceleration (it can obviously get slower).

I guess I don't understand. You're saying that when it decelerates, the speed won't decrease?

 

[ehild]

The potential energy is converted to kinetic energy so it would be moving fastest at x=4mm. I know that Total Energy = Potential Energy + Kinetic Energy but how do I know what the total energy is? Since it's oscillating, would the total energy of the system be entirely in the form of potential energy at x=2,8mm? If so, total energy would be 5J and its kinetic energy at x=4mm would be 4J. So v=sqrt(2E/m)=64.9m/s Does that sound right?

Correct! Great!

ehild

 

[Matterwave]

The potential energy is converted to kinetic energy so it would be moving fastest at x=4mm. I know that Total Energy = Potential Energy + Kinetic Energy but how do I know what the total energy is? Since it's oscillating, would the total energy of the system be entirely in the form of potential energy at x=2,8mm? If so, total energy would be 5J and its kinetic energy at x=4mm would be 4J. So v=sqrt(2E/m)=64.9m/s Does that sound right?

Correct! The reasoning is:
If the particle oscillates to 2 to 8 and does not go over those limits, then at those points all the energy of the particle is potential energy, if it had any kinetic energy left, it'd still be moving in that direction! Thus total energy=5J as you say.

@Torquescrew: If an object decelerates, it loses speed, that's the definition of deceleration. The point is, at the maximum speed of an object, the object may be slowing down (but not speeding up)!

For example, if I accelerate my car to 160mph and then slow down to stop, (thus the point that I reached 160 mph is the point of maximum speed); at 160mph (the maximum point), i can not be accelerating (or else I'd be going faster) but I can decelerate (to stop). I don't know how else to put this...

 

[jmm]

Sweet thanks!