Conservation of energy question.

[peripatein]

Hi,

Homework Statement

I have three elementary questions and would appreciate feedback on my attempt at answering them. Thanks in advance!

(1) Will the laws of conservation of energy be accurately preserved in the lab?
(2) When pushing a cart across a surface, how can energy losses due to friction be compensated for?
(3) When a weight and a cart are tied together by means of an inelastic cord through a set of 3 pulleys, what would be the relation between their movements? What would be the relation between their velocities? Which component will be preserved in this setup?

The Attempt at a Solution

(1) I think they wouldn't "accurately" be conserved, as there will always be loss of energy due to friction, gravitation, etc. to heat and other forms.
(2) I think tilting the cart, thus reducing the effective surface area, should make it easier. Moreover, the wheels could, for instance, be coated with rubber or some other material which would reduce the friction, though I am not sure that's what the question aimed at.
(3) I think the cord's length will be preserved in this setup and since it is inelastic the displacement of the cart and weight, including their velocities and acceleration, will all be the same.

 

[haruspex]

(2) I think tilting the cart, thus reducing the effective surface area, should make it easier.

According to what equation does friction depend on area of contact?

Moreover, the wheels could, for instance, be coated with rubber or some other material which would reduce the friction

Rubber reducing friction? If the cart is on wheels, where do you think frictional losses will occur? (Don't confuse friction with rolling resistance.)

(3) I think the cord's length will be preserved in this setup and since it is inelastic the displacement of the cart and weight, including their velocities and acceleration, will all be the same.

If the pulleys are on fixed axles, yes.

 

[peripatein]

Okay, and what about the conservation of energy in the lab? And pushing the cart at some angle, say arcctg alpha, which will cancel the friction, wouldn't that compensate for the loss of energy?

 

[peripatein]

I meant to write, arcctg (mu).

 

[haruspex]

Okay, and what about the conservation of energy in the lab?

I didn't answer that because I'm not at all sure what's wanted. Conservation of energy is a universal law: it applies everywhere. You cannot always use the law in analysing processes because energy is lost in ways that are hard to measure. Also, in the lab, you are in a rotating reference frame (Earth spin, Earth orbit, solar system orbit around galaxy...) so without making allowances for those you might, with incredibly accurate equipment, detect apparent violations of conservation laws.

And pushing the cart at some angle, say arcctg alpha, which will cancel the friction, wouldn't that compensate for the loss of energy?

It says 'compensate', which doesn't necessarily mean 'cancel'. It might mean just taking them into account in analysing the results. I can't think of a generic way to do that (or to cancel them), but I might be able to come up with some way for a specific experiment.