# Potential Energy of coffee mug Problem

1. A 0.342- kg coffee mug rests on a table top 0.67 m above the floor. What is the potential energy of the mug with respect to the floor?
B. What is its potential energy with respect to a counter top 1.1 m above the floor?

P.E.=mgh

## The Attempt at a Solution

i thought that i would do the problem exactly the same as i did the first.
(0.342)(9.8)(1.1)= P.E. because for the first problem i used the same thing except for 1.1 instead i used 0.67 for the first problem. The answer that i get for the second problem is 3.68676J but i'm told this is not right.
any help would be appreciated.

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cristo
Staff Emeritus
The distance you should use is not 1.1. Think about the situation. What is the difference in height between the coffeed mug and the counter?

you mean 0.43?

cristo
Staff Emeritus
That's correct

so i do the same thing only it would be (0.342)(9.8)(0.43)which is 1.441188J ?
-Why do you find the difference?

cristo
Staff Emeritus
Because you want the potential energy of the mug with resoect to the counter. Recall that the potential energy is defined as $V=mg\Delta h$ where $\Delta h$ is the change in height. For the first part $\Delta h=0.67-0$ since we define the ground to be the origin of the coordinate system. So, for the second part, $\Delta h=0.67-1.1$ with regard to the coordinate origin. Note that the change in height should strictly be -0.43, since, of course, the coffee mug has less potential energy on the table than it would have on the counter. You can argue this by taking the counter as the origin (since this is the point we want to calculate the potential with respect to) and thus the coffee cup is -0.43 (i.e. 0.43 metres down)

Oh ok i understand this , but the answer i got still doesn't seem to work?

cristo
Staff Emeritus
What do you mean "doesn't work?" Do you have the solution to the problem?

not the soulution its online homework it tells me i'm wrong but it does not say why or give any help and i hate it but i'm not very good at physics as you can probably tell.

cristo
Staff Emeritus
Hmm, well I'm not sure I can help much more! The answer is either 1.44 (or more correctly -1.44). If neither of these work, then the answer (on the online system) is wrong!

well i didn't try negative at first it is right though could you possibly explain why?

cristo
Staff Emeritus
The potential energy is measured with respect to some reference point, and we should make this point the origin of our coordinates. For 1. the origin is the ground, with positive direction upwards, and so h=0.67. For 2. the origin is the counter-top, also with positive direction upwards, and so the h=-0.43, since the coffee cup is below the counter.

oh i see thank you very much for all of your help i really appreciate it.

well, understand that sometimes the way we use energy is based on conventions that make it easily usable in some generalized formulas. So in order for this to work for the basic formula E(initial)=E(final) it needs to be negative. Say it starts by going up with some initial kinetic energy. To determine its speed at the countertop, you would need to say E(initial)=K(initial)+U(initial)<<which is negative. if you set this equal to energy at the top then it will work out. Note that the important thing here is keeping a consistent refrence frame. If we had chosen the table to be the refrence frame, your potential energy would start at zero and end up at a positive number--either way it works. Did that make any sense?

sorry--too late.

yes thank you