# Conservation of energy equation

1. Sep 2, 2010

### zoner7

1. The problem statement, all variables and given/known data
My professor has provided me with an equation, and my task is to write a conservation of energy problem whose solution would produce said equation.

Here is the equation:
(1/2)(3kg)(7m/s)^2 + 0 + (0.15)(3kg)(9.8m/s^2)(2.0m) = 0 + 0 + T(2.0m)

2. Relevant equations
Work internal = 0
W = F . d

3. The attempt at a solution

A 3 kilogram rabbit who lives on a planet with 15% the gravity of that of earth. During his daily run, while on top of a 2.0m hill, his speed peaks at 7m/s. At this point, what is his total energy?

This question accounts for the first two terms of the equation, both of the left side. I am still left wondering, however, what the T on the right side stands for. Note that this is a thermodynamics class; however, we have had less than an hour of class and have yet to learn any thermodynamics. Could T stand for temperature here? If so, how can I use this value in terms of energy?

2. Sep 2, 2010

### CompuChip

Temperature times length does not have the proper units (of course, all the terms should have units of energy, i.e. Joules).
Force times length, however, does. One word that comes to mind is tension... ?

3. Sep 2, 2010

### zoner7

ah hah.

Suppose my problem looks like this, then:

A 3 kilogram rabbit named Joe lives on a planet with 15% the gravity of that of earth. Joe loves to bungie jump. During one of his more adventurous endeavors, Joe ties a rope to himself and a bridge, leaving exactly 2m worth of slack. Joe calculates his initial jumping height such that the rope will become taught when he reaches 7m/s; his calculations report that he will be 2m above the ground at this time. Write a conversation of energy equation describing the rabbit's energy when the rope becomes taught.

Does this make sense? The tension on the rope is acting external to the system of the rabbit. Since the rabbit is 2m above the ground, and since gravitational potential energy is mgh, that should check out as well. What do you guys think?