Conservation of energy equation

AI Thread Summary
The discussion revolves around creating a conservation of energy problem based on a provided equation. The scenario involves a 3 kg rabbit on a planet with reduced gravity, who reaches a speed of 7 m/s while on a 2.0 m hill. The key challenge is understanding the term "T" in the equation, which the poster speculates could represent tension rather than temperature, as the units must align with energy. The proposed problem involves the rabbit bungee jumping, where the tension in the rope acts externally to the system, allowing for a proper conservation of energy equation. The overall aim is to ensure that all terms in the equation correspond to energy units, such as Joules.
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Homework Statement


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)


Homework Equations


Work internal = 0
W = F . d


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?
 
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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... ?
 
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?
 
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