An object starts with some amount of total mechanical energy. As it travels to its final point, work done by

An object starts with some amount of total mechanical energy. As it travels to its final point, work done by non-conservative forces does -130 Joules of work on the object and its final total mechanical energy is 30 Joules. What was the initial mechanical energy of the object in Joules?

30 - (-130) = 160J

To illustrate what happens, suppose a box, sliding horizontally, has 160J of kinetic energy initially. If there were no friction, it would keep its kinetic energy.

But if friction (a non-conservative force) does -130J of work, that mean it removes 130J of energy (converts 130J to heat), leaving 30J of kinetic energy..

You can think of the 130J being negative either in terms of:
- it REMOVES energy from the box or
- the direction of the friction force is opposite to the direction of displacement; if force is positive displacement is negative, Fxd is negative.

think of this like an energy budget..what you have at the end is equal to what you had at the beginning plus anything you earned minus anything you lost

here the final amount is 30J, and we "lost" 130J to friction, so there must have been 160J originally

in other words:

160J - 130J = 30J