What happens to gravitational potential energy, kinetic energy, and total mechanical energy of a cart as it rolls down a ramp?
If we were to treat the cart as an isolated system, the law of conservation of energy states that the total energy in the system remains the same. Assuming an absence of friction, as the cart rolls down the ramp the gravitational potential energy of the cart is converted completely to kinetic energy.
Mechanical energy of a system, that is the sum of the potential energy in the system and the kinetic energy in the system remains constant. The decrease in the potential energy as the cart rolls down is compensated by an increase in the kinetic energy of the cart.
In real life though, this is not the case as a part of the potential energy is converted to heat due to the presence of friction. This reduces the total kinetic energy and thereby the mechanical energy in the system.