Answer:
611.385 joules are converted to gravitational potential energy.
Explanation:
Let suppose that the cart begins at a height of 0 meters. The cart-spring system is conservative. By the Principle of Energy Conservation we have the following model:
(1)
Where:
, - Initial and final elastic potential energy, in joules.
, - Initial and final gravitational potential energy, in joules.
, - Initial and final translational kinetic energy, in joules.
And the energy converted to gravitational potential energy is calculated by (1) and definitions of translational kinetic and elastic potential energies:
(2)
Where:
- Spring constant, in newtons per meter.
- Initial compression of the spring, in meters.
- Mass, in kilograms.
- Final speed of the cart, in meters per second.
If we know that , , and , then the change in gravitational potential energy is:
611.385 joules are converted to gravitational potential energy.