Question

An object that is 0.5 m above the ground has the same

amount of potential energy as a spring that is stretched
0.5 m. Each distance is then doubled.
How will the potential energies of the object and the
spring compare after the distances are doubled?
The gravitational potential energy of the object will
be two times greater than the elastic potential energy
of the spring.
O The elastic potential energy of the spring will be four
times greater than the gravitational potential energy
of the object.
The elastic potential energy of the spring will be two
times greater than the gravitational potential energy
of the object.
O The potential energies will remain equal to one
another. HELP

Answer 1

The elastic potential energy of the spring will be two times greater than the gravitational potential energy of the object. This is because the elastic potential energy of a spring is proportional to the square of its displacement, while the gravitational potential energy of an object is proportional to its height. When the distances are doubled, the height of the object will be doubled, resulting in a doubling of its potential energy. However, the displacement of the spring will also be doubled, resulting in a four-fold increase in its elastic potential energy. Therefore, the elastic potential energy of the spring will be two times greater than the gravitational potential energy of the object.