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

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

The potential energies will remain equal to one another

The elastic potential energy of the spring will be two times greater than the gravitational potential energy of the object.

Step-by-step explanation:

Given:

Height of object, h = 0.5m

Displacement of spring = 0.5m

P. E of both object and spring are equal.

Also, each distance is doubled

Take the gravitational potential energy expression:

= m*g*h

Where, m = mass

g=acceleration due to gravity = 9.8m/s²

h = height

Also, take expression for elastic potential energy:

= ½KX²

Where, K = spring constant

X = spring's displacement.

Comparing both formulas, and substituting the values of H for 0.5 and X for 0.5, we can see that the elastic potential energy of the spring would be twice greater than the gravitational potential energy of the object.