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.

Explanation:

Let U₁ = mgx be the gravitational potential energy of the object and U₂ = 1/2kx² the elastic potential energy of the spring.

Since U₁ = U₂ = U at x = x₀ = 0.5 m.

if x = 2x₀,

The gravitational potential energy is U₃ = mg(2x₀)

= 2mgx₀

= 2U

The elastic potential energy of the spring is U₄ = 1/2k(2x₀)²

= 1/2k × 4x₀²

= 4(1/2kx₀²)

= 4U

Now, U₄/U₃ = 4U/2U = 2

U₄ = 2U₃

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

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