A 5.0 g marble is fired vertically upward using a spring gun. The spring must be compressed 8.0 cm if the marble is to just reach a target 20 m above the marble’s position on the compressed spring. (a) What is the change ΔUg in the gravitational potential energy of the marble–Earth system during the 20 m ascent? (b) What is the change ΔUs in the elastic potential energy of the spring during its launch of the marble? (c) What is the spring constant of the spring?

a. 0.98 J

b. -0.98 J

c. 306.25 J/m²

Explanation:

(a)

(b)

The increase in gravitational potential energy = decrease in elastic potential energy

Elastic potential energy = -0.980 J

(c) The spring constant can be calculated as follows:

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