A 5.0 gm marble is fired vertically upward using a spring gun. The spring must be compressed 8 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 in the gravitational potential energy of the marble-earth system during the 20m ascent.
(b) What is the change in the elastic potential energy of the spring during its launch of the marble

(a) Eu = m*g*h = 0.005*9.8*20

(b) Eu = Ek

To answer these questions, we need to understand the concepts of gravitational potential energy and elastic potential energy.

(a) The change in gravitational potential energy can be calculated using the equation:

ΔPE = mgh

where ΔPE is the change in gravitational potential energy, m is the mass of the object (marble), g is the acceleration due to gravity, and h is the change in height.

In this case, the change in height is given as 20 m. The mass of the marble is 5.0 gm, which is equal to 0.005 kg. The acceleration due to gravity is approximately 9.8 m/s^2.

So, substituting the values into the equation:

ΔPE = (0.005 kg) * (9.8 m/s^2) * (20 m)
= 0.98 Joules

Therefore, the change in the gravitational potential energy of the marble-earth system during the 20m ascent is 0.98 Joules.

(b) The change in elastic potential energy can be calculated using the equation:

ΔPE = (1/2)kx^2

where ΔPE is the change in elastic potential energy, k is the spring constant, and x is the displacement of the spring.

In this case, the displacement of the spring is given as 8 cm, which is equal to 0.08 m. However, we need to know the spring constant (k) to calculate the change in elastic potential energy.

Once the spring constant is known, we can substitute the values into the equation to find the change in elastic potential energy (ΔPE).

However, since the spring constant is not given in the question, we are unable to calculate the change in elastic potential energy without this information.

Therefore, the answer to part (b) cannot be determined without the spring constant value.