First, we need to calculate the total elastic potential energy stored in the ball when it is compressed. The formula for elastic potential energy is:

E = 0.5 * k * x^2

where:
E is the elastic potential energy,
k is the spring constant, and
x is the distance the spring is stretched or compressed.

Substituting the given values:

E = 0.5 * 2500 N/m * (0.18 m)^2
E = 0.5 * 2500 N/m * 0.0324 m^2
E = 40.5 J

This is the total amount of energy initially stored in the ball.

Next, we know that 28.5 J of this energy is transferred to the kinetic energy store. Therefore, the remaining energy must have been transferred to the thermal energy store.

So, the energy transferred to the thermal energy store is:

E_thermal = E_total - E_kinetic
E_thermal = 40.5 J - 28.5 J
E_thermal = 12 J

Therefore, 12 Joules of energy is transferred to the thermal energy store.

Question

First, we need to calculate the total elastic potential energy stored in the ball when it is compressed. The formula for elastic potential energy is:

E = 0.5 * k * x^2

where:
E is the elastic potential energy,
k is the spring constant, and
x is the distance the spring is stretched or compressed.

Substituting the given values:

E = 0.5 * 2500 N/m * (0.18 m)^2
E = 0.5 * 2500 N/m * 0.0324 m^2
E = 40.5 J

This is the total amount of energy initially stored in the ball.

Next, we know that 28.5 J of this energy is transferred to the kinetic energy store. Therefore, the remaining energy must have been transferred to the thermal energy store.

So, the energy transferred to the thermal energy store is:

E_thermal = E_total - E_kinetic
E_thermal = 40.5 J - 28.5 J
E_thermal = 12 J

Therefore, 12 Joules of energy is transferred to the thermal energy store.

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