Question

Жорсткість першої пружини у 9 разів більша від жорсткості другої, а видовжена другої в 9 разів більше від першої. Порівняти потенціальні енергії першої та другої пружини

Answer 1

Одинаковые F1=-k1*9x2 F2=-9k1*x2; F1/F2=1

Answer 2

Comparison of the Potential Energies of the First and Second Springs

To compare the potential energies of the first and second springs, we need to consider their respective stiffness and elongation values.

Given that the stiffness of the first spring is 9 times greater than the stiffness of the second spring, and the elongation of the second spring is 9 times greater than the elongation of the first spring, we can calculate the potential energies.

Let's denote the stiffness of the first spring as k1, the stiffness of the second spring as k2, the elongation of the first spring as x1, and the elongation of the second spring as x2.

According to the given information, we have the following relationships:

k1 = 9 * k2 (The stiffness of the first spring is 9 times greater than the stiffness of the second spring) x2 = 9 * x1 (The elongation of the second spring is 9 times greater than the elongation of the first spring)

The potential energy of a spring can be calculated using the formula:

PE = (1/2) * k * x^2

where PE is the potential energy, k is the stiffness, and x is the elongation.

Let's calculate the potential energies of the first and second springs using the given information.

The potential energy of the first spring (PE1) can be calculated as:

PE1 = (1/2) * k1 * x1^2

The potential energy of the second spring (PE2) can be calculated as:

PE2 = (1/2) * k2 * x2^2

Substituting the given relationships, we have:

PE1 = (1/2) * (9 * k2) * x1^2

PE2 = (1/2) * k2 * (9 * x1)^2

Simplifying these equations, we get:

PE1 = (9/2) * k2 * x1^2

PE2 = (81/2) * k2 * x1^2

Therefore, the potential energy of the first spring (PE1) is 9/2 times the potential energy of the second spring (PE2).

Please note that the specific values of the stiffness and elongation are not provided in the question, so we cannot calculate the exact potential energies. However, based on the given relationships, we can conclude that the potential energy of the first spring is 9/2 times the potential energy of the second spring.