Question

Длина пружины в недеформированном состоянии 10 см, а в деформированном - 15 см. На сколько изменилась потенциальная энергия пружины при растяжении, если её жёсткость 10 Н/м? Какую работу произвела пружина в этом случае?

Answer 1

Потенциальная энергия пружины находится по формуле: k*x^2/2. Соответственно, тебе нужно посчитать потенциальную энергию пружины для x=0,15м и x=0,01м, а затем вычесть их. Получится 0,112Дж

Работу, вероятно, можно найти как разность силы упругости после и до (я не уверен). Fупр = k*x. Аналогично считаешь, вычитаешь. Получится 1,4Дж

Answer 2

Calculation of Change in Potential Energy of the Spring

To calculate the change in potential energy of the spring, we need to determine the change in length of the spring and its stiffness.

Given: - Length of the spring in the undeformed state (initial length): 10 cm - Length of the spring in the deformed state (final length): 15 cm - Stiffness of the spring: 10 N/m

The change in length of the spring can be calculated as the difference between the final length and the initial length:

Change in length (Δx) = Final length - Initial length = 15 cm - 10 cm = 5 cm

The potential energy of a spring is given by the formula:

Potential energy (PE) = (1/2) * k * (Δx)^2

where: - k is the stiffness of the spring - Δx is the change in length of the spring

Substituting the given values into the formula, we can calculate the change in potential energy of the spring:

PE = (1/2) * 10 N/m * (0.05 m)^2 = 0.0025 J

Therefore, the change in potential energy of the spring during stretching is 0.0025 Joules.

Calculation of Work Done by the Spring

The work done by the spring can be calculated as the negative of the change in potential energy. This is because when the spring is stretched, it gains potential energy, and when it returns to its original position, it releases that energy.

Work done by the spring = - Change in potential energy = -0.0025 J

Therefore, the spring has done -0.0025 Joules of work in this case.

Please note that the negative sign indicates that the work done by the spring is in the opposite direction of the applied force.