Question

Груз весом 100 Н растянул пружину на 2 см. Какую работу нужно совершить, чтобы растянуть пружину от длины 20см до длины 30см, если ее длина в спокойном состоянии 15см.​

Answer 1

Ответ:

) y=x²­2x+2; x=­1; x=2, y=0 .

б) y= x²­8x+16; y= 6­x.

в) 2x­x²­y=0; y=0.

Answer 2

Calculation of Work Required to Stretch a Spring

To calculate the work required to stretch a spring from one length to another, we can use the formula:

Work = (1/2) * k * (x2^2 - x1^2)

Where: - Work is the work done on the spring (in joules). - k is the spring constant (in newtons per meter). - x1 is the initial displacement of the spring (in meters). - x2 is the final displacement of the spring (in meters).

In this case, we are given the following information: - The weight of the load is 100 N. - The spring was stretched by 2 cm (or 0.02 m) when the load was applied. - The initial length of the spring in its relaxed state is 15 cm (or 0.15 m). - We need to find the work required to stretch the spring from a length of 20 cm (or 0.20 m) to 30 cm (or 0.30 m).

Let's calculate the work required step by step:

1. Calculate the spring constant (k): - The spring constant represents the stiffness of the spring and is measured in newtons per meter. - We can calculate the spring constant using Hooke's Law: F = k * x, where F is the force applied to the spring and x is the displacement. - In this case, the force applied to the spring is the weight of the load, which is 100 N. - The displacement is 0.02 m. - Rearranging the formula, we get: k = F / x. - Substituting the values, we have: k = 100 N / 0.02 m. - Calculating, we find that k = 5000 N/m.

2. Calculate the initial and final displacements (x1 and x2): - The initial displacement (x1) is the difference between the initial length of the spring and the length when the load was applied. - The initial length of the spring is 0.15 m, and the length when the load was applied is 0.15 m + 0.02 m = 0.17 m. - Therefore, x1 = 0.17 m - 0.15 m = 0.02 m. - The final displacement (x2) is the difference between the final length of the spring and the length when the load was applied. - The final length of the spring is 0.30 m, and the length when the load was applied is 0.17 m. - Therefore, x2 = 0.30 m - 0.17 m = 0.13 m.

3. Calculate the work required: - Using the formula Work = (1/2) * k * (x2^2 - x1^2), we can substitute the values we calculated: - Work = (1/2) * 5000 N/m * (0.13 m^2 - 0.02 m^2). - Calculating, we find that Work = 0.5 * 5000 N/m * (0.0169 m^2 - 0.0004 m^2) = 0.5 * 5000 N/m * 0.0165 m^2. - Therefore, Work = 41.25 joules.

So, the work required to stretch the spring from a length of 20 cm to 30 cm is 41.25 joules.