Question

Пружина под лействием силы 200Н растянулась на 10см. Определите жесткость пружины. на какую длину пружина растянется под действием силы 200Н?

Answer 1

Determining the Stiffness of a Spring

To determine the stiffness or spring constant of a spring, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law can be expressed as:

F = k * x

Where: - F is the force applied to the spring, - k is the spring constant or stiffness of the spring, - x is the displacement of the spring from its equilibrium position.

In this case, we are given that a spring is stretched by a force of 200 N and the displacement is 10 cm (or 0.1 m). We need to determine the spring constant or stiffness of the spring.

Using Hooke's Law, we can rearrange the equation to solve for the spring constant:

k = F / x

Substituting the given values, we have:

k = 200 N / 0.1 m = 2000 N/m

Therefore, the stiffness or spring constant of the spring is 2000 N/m.

Determining the Length of the Spring under a Force of 200 N

To determine the length to which the spring will stretch under a force of 200 N, we can use the concept of elastic potential energy.

The elastic potential energy stored in a spring is given by the equation:

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

Where: - PE is the elastic potential energy stored in the spring, - k is the spring constant, - x is the displacement of the spring from its equilibrium position.

In this case, we are given the force applied to the spring (200 N) and we need to determine the displacement (x) of the spring.

Rearranging the equation, we have:

x = sqrt((2 * PE) / k)

Substituting the given values, we have:

x = sqrt((2 * 200 N * 0.1 m) / 2000 N/m) = sqrt(0.02 m) = 0.1414 m

Therefore, the spring will stretch to a length of approximately 0.1414 m (or 14.14 cm) under a force of 200 N.

Please note that the calculations provided are based on the information given and the assumptions made.