Question

Если на верхний конец вертикально расположенной спиральной пружины положить груз то пружина сожмется на Dl =3 мм на сколько сожмет пружину тот же груз упавший на конец пружины с высоты h=8 см

Answer 1

Составляем уравнения
kx1=mg; уравнение баланса
mgh=k(x2)^2/2 закон сохранения энергии
Решаем уравнение:
kx1*h=k(x2)^2/2
x2=0.021M=2,1см

Answer 2

Calculation of Spring Compression

To calculate the compression of a vertically positioned spiral spring when a load is applied to its upper end, we need to consider the given values of the compression distance (Dl = 3 mm) and the height from which the load falls onto the end of the spring (h = 8 cm).

Let's assume that the spring is ideal and obeys Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. In this case, the displacement is the compression distance.

To calculate the compression of the spring, we can use the potential energy equation:

mgh = (1/2)k(Dl)^2

Where: - m is the mass of the load - g is the acceleration due to gravity (approximately 9.8 m/s^2) - h is the height from which the load falls - k is the spring constant - Dl is the compression distance

We need to solve this equation for Dl.

Calculation Steps

1. Convert the height from centimeters to meters: h = 8 cm = 0.08 m. 2. Rearrange the equation to solve for Dl:

Dl = sqrt((2 * m * g * h) / k)

3. Substitute the given values into the equation:

Dl = sqrt((2 * m * 9.8 * 0.08) / k)

Now, we need the value of the spring constant (k) to complete the calculation. Unfortunately, the provided search snippets do not contain the necessary information to determine the spring constant or any other relevant details. Therefore, we cannot provide a specific numerical answer to the question.

Please note that the spring constant depends on the material and geometry of the spring, and it needs to be determined experimentally or provided in the problem statement.

If you have any additional information or specific values for the spring constant, we can further assist you in calculating the compression of the spring.