Question

Две сцепленные друг с другом пружины растягиваются за свободные концы в разные стороны. жесткость одной пружины равна 5000 Н/м, жесткость другой пружины 7500Н/м, суммарное удлинение пружин равно 5 см...с какой силой растягиваются пружины?

Answer 1

F=kx
k=(k1*k2)/(k1+k2)=(5000*7500)/(5000+7500)=3000Н/м
F=3000*0,05=150Н

Answer 2

Calculation of the Force:

To calculate the force with which the springs are stretched, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement or elongation of the spring.

Let's denote the force exerted by the first spring as F1 and the force exerted by the second spring as F2. The stiffness or spring constant of the first spring is given as 5000 N/m, and the stiffness of the second spring is given as 7500 N/m. The total elongation of the springs is given as 5 cm.

According to Hooke's Law, the force exerted by a spring can be calculated using the formula:

F = k * x

Where: - F is the force exerted by the spring, - k is the spring constant or stiffness of the spring, and - x is the displacement or elongation of the spring.

Since the springs are stretched in opposite directions, the forces exerted by the two springs will have opposite signs. Therefore, we can write the equation as:

F1 - F2 = k1 * x - k2 * x

Substituting the given values: - k1 = 5000 N/m - k2 = 7500 N/m - x = 5 cm = 0.05 m

We can now calculate the force:

F1 - F2 = (5000 N/m) * (0.05 m) - (7500 N/m) * (0.05 m)

Calculating the above expression, we find:

F1 - F2 = 250 N - 375 N = -125 N

Therefore, the springs are stretched with a force of -125 N. The negative sign indicates that the forces exerted by the two springs are in opposite directions.

Please note that the negative sign indicates the direction of the force and does not affect the magnitude of the force.