Question

Длина нерастянутой пружины 10 см. Когда к пружине подвесили груз, ее длина увеличилась до 16 см. Какова масса груза, если жесткость пружины равна 60 Н/см?

Answer 1

Calculation of the Mass of the Load

To calculate the mass of the load, we can use 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. The formula for Hooke's Law is:

F = kx

Where: - F is the force exerted by the spring, - k is the spring constant (also known as the stiffness or the modulus of elasticity), - x is the displacement of the spring from its equilibrium position.

In this case, the initial length of the spring (when it is not stretched) is 10 cm, and when the load is attached, the length of the spring increases to 16 cm. The change in length of the spring is 16 cm - 10 cm = 6 cm = 0.06 m.

The stiffness of the spring is given as 60 N/cm = 60 N/0.01 m = 6000 N/m.

Using Hooke's Law, we can calculate the force exerted by the spring:

F = kx = 6000 N/m * 0.06 m = 360 N

The force exerted by the spring is equal to the weight of the load. Therefore, the mass of the load can be calculated using the formula:

F = mg

Where: - m is the mass of the load, - g is the acceleration due to gravity (approximately 9.8 m/s^2).

Rearranging the formula, we can solve for the mass of the load:

m = F / g = 360 N / 9.8 m/s^2 ≈ 36.73 kg

Therefore, the mass of the load is approximately 36.73 kg.