Question

К пружине длиной 12 см, жёсткость которой 500 Н/м подвесили груз массой 3 кг. Какой стала длина пружины?

Answer 1

K=500 
x=0,1m 
m=2 
dx-? 
F=-kx 
F1=0,1*500=50 
F=F1+Fт 
Fт=mg 
Fт=20 
F=20+50=70 
F=-kdx 
dx=F/k 
dx=70/500=0,14m 
dx-это будет длина пружины после подвешивания груза,она равна 1,14 метров или 14 см

Answer 2

Calculation of the New Length of the Spring

To calculate the new length of the spring after hanging a mass from it, 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.

Hooke's Law can be expressed as:

F = kx

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

In this case, we know the following information: - The length of the spring before hanging the mass is 12 cm. - The stiffness of the spring is 500 N/m. - The mass hanging from the spring is 3 kg.

To find the new length of the spring, we need to calculate the displacement of the spring from its equilibrium position.

Let's proceed with the calculation.

Calculation Steps:

1. Convert the length of the spring from centimeters to meters: - Length of the spring = 12 cm = 0.12 m.

2. Calculate the force exerted by the spring using Hooke's Law: - F = kx - F = 500 N/m * x

3. Calculate the weight of the hanging mass: - Weight = mass * acceleration due to gravity - Weight = 3 kg * 9.8 m/s^2

4. Equate the force exerted by the spring to the weight of the hanging mass: - F = Weight - 500 N/m * x = 3 kg * 9.8 m/s^2

5. Solve for x (displacement of the spring): - x = (3 kg * 9.8 m/s^2) / (500 N/m)

6. Calculate the new length of the spring: - New length = Length of the spring + x

Let's calculate the new length of the spring.

Calculation:

1. Convert the length of the spring from centimeters to meters: - Length of the spring = 0.12 m.

2. Calculate the force exerted by the spring using Hooke's Law: - F = 500 N/m * x

3. Calculate the weight of the hanging mass: - Weight = 3 kg * 9.8 m/s^2

4. Equate the force exerted by the spring to the weight of the hanging mass: - 500 N/m * x = 3 kg * 9.8 m/s^2

5. Solve for x (displacement of the spring): - x = (3 kg * 9.8 m/s^2) / (500 N/m)

x = 0.0588 m

6. Calculate the new length of the spring: - New length = Length of the spring + x

New length = 0.12 m + 0.0588 m

New length = 0.1788 m

Therefore, the new length of the spring is 0.1788 meters.

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