Question

Если растягивать пружину силой 8 Н, длина пружины равна 14 см; если сжимать ее силой 8 Н, длина пружины 10 см. Какова будет длина пружины, если сжимать ее силой 4 Н?

Answer 1

Fупр=-kL      k=F/L       L=F/K
K=8-(-8)/14-10= 16/4=4H/см
L=8/ 4=2см
при отсутствии нагрузки пружина имеет длину: 14см-2см=12см
при сжатии силой 4H длина пружины уменьшится на: L=4/4=1см
12см-1см=11см
Ответ: длина пружины будет=11см

Answer 2

Calculation of the Length of a Spring

To calculate the length of a spring when compressed with a force of 4 N, we can use Hooke's law, which states that the force applied to a spring is directly proportional to the displacement of the spring from its equilibrium position.

According to the information provided, when the spring is stretched with a force of 8 N, its length is 14 cm. When the spring is compressed with a force of 8 N, its length is 10 cm.

Let's denote the original length of the spring as L0, the force applied as F, and the length of the spring as L.

From the given information, we can set up the following equations:

1. When the spring is stretched: - L0 + ΔL = 14 cm - F = 8 N

2. When the spring is compressed: - L0 - ΔL = 10 cm - F = 8 N

To find the length of the spring when compressed with a force of 4 N, we can use the equation derived from Hooke's law:

F = k * ΔL

Where k is the spring constant.

Now, let's solve the equations to find the spring constant and the length of the spring when compressed with a force of 4 N.

Solution:

From equation 1, we can find the spring constant (k):

ΔL = 14 cm - L0

From equation 2, we can find the spring constant (k):

ΔL = L0 - 10 cm

Setting the two equations equal to each other:

14 cm - L0 = L0 - 10 cm

Simplifying the equation:

2 * L0 = 24 cm

L0 = 12 cm

Now, we can find the spring constant (k):

ΔL = 14 cm - 12 cm = 2 cm

F = k * ΔL

8 N = k * 2 cm

k = 4 N/cm

Using the spring constant (k) and the force of 4 N, we can find the length of the spring (L):

F = k * ΔL

4 N = 4 N/cm * ΔL

ΔL = 1 cm

L0 - ΔL = L

12 cm - 1 cm = 11 cm

Therefore, the length of the spring when compressed with a force of 4 N is 11 cm.

Conclusion:

When a spring is compressed with a force of 4 N, its length is 11 cm.