Question

Пружина длиной 3 см при нагрузке 25 Н удлинилась на 2 мм. Определите длину пружины при нагрузке 100 Н.

Answer 1

Дано:
l=3cм= 0.03м
F1= 25Н
x1= 2 мм= 0.002м
F2=100Н
x2=?
___________(k-  коэффициент жесткость пружины)_
F1= kx1  
 k=F1/x1= 25/0.002=12500 Н/м
F2=kx2
x2= F2/k= 100/12500=0.008м или 8 мм
 
новая длина пружины (l+x2)  38мм или 3 см 8 мм

Answer 2

Calculation of the Length of the Spring

To determine the length of the spring when subjected to a load of 100 N, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the extension or compression of the spring. Mathematically, it can be expressed as:

F = kx

Where: - F is the force applied to the spring, - k is the spring constant, and - x is the extension or compression of the spring.

In this case, we are given that the spring lengthens by 2 mm (0.002 m) when subjected to a load of 25 N. We can use this information to calculate the spring constant (k) using the formula:

k = F / x

Substituting the given values, we have:

k = 25 N / 0.002 m = 12,500 N/m.

Now, we can use the calculated spring constant to determine the length of the spring when subjected to a load of 100 N. Let's denote the length of the spring in this case as L.

Using Hooke's Law, we can rearrange the formula to solve for x:

x = F / k

Substituting the values, we have:

x = 100 N / 12,500 N/m = 0.008 m

Therefore, the spring elongates by 0.008 m (or 8 mm) when subjected to a load of 100 N.

To find the total length of the spring when subjected to a load of 100 N, we add the elongation to the original length of the spring. Given that the original length of the spring is 3 cm (0.03 m), we have:

L = 0.03 m + 0.008 m = 0.038 m

Therefore, the length of the spring when subjected to a load of 100 N is 0.038 m (or 3.8 cm).

Please note that the calculations above are based on the assumption that the spring follows Hooke's Law and that the relationship between force and extension is linear within the given range.

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