Question

4.3. Початкова довжина пружини 8 см. Під дією сили 1 Н пружина видовжилася, і її довжина стала дорівнювати 12 см. Якою буде довжина пружини, якщо на неї діятиме сила 0,25 Н? С объясненим пожалуйста ​

Answer 1

Ответ: 9см

Объяснение:

Дано:

L0=8cм=0,08м

F1=1Н

L1=12см=0,12м

F2=0,25Н

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L2?

F=kx

k=F1/x1

x1=L1-Lo=0,12-0,08=0,04м

k=1/0,04=25Н/м

х2=F2/k=0,25/25=0,01м=1см

L2=Lo+x2=8+1=9cм

Answer 2

To solve this problem, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, this can be expressed as:

F = k * x

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

In this case, we are given the initial length of the spring (8 cm) and the force applied to the spring (1 N), which caused the spring to elongate to a length of 12 cm. We can use this information to find the spring constant (k) using the formula:

k = F / x

Substituting the given values, we have:

k = 1 N / (12 cm - 8 cm) = 1 N / 4 cm = 0.25 N/cm

Now, we can use the spring constant to find the new length of the spring when a force of 0.25 N is applied. Again, using Hooke's Law:

F = k * x

Substituting the values, we have:

0.25 N = 0.25 N/cm * x

Solving for x, we find:

x = 1 cm

Therefore, when a force of 0.25 N is applied to the spring, the length of the spring will be 1 cm.

Please note that the calculations above assume that the spring obeys Hooke's Law and that the relationship between force and displacement is linear. Additionally, the units used in the calculations are consistent (e.g., cm for length and N for force).