Question

При уменьшении длины спиральной пружины на 3.5 см. возникает сила упругости 1.4 кН ,найти жёсткость пружины.

Answer 1

Закон Гука: Fy = - kΔx
Fy - сила упругости (Н)
k - жесткость пружины (Н/м)
Δx - удлинение пружины (м), иногда вместо х используют l (эль маленькая)

Дано:
Δx= - 3,5 см= - 0,035 м (СИ) Т.к. пружина уменьшалась, то Δх - отрицательная
Fy= 1,4 кН=1400 Н (СИ)

Найти: k - ?

Решение: Fy = -kΔx
Отсюда k=-Fy/Δx
Подставляем значения в СИ, находим k
k=-1400/-0,035 = 40000 (Н/м)

Большеватое значение... Если что проверьте, т.к. может есть ошибки! Если есть, то пишите, очень нужно знать!

Answer 2

Calculation of the Spring Constant

To find the spring constant (also known as the stiffness or force constant) of a spring, 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 = k * x

Where: - F is the force exerted by the spring, - k is the spring constant, - x is the displacement of the spring from its equilibrium position.

In this case, we are given that a decrease in the length of the spiral spring by 3.5 cm results in a force of 1.4 kN (kilonewtons). We need to find the spring constant.

Let's assume that the displacement of the spring is 3.5 cm (since the length decreased by 3.5 cm). The force exerted by the spring is given as 1.4 kN.

Using Hooke's Law, we can rearrange the equation to solve for the spring constant:

k = F / x

Substituting the given values:

k = 1.4 kN / 3.5 cm

Now, we need to convert the units to a consistent system. Let's convert the force from kilonewtons to newtons and the displacement from centimeters to meters:

1 kN = 1000 N 1 cm = 0.01 m

Substituting the converted values:

k = (1.4 kN * 1000 N/kN) / (3.5 cm * 0.01 m/cm)

Simplifying the equation:

k = 400 N / 0.035 m

Calculating the spring constant:

k = 11,428.57 N/m

Therefore, the spring constant of the spiral spring is approximately 11,428.57 N/m.