Question

В нерастянутом состоянии пружина имела длину 88 мм в результате её удлинения до 120 мм возникла сила упругости равная 120Н.Опеределите длину этой пружины в том случае когда дейсвующая сила равна 90 Н

Answer 1

F=k x
при х=120-88=32 сила=120, откуда k=120/32=3,75
при F=90 =3,75*x
x = 24 = L-88
L=24+88=112

Answer 2

Calculation of the Length of the Spring

To determine the length of the spring when the applied force is 90 N, we can use the concept of Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the extension or compression of the spring, as long as the elastic limit is not exceeded.

In this case, we are given that the spring had an initial length of 88 mm and an extension to 120 mm when a force of 120 N was applied. We need to find the length of the spring when the force is 90 N.

Let's assume the initial length of the spring is represented by L and the length of the spring when the force is 90 N is represented by L'.

According to Hooke's Law, the force exerted by the spring is given by:

F = k * ΔL

Where: - F is the force applied to the spring - k is the spring constant - ΔL is the change in length of the spring

We can rearrange the equation to solve for the change in length:

ΔL = F / k

Since the spring constant remains constant, we can write:

ΔL / F = L / F = L' / 90

Now, we can solve for L':

L' = (L / F) * 90

Substituting the given values, we have:

L' = (88 mm / 120 N) * 90 N

Calculating this expression, we find:

L' ≈ 66 mm

Therefore, when the applied force is 90 N, the length of the spring is approximately 66 mm.