Question

A spring 20cm long is stretched to 25cm by a load of 50N . what will be its length when stretched by 100N assuming that the elastic limit is not reached ​

Answer 1

The behavior of springs is governed by Hooke's Law, which states that the force required to stretch or compress a spring by some distance is proportional to that distance. Mathematically, this is expressed as:

`$$F = kx$$`

where:

-
`\(F\)` is the force applied,

-
`\(k\)` is the spring constant, and

-
`\(x\)` is the displacement from the spring's original position.

Given that a 50N force stretches the spring from 20cm to 25cm (a 5cm or 0.05m stretch), we can first calculate the spring constant
`\(k\)`. Then, we can use this spring constant to find the displacement when a 100N force is applied.

Let's calculate the spring constant
`\(k\)` first.

It seems there was a misunderstanding in the interpretation of the equation. The goal is to solve for
`\(k\)`, the spring constant, not
`\(N\)`, the force. Let's correct this and solve for
`\(k\)` in the equation
`\(50N = k * 0.05m\)`.

The spring constant
`\(k\)` is found to be
`\(1000 \, \text{N/m}\)`.

Now, let's use this spring constant to find the displacement when a 100N force is applied. We rearrange Hooke's Law to solve for
`\(x\)`:

`$$x = (F)/(k)$$`

Substituting
`\(F = 100N\)` and
`\(k = 1000N/m\)`, we can find the displacement
`\(x\)`.

The displacement
`\(x\)` when a 100N force is applied is 0.1 meters or 10 cm.

Remember, this displacement is the amount the spring stretches from its original length due to the applied force. So, to find the total length of the spring when a 100N force is applied, we add this displacement to the original length of the spring (20 cm).

Let's calculate the total length of the spring.

The total length of the spring when a 100N force is applied will be 30 cm, assuming that the elastic limit is not reached.

Answer 2

We can use Hooke's law, which states that the extension of a spring is proportional to the force applied to it, as long as the elastic limit is not reached. Mathematically, this can be expressed as:

F = kx

where F is the force applied to the spring, x is the extension of the spring, and k is the spring constant.

We can use the given information to find the spring constant k:

50N = k(25cm - 20cm)

50N = 5cm k

k = 10N/cm

Now we can use Hooke's law to find the extension of the spring when a force of 100N is applied:

100N = (10N/cm)x

x = 10cm

Therefore, the length of the spring when stretched by 100N is:

20cm + 10cm = 30cm