Q. 33.6( 5 Votes )

# When a weight is suspended by a spring, the extension is proportional to the weight. Explain how this can be used to mark weights on a spring balance.

Answer :

Let the different position of spring 0, 1 and 2.

Position 0 shows the situation when no load is applied on the spring

Position 1 shows the situation when a load of w_{1} is applied on the spring.

We can see that there is an extension of x cm from the initial position.

Position 2 shows the situation when a load of w_{2} is applied on the spring.

We can see that there is extension of x_{2} cm from the initial position.

It is given in the question that; the extension is proportional to the applied load.

So, any extension x will be proportional to the weight w that produces that extension.

We can write: x = a constant k × w

⇒ x = kw

⇒

The constant ‘k’ is called the spring constant. Every spring will have a particular value of spring constant. We want to find this constant for our spring.

For that, we adopt the following procedure:

Put a known weight w_{1}. Measure the extension x_{1}.

Then

Put another known weight w_{2}. Measure the extension x_{2}.

Then

Since k is a constant, we will get the same value for k in both the weight.

Repeat the trial with several known weights. In all cases we will get the same k.

Once k is obtained, we can make the markings on the spring balance.

The spring is fixed inside an outer casting. Markings are made on this casing.

When the spring is at Zero load position, mark that position on the casing as 0kg.

Now we want to mark the 1kg position

Let the extension for a load of 1kg be x_{1} kg

x_{1} = k × 1 kg = k

we have already calculated k. so we get x_{1} kg.

Measure this x_{1} kg from the 0kg mark on the casing and mark it as 1kg.

Now we want to mark the 2kg position

Let the extension for a load of 2kg be x_{2} kg

X_{2} = k × 2 kg = 2k

we have already calculated k. so we get x_{2} kg.

Measure this x_{2} kg from the 0kg mark on the casing and mark it as 2kg.

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