Question

An elastic wire expands by 2cm when load of 40g hangs from it. What additional load will be required to cause a further extension of 4cm

Answer 1

Answer:
An additional load of 80g will be required to cause a further extension of 4cm.

Step by step explanation:
To find the additional load required to cause a further extension of 4cm, we can use the concept of proportionality.

The extension of the wire is directly proportional to the load applied. This means that the ratio of the extension to the load remains constant.

In this case, we have an initial extension of 2cm when a load of 40g is applied. We can set up the following proportion:

2cm / 40g = 4cm / x

Cross-multiplying, we get:

2cm * x = 40g * 4cm

2x = 160g cm

To find the additional load required, we need to solve for x:

x = 160g cm / 2
x = 80g

Therefore, an additional load of 80g will be required to cause a further extension of 4cm.

Answer 2

To solve this problem, we can use Hooke's Law, which states that the extension of an elastic material is directly proportional to the force applied to it.

First, let's convert the mass of the load from grams to kilograms:
Mass of the load = 40 g = 0.04 kg

Next, we need to find the spring constant of the wire. The spring constant (k) is a measure of the stiffness of the wire and represents the force required to produce a unit extension. We can find it by dividing the force (weight) by the extension.

Given:
Extension 1 = 2 cm = 0.02 m
Force 1 = Weight = 0.04 kg × 9.8 m/s^2 (acceleration due to gravity) = 0.392 N

Using Hooke's Law, we can calculate the spring constant:
k = Force 1 / Extension 1
k = 0.392 N / 0.02 m
k = 19.6 N/m

Now that we have the spring constant (k), we can calculate the additional load required to cause a further extension of 4 cm.

Given:
Extension 2 = 4 cm = 0.04 m

Using Hooke's Law:
Force 2 = k × Extension 2
Force 2 = 19.6 N/m × 0.04 m
Force 2 = 0.784 N

Therefore, an additional load of 0.784 N will be required to cause a further extension of 4 cm.