An elastic cord can be be stretched to its elastic limit by a load of 2n if a 35cm length of the cord is extended 0.6cm by a force of 0.5n what will be the length of the cord when the stretching for is 2.5n
We can use the formula for Hooke's law: stress = force/area = (spring constant) x (strain)
In this case, we are given that the cord can be stretched to its elastic limit by a load of 2n, which means that the strain at this point is:
strain = (change in length) / (original length) = 0.6 cm / 35 cm = 0.0171
We can use this to find the spring constant:
stress = (2 n) / (area) = (spring constant) x (0.0171)
spring constant = (2 n) / (area x 0.0171)
We are then asked to find the length of the cord when the stretching force is 2.5n. From Hooke's law, we know that:
stress = (spring constant) x (strain)
We can rearrange this to solve for the new change in length:
(change in length) = (spring constant) x (strain) x (new force)
(change in length) = [(2 n) / (area x 0.0171)] x (0.0171) x (2.5 n)
(change in length) = 2.941 cm
Finally, we can add this change in length to the original length of the cord to find the new length:
(new length) = (original length) + (change in length)
(new length) = 35 cm + 2.941 cm
(new length) = 37.941 cm
Therefore, the length of the cord when the stretching force is 2.5n will be 37.941 cm.
To find the length of the cord when the stretching force is 2.5N, we can use the concept of proportionality.
Let's first calculate the proportionality constant for the elastic cord.
Extension = Proportionality Constant × Force
We have the values for extension (0.6 cm) and force (0.5 N). Substituting these values into the formula, we can solve for the proportionality constant.
0.6 cm = Proportionality Constant × 0.5 N
Proportionality Constant = 0.6 cm / 0.5 N
Proportionality Constant = 1.2 cm/N
Now, let's find the extension for a force of 2.5N. We'll use the same formula, with the proportionality constant we just found.
Extension = 1.2 cm/N × 2.5 N
Extension = 3 cm
To find the total length of the cord when the stretching force is 2.5N, we need to add the extension to the original length.
Total Length = Original Length + Extension
Total Length = 35 cm + 3 cm
Total Length = 38 cm
Therefore, the length of the cord when the stretching force is 2.5N will be 38 cm.