Question
The spring stretches from 10cm to 22cm when a force of 4N is applied.if it obeys Hooke's law ,its total length in cm when a force of 6N is applied is?
Answers
GPT 3.5
According to Hooke's law, the force applied is directly proportional to the extension of the spring. Mathematically, this can be represented as:
F = kx
where F is the force applied, k is the spring constant, and x is the extension of the spring.
To find the spring constant, we can use the given information that the spring stretches from 10cm to 22cm when a force of 4N is applied. The extension of the spring is:
x = 22cm - 10cm = 12cm = 0.12m
The force applied is 4N, so we can rearrange the equation to solve for k:
k = F/x = 4N / 0.12m = 33.33 N/m
Now, we can determine the extension of the spring when a force of 6N is applied. Rearranging the equation, we have:
x = F/k = 6N / 33.33 N/m = 0.18m
To find the total length of the spring, we add the original length to the extension:
Total length = Original length + Extension
Total length = 10cm + 18cm = 28cm
Therefore, when a force of 6N is applied, the total length of the spring is 28cm.
F = kx
where F is the force applied, k is the spring constant, and x is the extension of the spring.
To find the spring constant, we can use the given information that the spring stretches from 10cm to 22cm when a force of 4N is applied. The extension of the spring is:
x = 22cm - 10cm = 12cm = 0.12m
The force applied is 4N, so we can rearrange the equation to solve for k:
k = F/x = 4N / 0.12m = 33.33 N/m
Now, we can determine the extension of the spring when a force of 6N is applied. Rearranging the equation, we have:
x = F/k = 6N / 33.33 N/m = 0.18m
To find the total length of the spring, we add the original length to the extension:
Total length = Original length + Extension
Total length = 10cm + 18cm = 28cm
Therefore, when a force of 6N is applied, the total length of the spring is 28cm.