A spider spring of a spring balance is 25cm long when 5N weight hang on it and 30cm long when the weight is 10N what is the length of the spring it is weigth is 3N assuming hooke's law is obeyed?
k= changforce/changlenght=(10-5)/(30-25)=1N/cm
so at 3N, it will be 2cm shorter than 25cm.
Good
To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its extension or compression. The formula for Hooke's Law is:
F = kx
Where:
F is the force applied to the spring,
k is the spring constant, and
x is the elongation or compression of the spring.
In this case, we are given the lengths of the spring and the weights applied, and we need to find the length when a 3N weight is applied. We can use the proportionality of the spring constant (k) to solve this problem.
Let's first calculate the spring constant using the given information:
For the first scenario when a 5N weight is applied, the length of the spring is 25cm. This can be written as:
5N = k * 25cm (equation 1)
For the second scenario when a 10N weight is applied, the length of the spring is 30cm. This can be written as:
10N = k * 30cm (equation 2)
Now, let's solve equations 1 and 2 simultaneously to find the value of k:
5N = k * 25cm
10N = k * 30cm
Dividing equation 2 by equation 1, we get:
(10N/5N) = (k * 30cm) / (k * 25cm)
2 = 30cm / 25cm
2 = 1.2
Now, we have the value of k, which is 1.2 (N/cm). To find the length of the spring when a 3N weight is applied, we can rearrange Hooke's Law formula:
F = kx
3N = 1.2 (N/cm) * x
Dividing both sides of the equation by 1.2 (N/cm), we get:
3N / 1.2 (N/cm) = x
2.5cm = x
Therefore, the length of the spring when a 3N weight is applied is 2.5cm.