The spiral spring of a spring balance is 25.0cm long when 5N hangs on it as and 30.0cm long when the weight is 10N

What is the length of the spring
If the weight is 3N assuming hooke's law is obeyed?

k = (10N-5N)/(30cm-25cm) = 5N/5cm = 1N/cm . = spring constant.

Lo + (1cm/N * 5N) = 25.
Lo + 5 = 25,
Lo = 20 cm = Initial length.

L = Lo + (1cm/N * 3N) = 20 + 3 = 23 N. = Length with 3N-Wt.

Its okay that was an assignment

Bravoooooo

extension is proportional to the force

5 N extends the spring 5 cm ... 1 N/cm

relaxed length is 20.0 cm

spring is 23.0 cm with a 3 N weight

Well it's really good 👍

To find the length of the spring when a weight of 3N is applied, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Let's start by finding the spring constant, which is a measure of the stiffness of the spring. We can use the formula:

k = (F / x)

Where:
k is the spring constant
F is the force applied
x is the displacement from the equilibrium position

Using the given information, when a weight of 5N hangs on the spring, the length is 25.0cm. Assuming that 25.0cm is the equilibrium position of the spring, the displacement from the equilibrium position is zero, and therefore the force applied is also zero.

k = (0 / 0)

Since the force and displacement are zero, we cannot determine the spring constant using this information.

To find the length of the spring when a weight of 3N is applied, we can use the concept of proportionality between the force and the displacement. We can set up a ratio with the known lengths and forces:

(Length 1) / (Force 1) = (Length 2) / (Force 2)

Using the given information:
(25.0cm) / (5N) = (Length 2) / (3N)

Cross-multiplying:
(25.0cm) * (3N) = (5N) * (Length 2)

Simplifying:
(75.0 cm*N) = (5N) * (Length 2)

Divide both sides by 5N:
(75.0 cm*N) / (5N) = Length 2

Simplifying:
Length 2 = 15.0cm

Therefore, when a weight of 3N is applied, assuming Hooke's Law is obeyed, the length of the spring will be 15.0cm.