To address your question about the spring scale and the weights, let's break this down step by step. We’ll first consider the scenario where all the weights are removed from the spring and then analyze how to find the weight \( W \) when a specific weight is applied. Understanding spring scales involves grasping the concepts of force and elasticity.

Initial Pointer Position

When there are no weights applied to the spring, the spring is in its natural, unextended state. This means that the pointer will indicate the zero mark on the scale. The zero mark is typically where the scale begins, representing no force acting on the spring. Therefore, when all weights are removed, the pointer will point to the zero mark.

Determining the Weight W

Next, let's find the weight \( W \) that corresponds to the displacement of the spring when a weight is hung on it. A spring works on the principle of Hooke’s Law, which states that the force exerted by a spring is proportional to its extension or compression from its rest position. Mathematically, this is expressed as:

• F = kx

Where:

• F is the force applied (in Newtons),
• k is the spring constant (in N/m), and
• x is the displacement of the spring from its equilibrium position (in meters).

In the context of your question, the weight \( W \) can be defined as the force due to gravity acting on that weight:

• W = mg

Where:

• m is the mass of the weight (in kilograms), and
• g is the acceleration due to gravity (approximately 9.81 m/s²).

Steps to Find W

To find the weight \( W \) when a weight is applied to the spring, you need to follow these logical steps:

1. Measure the displacement x of the spring when the weight is attached.
2. Determine the spring constant k if it’s not already provided. This can often be calculated from previous measurements of known weights and their corresponding displacements.
3. Using Hooke’s Law, calculate the force exerted by the spring: F = kx.
4. Set the force equal to the weight to find \( W \): hence \( W = kx \).

Example Calculation

For instance, if the spring constant \( k \) is 200 N/m and the spring extends by 0.1 m when a weight is hung, the calculation for \( W \) would be:

• Using Hooke’s Law: F = kx = 200 N/m * 0.1 m = 20 N.
• Thus, the weight \( W \) is 20 N. To find the mass, you would use \( m = W/g = 20 N / 9.81 m/s² ≈ 2.04 kg \).

This method allows you to find the weight corresponding to the extension of the spring accurately. If you have specific values for the spring constant or the displacements, you can plug those into the formulas to obtain your results. Understanding these principles will give you a solid foundation in how springs and scales operate in physics.