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Hooke's Law is a fundamental principle in physics that describes how a spring stretches in response to an applied force. The law is expressed by the equation: \( F = k \times x \). Here, \( F \) represents the force applied to the spring (often the weight of an object), \( k \) is the spring constant (or proportionality constant), and \( x \) is the elongation or compression of the spring. When a spring obeys Hooke's Law, the relationship between the force and the extension is linear. This means the force needed to stretch or compress the spring is proportional to the distance it is stretched or compressed. In simpler terms, if you double the applied force, the spring stretches twice as much.

Before utilizing Hooke's Law, you need to calculate the weight of the object. Weight is the force exerted by gravity on an object and can be calculated using the formula: \( W = m \times g \). Here, \( W \) is the weight, \( m \) is the mass of the object, and \( g \) is the gravitational acceleration (approximated as \( 9.81 \text{ m/s}^2 \)). For instance, if we have an object with a mass of 5 kg, the weight calculation would be: \( W = 5 \text{ kg} \times 9.81 \text{ m/s}^2 = 49.05 \text{ N} \). This weight is the force applied to the spring in the Hooke's Law equation.

When dealing with physics problems, it's crucial to ensure that all units are consistent. In many cases, you might need to convert between different units. For instance, if the deflection of a spring is given in centimeters but the standard units for Hooke's Law are meters, a unit conversion must be made. To convert centimeters to meters, you divide by 100 because there are 100 centimeters in a meter. So, a deflection of 8 cm would be converted to: \( 8 \text{ cm} = 8 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 0.08 \text{ m} \). Proper unit conversion ensures accuracy in your calculations and consistency across formulas.

In this context, the proportionality constant is the spring constant \( k \). This constant \( k \) indicates the stiffness of a spring and can be calculated using Hooke's Law: \( F = k \times x \). Rearranging this formula to solve for \( k \) gives: \( k = \frac{F}{x} \). Given the force (or weight) \( F \) is 49.05 N, and the deflection \( x \) is 0.08 m, the spring constant is: \( k = \frac{49.05}{0.08} \text { N/m} = 613.125 \text{ N/m} \). If asked for the spring constant in N/cm, an additional conversion is needed. Since 1 m = 100 cm, the conversion would be: \( k = 613.125 \text{ N/m} \times \frac{1 \text{ m}}{100 \text{ cm}} = 6.13125 \text{ N/cm} \). This constant helps us understand how much force is needed to stretch or compress the spring by a specific amount.