Elasticity

Given: A string suspended from the ceiling is subjected to two downward forces and , resulting in lengths and respectively. We are asked to find the actual length of the string.

Concept: The actual length of the string is related to the forces applied to it. The string follows Hooke's law, which states that the extension or compression in the string is proportional to the applied force. When two different forces and cause different extensions and , we can use the principle of superposition to calculate the actual length of the string.

Approach: - The forces and are proportional to the extensions and , respectively. This means the relationship between force and extension can be expressed as: This constant is the stiffness of the string. - The actual length is the length corresponding to zero force, which can be calculated by the formula:

Final Answer: The actual length of the string is given by: