### Problem Statement1. A fisherman's spring scale stretches 3.9 cm when a 2.7 kg fish hangs from it. - **(A)** What is the spring constant of the scale?### Diagram and Explanation**Explanation**: When a mass is hung from a spring scale, the force due to the weight of the mass causes the spring to stretch. The relationship between the force, spring constant, and displacement is given by Hooke's Law:\[ F = k \cdot x \]where:- \( F \) is the force exerted by the weight of the fish,- \( k \) is the spring constant,- \( x \) is the displacement of the spring.**Given Values**:- Mass of the fish, \( m = 2.7 \, \text{kg} \)- Displacement of the spring, \( x = 3.9 \, \text{cm} = 0.039 \, \text{m} \)Since the force \( F \) is caused by the weight of the fish, we can calculate it using:\[ F = m \cdot g \]where \( g \approx 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.### Calculation1. Calculate the force exerted by the fish: \[ F = 2.7 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 26.46 \, \text{N} \]2. Using Hooke's Law to find the spring constant \( k \): \[ 26.46 \, \text{N} = k \times 0.039 \, \text{m} \] \[ k = \frac{26.46 \, \text{N}}{0.039 \, \text{m}} = 678.46 \, \text{N/m} \]**Answer**: The spring constant of the scale is approximately \( 678.46 \, \text{N/m} \).

Name: ### Problem Statement1. A fisherman's spring scale stretches 3.9 cm w
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: ### Problem Statement1. A fisherman's spring scale stretches 3.9 cm when a 2.7 kg fish hangs from it. - **(A)** What is the spring constant of the scale?### Diagram and Explanation**Explanation**: When a mass is hung from a spring scale, the forc