Question

Hooke's Law In Exercises 3-10, use Hooke's Law to determine the variable force in the spring problem. A force of 800 newtons stretches a spring 70 centimeters on a mechanical device for driving fence posts. Find the work done in stretching the spring the required 70 centimeters.

Short answer

The work done in stretching the spring required 70 centimeters is 280 Joules.

Step-by-step solution

Understand Hooke's Law and Work Done

Hooke’s Law is represented by \( F = kx \), where F is the force applied on the spring, k is the spring constant, and x is the extension in the spring. The work done on the spring can be calculated using the formula \( W = 0.5 * F * x \)

Derive Spring Constant

We can use Hooke's Law to find the spring constant: \( k = F / x\). Substituting the values, we find \( k = 800N / 0.7m = 1142.86 N/m \)

Calculate Work Done

Next, we can calculate the work done stretching the spring the required distance, using the formula \( W = 0.5 * F * x \): Substituting the provided values and the derived spring constant: \( W = 0.5 * 800N * 0.7m = 280 Joules \)