# Achieving Higher Speed: Calculating the Required Sheave Diameter

## Explanation:

**Understanding the Problem:** The contractor's goal is to increase the car speed from 100 feet per minute (fpm) to 125 fpm. The current setup utilizes a 12-inch sheave for this purpose.

**Solution Approach:** To determine the required sheave size needed to achieve the desired speed increase while keeping the motor rotation speed constant, we can use the concept of pulleys and ratios.

**Calculating the Increase:** The speed needs to be increased by 25% (from 100 fpm to 125 fpm). To maintain the same motor rotation speed, the sheave diameter must be adjusted proportionally.

**Required Sheave Diameter:** Since the current sheave is 12 inches in diameter, increasing it by 25% results in a new sheave diameter of 15 inches. This adjustment ensures that the car reaches the desired speed while the motor continues operating at the same speed.

**Conclusion:** By increasing the sheave diameter from 12 inches to 15 inches, the contractor can effectively raise the car speed from 100 fpm to 125 fpm without altering the motor rotation speed. This adjustment optimizes the system for the desired performance improvement.