Aline shaft rotating at 250 rpm is connected to a grinding wheel by the pulley assembly shown. If the grinder shaft must turn at 1050 rpm , what size pulley should be attached to the line shaft? If the grinder shaft must turn at 1050 rpm, a \( \square \) in. pulley should be attached to the line shaft.

To achieve the desired speed of 1050 rpm on the grinder shaft from a line shaft rotating at 250 rpm, you can use the pulley ratio formula. The speed ratio is given by the formula: \[ \text{Pulley Ratio} = \frac{\text{Speed of Line Shaft}}{\text{Speed of Grinder Shaft}} = \frac{250}{1050} = \frac{5}{21} \] Now, if we denote the diameter of the line shaft pulley as \( D_1 \) (which is yet to be determined) and the diameter of the grinder pulley as \( D_2 \), then you can use the formula: \[ \frac{D_2}{D_1} = \frac{5}{21} \] This means that for every 21 inches of the line shaft pulley diameter, the grinder pulley should be 5 inches. So if you choose \( D_2 \) to be 5 inches, then: \[ D_1 = (21/5) \times D_2 = (21/5) \times 5 = 21 \text{ inches} \] Thus, a 21-inch pulley should be attached to the line shaft to ensure the grinder turns at 1050 rpm. Let the exciting world of pulleys inspire you! Did you know that the pulley system dates back to ancient Greece? Archimedes famously used pulleys to move heavy objects, showing just how ingenious this simple machine can be! It’s fascinating how the principles of mechanics from more than two thousand years ago are still utilized in today's technology. For a deep dive into the world of mechanical advantage and pulley systems, consider exploring "The Science of Simple Machines." It's packed with fun experiments and detailed explanations, making it a perfect read for anyone wanting to grasp the practical applications of these concepts in modern machinery. Plus, there's a good chance it’ll spark your creativity for your next DIY project!