🔍 Key Concepts

• Gear ratios: For meshed gears, speed is inversely proportional to the number of teeth on each gear. • Power and efficiency: Output horsepower = input horsepower × efficiency (expressed as a decimal). • Direction of speed change when a large gear drives a small gear.

💭 Think About

• First, decide whether the output horsepower at shaft B should be greater than, equal to, or less than 30 HP when the efficiency is 67%. What simple formula links these three values? • Looking at the illustration, is shaft B attached to the larger gear or the smaller gear? When a large gear drives a smaller gear, does the smaller gear turn faster or slower than the large one? • Use the relative size (or tooth count X vs. Y) to estimate the speed ratio between shaft A and shaft B, then apply that ratio to 300 rpm.

✅ Before You Answer

• Compute output power using HP_out = HP_in × efficiency and compare that with the choices (watch units and rounding). • Confirm which gear (A or B) has more teeth, and therefore which shaft must have the higher rpm. • Verify that your chosen answer matches both the expected horsepower from efficiency and the expected speed change from the gear size ratio.