This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to calculate the gear ratio and the speed of the driven gear: Step 1: Identify the given values. The driving gear has N_1 = 30 teeth. The speed of the driving gear is S_1 = 100 rev/min. The driven gear has N_2 = 40 teeth. A) Calculate the gear ratio. The gear ratio (GR) is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. GR = (N_2)/(N_1) Substitute the given values: GR = (40)/(30) GR = (4)/(3) GR ≈ 1.333 The gear ratio is 4/3 or 1.333. B) Calculate the speed of the driven gear. The relationship between the number of teeth and the speeds of the gears is given by the formula: N_1 S_1 = N_2 S_2 Where S_2 is the speed of the driven gear. Rearrange the formula to solve for S_2: S_2 = (N_1 S_1)/(N_2) Substitute the given values: S_2 = 30 teeth × 100 rev/min40 teeth S_2 = (3000)/(40) rev/min S_2 = 75 rev/min The speed of the driven gear is 75 rev/min. Send me the next one 📸