PLEASE DO NOT USE CHAT GPT, I WILL REPORT IT

The gears shown in the following figure have a module of 10 mm and a pressure angle of 20. The pinion (gear 2) rotates at 1200 rpm cw with a power input of 150 kW. Gears 3 and 4 are idlers. N = 18t, N3 =32t, N, = 18t, N; =48t SRop o0 oW Determine the following: Pitch diameters of each gear. The tangential Force from gear 3 to gear 2. The radial force from gear 3 to gear 2 The input torque on shaft a. Draw the free body diagram for gear 2. The tangential forces exerted on gears 3 and 4 The radial forces exerted on gears 3 and 4. Draw the free body diagram for gears 3 and 4. Step 1: Given Data . Module (m): 10 mm Pressure Angle (): 20 . Speed of Pinion (N2): 1200 rpm (clockwise) . Input Power (P): 150 kW Number of teeth: Gear 2 (Pinion): N2 = 18 . Gear 3: N3 = 32 Gear 4: N4 = 18 Gear 5 (Driven gear): N, = 48 Step 2: Formula Recap . Pitch Diameter: d = m . N Tangential Force: Ft = 2P ov = DidN2 (linear velocity) . Radial Force: F, = Ft . tan() . Torque: T = 279 a. Pitch Diameters For each gear, d = m . N d3 = 10 . 32 = 320, mm . d4 = 10 . 18 = 180, mm . d5 = 10 . 48 = 480, mm Pitch Diameters: . Gear 2: 180 mm Gear 3: 320 mm . Gear 4: 180 mm Gear 5: 480 mm b. Tangential Force from Gear 3 to Gear 2 1. Calculate Linear Velocity v: v = (60 2 = 1:180, 200 = 11309.73 mm/s = 11.31 m/s 11.31 Ft = 2P _ 2:160000 = 26537.3 N Tangential Force: Ft = 26537.3, N c. Radial Force from Gear 3 to Gear 2 F, = F . tan($) = 26537.3 . tan(20) = 9650.6 N Radial Force: F, = 9650.6, N d. Input Torque on Shaft a T = P:60 - 150000-60 = 1193.66 Nm Input Torque: 7 = 1193.66, Nm e. Free Body Diagram for Gear 2 The free body dia 1. Tangential Force (from Gear 3): Ft = 26537.3, N 2. Radial Force (from Gear 3): F, = 9650.6, N 3. These forces act at the pitch circle radius of 90 mm. f. Tangential Forces on Gears 3 and 4 Since Gears 3 and 4 are idlers, they transmit the same tangential force: F13 = Ft4 = Ft = 26537.3N g. Radial Forces on Gears 3 and 4 F,3 = F,4 = F . tan($) = 26537.3 . tan(20) = 9650.6 Nh. Free Body Diagrams for Gears 3 and 4 The diagrams will include: 1. Tangential Forces: F; = 26537.3, N acting tangentially at the pitch circle. 2. Radial Forces: I, = 9650.6, N acting radially inward. 3. Equal and opposite reactions due to adjacent gears