This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Here are the solutions to the questions from the image: QUESTION 1 1.1 Give TWO examples where the individual production method could be applied. Shipbuilding* Custom-made furniture* 1.2 State TEN principles of a good workshop layout. 1. Flow of work: Materials and products should move smoothly with minimal backtracking. 2. Space utilization: Efficient use of all available space. 3. Accessibility: Easy access to machines, tools, and work areas. 4. Safety: Minimize hazards and provide clear emergency routes. 5. Flexibility: Ability to adapt to changes in production. 6. Communication: Facilitate easy interaction among workers. 7. Supervision: Allow for effective monitoring of work. 8. Comfort and environment: Good lighting, ventilation, and temperature control. 9. Minimization of material handling: Reduce movement of materials. 10. Orderliness and cleanliness: Promote a tidy and organized workspace. QUESTION 2 2.1 The following are the particulars of an open flat-belt drive between a motor and a machine: Belt speed = 900 m/min Centre distance between shafts = 4.5 m Speed of motor = 1400 r/min Contact angle on motor pulley = 182^ Power = 14.5 kW Speed of machine = 2300 r/min Contact angle on machine pulley = 178^ Thickness of belt = 5 mm Maximum allowable tension = 160 N per cm width of belt Coefficient of friction = 0.3 2.1.1 Calculate the diameter of the pulleys. Step 1: Convert belt speed to meters per second. v = 900 m/min = (900)/(60) m/s = 15 m/s Step 2: Calculate the diameter of the motor pulley (D_m). The formula for belt velocity is v = ( D N)/(60). Rearranging for diameter: D_m = (60v)/( N_m) D_m = 60 × 15 m/s × 1400 r/min = (900)/(1400) m ≈ 0.2047 m D_m ≈ 204.7 mm Step 3: Calculate the diameter of the machine pulley (D_mach). D_mach = (60v)/( N_mach) D_mach = 60 × 15 m/s × 2300 r/min = (900)/(2300) m ≈ 0.1244 m D_mach ≈ 124.4 mm The diameters of the pulleys are 204.7 mm and 124.4 mm. 2.1.2 Calculate the width of the belt in mm. Step 1: Calculate the effective tension (F_1 - F_2). P = (F_1 - F_2)v F_1 - F_2 = (P)/(v) = 14.5 × 10^3 W15 m/s ≈ 966.67 N Step 2: Determine the smaller contact angle and convert it to radians. The smaller contact angle is _mach = 178^. _rad = 178^ × ()/(180^) ≈ 3.1067 rad Step 3: Calculate the ratio of tensions (F_1)/(F_2). (F_1)/(F_2) = e^ _rad = e^0.3 × 3.1067 = e^0.93201 ≈ 2.5397 Step 4: Solve for F_1 (tight side tension). We have F_1 - F_2 = 966.67 and F_1 = 2.5397 F_2. Substitute F_1 into the first equation: 2.5397 F_2 - F_2 = 966.67 1.5397 F_2 = 966.67 F_2 = (966.67)/(1.5397) ≈ 627.83 N F_1 = 2.5397 × 627.83 ≈ 1594.5 N Step 5: Calculate the width of the belt. The maximum allowable tension is 160 N/cm. The tight side tension F_1 is the maximum tension. Width = (F_1)/(Max allowable tension per cm) = 1594.5 N160 N/cm ≈ 9.966 cm Convert to mm: Width = 9.966 cm × 10 mm/cm ≈ 99.66 mm The width of the belt is 99.66 mm. 2.1.3 Calculate the length of the belt in metres. Step 1: Use the formula for the length of an open flat belt drive. L = ( D_m + D_mach2 ) + 2C + (D_m - D_mach)^24C Using D_m = 0.2047 m, D_mach = 0.1244 m, and C = 4.5 m: L = ( (0.2047 + 0.1244)/(2) ) + 2(4.5) + ((0.2047 - 0.1244)^2)/(4(4.5)) Step 2: Perform the calculations. L = ( (0.3291)/(2) ) + 9 + ((0.0803)^2)/(18) L = (0.16455) + 9 + (0.00644809)/(18) L ≈ 0.5170 + 9 + 0.000358 L ≈ 9.517358 m The length of the belt is 9.52 m. 2.2 Calculate the number of V belts required for this drive if the maximum allowable tension per belt is 900 N and the belt has to transmit 30 kW. Step 1: Calculate the belt velocity (v). v = ( D N)/(60) = × 0.25 m × 1800 r/min60 s/min = 7.5 m/s ≈ 23.56 m/s Step 2: Calculate the centrifugal tension (F_c). F_c = m v^2 = 0.5 kg/m × (23.56 m/s)^2 ≈ 277.58 N Step 3: Calculate the effective coefficient of friction (_e) for a V-belt. The angle of the V-groove is 2 = 40^, so = 20^. _e = ()/( ) = (0.25)/( 20^) ≈ (0.25)/(0.3420) ≈ 0.7310 Step 4: Convert the contact angle to radians and calculate _e . _rad = 140^ × ()/(180^) ≈ 2.4435 rad _e _rad = 0.7310 × 2.4435 ≈ 1.7860 Step 5: Calculate the ratio of tensions (F_1 - F_c)/(F_2 - F_c). (F_1 - F_c)/(F_2 - F_c) = e^_e _rad = e^1.7860 ≈ 5.965 Step 6: Calculate the tensions F_1 and F_2 per belt. Given maximum allowable tension per belt F_1 = 900 N. 900 N - 277.58 NF_2 - 277.58 N = 5.965 622.42 NF_2 - 277.58 N = 5.965 F_2 - 277.58 N = 622.42 N5.965 ≈ 104.34 N F_2 = 104.34 N + 277.58 N = 381.92 N Step 7: Calculate the power transmitted per belt (P_belt). P_belt = (F_1 - F_2)v = (900 N - 381.92 N) × 23.56 m/s P_belt = 518.08 N × 23.56 m/s ≈ 12204.6 W ≈ 12.20 kW Step 8: Calculate the number of belts required. Number of belts = Total power to transmitPower per belt = 30 kW12.20 kW ≈ 2.459 Since the number of belts must be a whole number, round up. The number of V belts required is 3. Got more? Send 'em!