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Task 1 Among its products is the power transducer. The product is an electrical isolation transducer of single-phase active and reactive power measurement, complete isolation between input and output signals. It is designed to measure power, reactive power and power factor. The product is widely used in electricity, communications, railways, industrial control and other fields. The transducer weights 0,1-pound 1-500-volt, 0.5-700 A, the size is 76mmx32mmx2inch. The response time of the transducer is 250 ms. (a) 1. What is the volume of the transducer in cubic m? 2. How many transducers can be packed in box of 1m X 0.5 m X 1m? 3. If the factory produces 500 transducer per hour, how many minutes are needed to produce 50 kg of the transducer? 4. If the production line needs maintenance every 100,000 transducer. Find to the nearest integer how many weeks are needed to be sent to maintenance if the production rate is 100 transducer/min which operates 8 hours/ day and 5 days / week.

Answer :

Final answer:

The volume of the transducer is approximately 0.0001235 cubic meters. Approximately 4050 transducers can be packed in a box of 1m x 0.5m x 1m. It would take approximately 132.24 minutes to produce 50 kg of transducers. Approximately 2.4 weeks are needed to send the transducers for maintenance.

Explanation:

Calculations related to the power transducer

  1. Volume of the transducer: To find the volume of the transducer, we need to convert the given dimensions from different units to a common unit. The given dimensions are 76mm x 32mm x 2inch. Converting 2 inches to millimeters, we get 50.8mm. Now, we can calculate the volume using the formula: Volume = Length x Width x Height. Substituting the values, we get Volume = 76mm x 32mm x 50.8mm = 123,494.4 cubic millimeters. Converting this to cubic meters, we divide by 1,000,000,000 (1 cubic meter = 1,000,000,000 cubic millimeters). Therefore, the volume of the transducer is approximately 0.0001235 cubic meters.
  2. Number of transducers in a box: The given dimensions of the box are 1m x 0.5m x 1m. To find the number of transducers that can be packed in the box, we need to calculate the volume of the box and divide it by the volume of one transducer. The volume of the box is 1m x 0.5m x 1m = 0.5 cubic meters. Dividing this by the volume of one transducer (0.0001235 cubic meters), we get approximately 4050 transducers.
  3. Time to produce 50 kg of transducers: The weight of one transducer is given as 0.1 pound. Converting this to kilograms, we get 0.04536 kg. To find the number of transducers needed to produce 50 kg, we divide 50 kg by the weight of one transducer (0.04536 kg). This gives us approximately 1102 transducers. Since the factory produces 500 transducers per hour, we can calculate the time needed to produce 1102 transducers by dividing 1102 by 500 and multiplying by 60 (to convert hours to minutes). Therefore, it would take approximately 132.24 minutes to produce 50 kg of transducers.
  4. Time to send transducers for maintenance: The production rate is given as 100 transducers per minute. The production line operates 8 hours per day and 5 days per week. To find the number of transducers produced in a week, we multiply the production rate by the number of minutes in an hour (60) and the number of hours in a day (8), and then multiply by the number of days in a week (5). This gives us 100 x 60 x 8 x 5 = 240,000 transducers. Since maintenance is required every 100,000 transducers, we divide 240,000 by 100,000 to find the number of weeks needed for maintenance. Therefore, approximately 2.4 weeks are needed to send the transducers for maintenance.

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