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(b) The company is conducting set of experiments to maximize the time needed to discharge the battery. It was found that the time (t) is proportional to different powers of acceleration (a) , mass (m), and energy (E) of the battery. Use dimensional homogeneity to find the formula of the time and the value of overall dimensionless proportional constant usingt=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 137 km/hr, and the mass is 1437pound. (c) Assume that the charge capacity of the battery can be given by the following formula: Q = Gnm³V¯21?w0.5. E² Where m is the mass of the cell of the battery in kg, V is the voltage of the battery in volts, l is the length of the cell in m, w is the width of the cell in m, and E is the Energy of the cell in kWh, and n is the number of cells in the pack. If n = 100, m = 37pound, 1= 25 cm, w= 5 cm, V=338 V and E=37kWh. Find the value 1. of dimensionless constant G?

(b) The company is conducting set of experiments to maximize the time needed to discharge the battery. It was found that the time (t) is proportional to different powers of acceleration (a) , mass (m), and energy (E) of the battery. Use dimensional homogeneity to find the formula of the time and the value of overall dimensionless proportional constant usingt=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 137 km/hr, and the mass is 1437pound. (c) Assume that the charge capacity of the battery can be given by the following formula: Q = Gnm³V¯21?w0.5. E² Where m is the mass of the cell of the battery in kg, V is the voltage of the battery in volts, l is the length of the cell in m, w is the width of the cell in m, and E is the Energy of the cell in kWh, and n is the number of cells in the pack. If n = 100, m = 37pound, 1= 25 cm, w= 5 cm, V=338 V and E=37kWh. Find the value 1. of dimensionless constant G?

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(b) The company is conducting set of experiments to maximize the time needed to discharge the battery. It was found that the time (t) is proportional to different powers of acceleration (a) , mass (m), and energy (E) of the battery. Use dimensional homogeneity to find the formula of the time and the value of overall dimensionless proportional constant usingt=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 137 km/hr, and the mass is 1437pound. (c) Assume that the charge capacity of the battery can be given by the following formula: Q = Gnm³V¯21²w0.5, E² Where m is the mass of the cell of the battery in kg, V is the voltage of the battery in volts, l is the length of the cell in m, w in kWh, and n is the number of cells in the pack. If n = 100, m = 37pound, 1= 25 cm, w= 5 cm, V=338 V and E=37kWh. Find the value the width of the cell in m, and E is the Energy of the cell 1. of dimensionless constant G?
Transcribed Image Text:(b) The company is conducting set of experiments to maximize the time needed to discharge the battery. It was found that the time (t) is proportional to different powers of acceleration (a) , mass (m), and energy (E) of the battery. Use dimensional homogeneity to find the formula of the time and the value of overall dimensionless proportional constant usingt=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 137 km/hr, and the mass is 1437pound. (c) Assume that the charge capacity of the battery can be given by the following formula: Q = Gnm³V¯21²w0.5, E² Where m is the mass of the cell of the battery in kg, V is the voltage of the battery in volts, l is the length of the cell in m, w in kWh, and n is the number of cells in the pack. If n = 100, m = 37pound, 1= 25 cm, w= 5 cm, V=338 V and E=37kWh. Find the value the width of the cell in m, and E is the Energy of the cell 1. of dimensionless constant G?
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