Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0 V batteries of a 740 kg electric car be able to supply:
(a) To accelerate from rest to 25.0 m/s in 1.00 min?
(b) To climb a 200 m high hill in 2.00 min at a constant 25.0 m/s speed while exerting 475 N of force to overcome air resistance and friction?
(c) To travel at a constant 25.0 m/s speed, exerting a 475 N force to overcome air resistance and friction?
To find the current that the 12.0 V batteries must supply for each scenario, we need to use the power equation:
Power = Voltage × Current
Given that the efficiency of the motor is 95.0% or 0.95, the effective power produced by the motor is:
Effective Power = Efficiency × Power
For each scenario, we'll need to calculate the power required and then divide it by the battery voltage to find the current.
(a) To accelerate from rest to 25.0 m/s in 1.00 min:
First, we need to find the work done to accelerate the car using the equation:
Work = (1/2) × mass × velocity^2
Plugging in the given values, we have:
Work = (1/2) × 740 kg × (25.0 m/s)^2
Next, we need to find the time taken in seconds, given that it is given in minutes:
Time = 1.00 min × 60 s/min
Using the equation for power, we can find the power required:
Power = Work / Time
Finally, we can calculate the current:
Current = Power / Voltage
(b) To climb a 200 m high hill in 2.00 min at a constant 25.0 m/s speed while exerting 475 N of force to overcome air resistance and friction:
First, we calculate the power required using the equation:
Power = force × velocity
Power = 475 N × 25.0 m/s
Next, we convert the time to seconds:
Time = 2.00 min × 60 s/min
Now we can calculate the current:
Current = Power / Voltage
(c) To travel at a constant 25.0 m/s speed, exerting a 475 N force to overcome air resistance and friction:
Similar to the previous scenario, we calculate the power required using the equation:
Power = force × velocity
Power = 475 N × 25.0 m/s
Finally, we can calculate the current:
Current = Power / Voltage
Remember that these calculations are based on the given assumptions, and they may not account for all real-world factors.