a) A car engine produces a torque of 300 Nm while rotating at 300 rpm. What is t

Question

a) A car engine produces a torque of 300 Nm while rotating at 300 rpm. What is the power it produces?

b) A common smartphone battery has a capacity of 8 Watt-hours (note this is a unit of
energy) when fully chared. Suppose the car engine from part (a) is connected to an
electrical generator which is used to charge this battery. How long will it take to charge to
full capacity?

c) An 80 kg person climbs up a hill. If the work done in climbing is equal to the total energy of the battery from part (b), how high is the hill?

d) The energy content of sugar is about 17 J/mg (Joule per milligram). How many grams of sugar must the person from part (c) consume to have sufficient energy to climb the hill if metabolism is 20% efficient (meaning only 20% of food energy is converted to useful work)?

**Can someone please explain this to me step by step? Thank you.

Explanation / Answer

a) power = torque * angular speed

here torque = 300 Nm
angular speed = 300 rpm = 300 * 2*pi / 60 rad / sec = 31.41593 rad/sec

so.. pwer = 300 * 31.41593 = 9424.77796 W


b) total energy of battery = 8 Watt hour = 8 * 3600 = 28800 J

so.. time taken = total energy of battery / power of car = 28800 / 9424.77796 = 3.0557749 secs

c)
total energy of battery = 8 Watt hour = 8 * 3600 = 28800 J

let the heoght of the hill be h

so.. mass * g * h = 28800
80 * 9.81 * h = 28800
so.. h = 36.69725 m

d) Let the total energy from sugar required bee E ..

so.. here .. we know that 0.2 * E = 28800
so.. E = 28800 / 0.2 = 144000 J

so.. amount of sugar = 144000 / 17 = 8470.588 mg of sugar = 8.470588 grams

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