An electric motor consumes 9.00 kJ of electrical energy in 1.00 min. If one-third of this energy goes into heat and other forms of internal energy of the motor, with the rest going to the motor output, how much torque will this engine develop if you run it at 2500 rpm?

Video transcript

welcome back everybody. We are given an electric motor and we are told in a drill and we are told that this drill uses 100 and village jewels of energy every five Minutes. We're also told that 1/4 of this energy is lost to internal energy, but that the other 3/4 of our electricity is then turned into work. We're also told that the drill rotates at around 3000 rpm and we are asked to find the torque developed in the motor. We're looking at our equations to find torque. The one that is most obvious to me is this one right here that are torque times our revolutions per minute, given by that lower case omega. There is equal to our work divided by our time. Now, in order to isolate torque, I'm actually gonna divide both sides by our omega here. These terms are going to cancel out. And we get that our torque equal to our work divided by our time times our omega. Before we can find this torque, we got to make sure that all these variables are in the correct unit. So let's go ahead and do some conversions here. What we are told that our work is 3/4 of our electricity and we are looking for this to be in jewels were given that it's and 80 kg jewels. So this is equal to 180, jewels and 3/4 Time this when you plug into a calculator, you get 135, yours. Great. Now for our time, we're actually going to be looking for seconds here. So we have five minutes. We're gonna multiply that by 60 seconds per minute and we get a total time of 300 seconds. Easy enough. Now are challenging one here is we have our omega given in revolutions per minute, but we need it in radiance per second. So I'm gonna multiply this well in one minute there is 60 seconds and in one revolution there is too. I radiance these terms cancel out right here. When you plug this into your calculator, you are left with 314 radiance per second. Now that we have all the correct units, let's go ahead and find our torque. Our torque. Sorry here, a little bit of a squiggly on top. Our torque is equal to our work of 135,000 joules divided by our time of 300 seconds. On the bottom here multiplied by 314 radiance per second. Which when you plug into your calculator you get an answer of 1.43 Newton m corresponding. You answer choice. C Thank you guys so much for watching. Hope this video helped. We will see you all in the next one