On a part-time job, you are asked to bring a cylindrical iron rod of length 85.8 cm and diameter 2.85 cm from a storage room to a machinist. Will you need a cart? (To answer, calculate the weight of the rod.)

Video transcript

Hey everyone in this problem. We're told that a male worker can safely lift 250 newtons at the workplace. A disc is made of copper and it has a thickness of one centim and a diameter of 58 cm. Were asked whether a single male worker can safely lift the disk alone. All right. So, what we wanna do? Okay, we're kind of giving a hint about this is we want to figure out what is the weight of the disk. OK? If we can find the weight of the disk then we can compare it to this safe limit on lifting of 250 newtons. Okay. And see whether it's bigger than that or less than that. All right. So, if we're looking for the weight, recall that the weight the disk is just gonna be given by the mass times the acceleration due to gravity. Well, we know the acceleration due to gravity, but we aren't told the mask of the mass story of the disc. We're told information with its thickness its diameter. We know what it is made of. Okay, so let's recall that we can relate the mast, the density and the volume. So the density rho is equal to the mass divided by the volume. V. Okay, now, the density. Okay. We know the density of copper. This is a value that we can look up in a table in our textbooks or a table that your professor provides for you. Okay. And that's gonna be 8.96 Times 10 to the three and the unit is kg per meter cubed. So this is going to be equal to the mass m that we're looking to find so that we can calculate the weight divided by the volume. Now we're talking about a disc is when we think of a disk it's gonna be like a really thin cylinder. So the calculation for volume is going to be like calculating the volume for a cylinder. So we have pie R squared times a height. H. Alright now our density has a unit with meters cute. So when we're looking at our radius R and R height H we want these to also be in meters. Okay so we're given centimeters let's go ahead and do some conversions on the right hand side of our page. So the radius R. Okay well this is going to be half the diameter. So we have a diameter of 58 centimeters. Okay, the radius is gonna be half of that. Okay, so this is gonna be 29 cm. And then we want to convert to meters. So we're gonna multiply. Okay, for every one m we have 100 centimeters and so we divide by 100. The unit of centimeter divides out and we're left with 0. m. Similarly for height. Okay we have a height of one centimeter. Okay, the thickness of that disk you can think of as the height of our cylinder and again multiplying by one m per centimeters. Okay so we divide by 100 the unit of centimeter divides out. We're left with 0.1 m. Okay, and that's a typical conversion. Okay, centimeters to meters. You divide by 100. Alright, so getting back to our equation. Okay, we can fill in these values now. So on the left hand side we have 8.96 times 10 to the three kg per meter. Cute. And this is going to be equal to the mass M that we're looking for divided by pi The radius squared. So 0.29 m squared Times The Height. 0.01 m. All right. So if we rearrange, Okay, we multiply up, we do that calculation. The mass m we're gonna find is equal to 0.673 kg approximately. Okay, so our units here we have kilograms per meters cubed on the left. Okay. And then in the denominator on the right, we had meters squared times meter. So we're gonna get meters cubed there. So when we multiply the unit of meters cubed, divides out and we're left with just kilograms. Okay, so our units work out there. Um and that's great now that we have our masks, we can go ahead and find our weight that we're looking for. Okay, so the weight of the disk again is going to be the mass times the acceleration due to gravity. They are mass. We just found to be 23.673 kg in the acceleration due to gravity we know is 9.8 m/s squared. If we multiply these, we're going to get a weight of the disk of 231. newtons approximately. Okay, so this is the weight of the disk. And now the question is, can one single worker lift it safely alone? Okay, well we're told that they can lift 250 newtons safely alone. The weight of the disk. Okay. Which is 231.9954 Newtons is less than 250 newtons. Okay. Which means that one worker will be able to lift this on their own. So we go back up to our answer choices. A single worker will be able to lift the disk alone. Okay? Yes. So we're looking at C. R. D. And then they can lift it alone because it weighs less than that. 250 newtons. Okay, so we have answer choice D. Here. Thanks everyone for watching. I hope this video helped see you in the next one.