WEBVTT 00:00:00.000 --> 00:00:03.240 This is College Physics Answers with Shaun Dychko. 00:00:03.420 --> 00:00:06.860 This pulley system is a hoist for a car engine 00:00:06.860 --> 00:00:09.380 that has a mass of 115 kilograms 00:00:09.660 --> 00:00:12.720 and we can see that the mechanical advantage is 2 00:00:12.800 --> 00:00:16.580 because the tension force that's being applied here 00:00:16.580 --> 00:00:22.040 is being exerted twice upwards on this engine 00:00:22.320 --> 00:00:27.160 and so there's one tension applied and that's 00:00:27.220 --> 00:00:29.940 being multiplied by 2 in the end 00:00:29.940 --> 00:00:32.540 and so that's where the mechanical advantage comes from. 00:00:32.940 --> 00:00:33.920 Okay! 00:00:34.000 --> 00:00:36.080 So mechanical advantage is defined as 00:00:36.080 --> 00:00:38.740 the output force divided by the input force 00:00:38.780 --> 00:00:41.600 and the input force is the tension in the rope 00:00:41.820 --> 00:00:48.560 and the output force is the total force on this bottom pulley 00:00:48.620 --> 00:00:49.980 so this is the output force 00:00:49.980 --> 00:00:52.420 and that's gonna be equal to the weight of the engine. 00:00:52.800 --> 00:00:55.380 So we substitute mg in place of F o 00:00:55.380 --> 00:00:57.760 and T in place of F i 00:00:57.760 --> 00:00:59.500 and then our job is to solve for T; 00:00:59.500 --> 00:01:01.100 we want to know the tension in the rope. 00:01:01.160 --> 00:01:05.280 So we multiply both sides by T over mechanical advantage 00:01:06.660 --> 00:01:09.340 so T is mg over MA. 00:01:09.440 --> 00:01:12.480 So that's 115 kilograms times 9.80 newtons per kilogram 00:01:12.480 --> 00:01:15.920 divided by 2 which is 564 newtons. 00:01:16.680 --> 00:01:19.260 In part (b), we are asked, what is the force 00:01:19.260 --> 00:01:23.080 applied by the ceiling upwards on this whole assembly? 00:01:23.320 --> 00:01:29.480 We can see that there's one force upwards in total on this assembly 00:01:29.540 --> 00:01:31.860 and there are two forces downwards: 00:01:31.860 --> 00:01:34.820 there's gravity downwards on the engine 00:01:34.820 --> 00:01:39.500 and then there's this applied force... this tension downwards as well 00:01:39.720 --> 00:01:41.860 and so those two are added together down 00:01:41.860 --> 00:01:45.480 and they have to together equal the force upwards on the ceiling. 00:01:45.680 --> 00:01:48.660 So that's 563.5 newtons—tension— 00:01:48.660 --> 00:01:52.200 plus 115 kilograms times 9.8 newtons per kilogram 00:01:52.260 --> 00:01:56.580 which is 1690 newtons in total exerted by the ceiling upwards 00:01:56.580 --> 00:01:58.440 on the whole assembly.