WEBVTT 00:00:00.047 --> 00:00:02.757 This is College Physics Answers with Shaun Dychko. 00:00:03.211 --> 00:00:06.350 We have a free body diagram of the cart being pushed by the nurse. 00:00:06.655 --> 00:00:12.031 It consists of an applied force at an angle of 35 degrees below the horizontal 00:00:12.648 --> 00:00:15.897 and has friction force going straight back 60 newtons. 00:00:16.297 --> 00:00:19.867 There’s a normal force going straight up and gravity going down. 00:00:20.992 --> 00:00:24.514 The mass of the cart is 28 kilograms and its acceleration is zero 00:00:24.539 --> 00:00:27.194 because we’re told that it’s going to be pushed at constant speed. 00:00:28.109 --> 00:00:30.686 So the net force in the x direction 00:00:30.813 --> 00:00:34.218 is the x component of this applied force minus the friction 00:00:34.391 --> 00:00:36.241 and that’s going to be mass times acceleration 00:00:36.508 --> 00:00:39.421 but we know that acceleration is zero so we replace that with a zero 00:00:39.446 --> 00:00:40.515 on the right side. 00:00:40.633 --> 00:00:44.858 On the left side, we’ll replace Fax with the applied force times cos theta 00:00:45.320 --> 00:00:50.819 because Fax is the adjacent leg of this triangle here. 00:00:56.380 --> 00:00:58.801 Ultimately we’re trying to find out what is this applied force 00:00:58.826 --> 00:01:00.512 needed to move at constant speed. 00:01:01.086 --> 00:01:04.762 So we’ll add friction to both sides 00:01:06.742 --> 00:01:08.660 and then divide both sides by cos theta, 00:01:08.852 --> 00:01:11.582 and we get the applied force is friction divided by cos theta, 00:01:11.726 --> 00:01:14.402 so that’s 60 newtons divided by cos 35 00:01:14.484 --> 00:01:16.594 which is 73.2 newtons.