Crane. A 15,000 N crane pivots around a friction-free axle...

Crane. A 15,000 N crane pivots around a friction-free axle at its base and is supported by a cable making a 25° angle with the crane. The crane is 16 m long and is not uniform, its center of gravity being 7.0 m from the axle as measured along the crane. The cable is attached 3.0 m from the upper end of the crane. The crane is raised to 55° above the horizontal holding an 11,000 N pallet of bricks by a 2.2 m cord (whose mass is negligible). Find the tension in the cable as well as the horizontal and vertical components of the force that the axle exerts on the crane.

Transcript

00:01 Okay, we have a crane that weighs 1 ,500 newtons.

00:06 And there's a cable, 25 degree angle with the crane, 16 meters long, center of gravity is 8 meters from the axle.

00:16 And then it's holding a ton of, or a 1 ,100 newton pallet of bricks by this cord.

00:23 Find the tension in the cable and the horizontal and vertical components of force from the axle.

00:29 So, let's draw this here.

00:38 So there's the ground.

00:46 Okay, we're going 55 degrees here.

00:55 Okay, and then there's your cable.

00:58 That's 25 degrees from that.

01:02 So 55 minus 25, so 30 degrees here.

01:19 I'll just draw the forces here.

01:23 So that's tension from the cable.

01:27 Then we have the other cable tension, which is just due to the weight of the bricks, right? we could solve that really easily.

01:33 We'll just skip that step.

01:36 Then we have the weight of the crane itself, which acts at its center of mass, which is 7 meters from the axle.

01:47 We'll call the weight of the crane just w.

01:54 And then we have some reaction from the axle.

01:59 Y, and some reaction from the axle x.

02:04 Okay, let's put these angles on here.

02:06 So, 55 degrees, that makes this a 35 degree angle, makes this a 35 degree angle, this is 25 degrees, okay, and initially we're gonna do, we're gonna look at torque, okay, because we wanna solve for tension, and we don't know rx and r, so torque is our best best place to start.

02:39 So the sum of the torques, the moments, whatever you want to call them, equals zero.

02:45 Let's sum about, you put a big green blob there.

02:51 We're going to sum about that axle there, okay? we're going to say this direction is positive.

02:58 Okay.

03:01 I'm going to put some measurements on here.

03:03 So it's 16 meters long...