The uniform beam shown in the diagram has weight w. The beam...

The uniform beam shown in the diagram has weight w. The beam is pivoted to a vertical wall at one end and supported by a horizontal massless string attached to the beam and the wall as shown in the diagram with ? = 60°. A crate of the same weight w as the beam is hanging at the free end of the beam. The whole system is at equilibrium. (a) Draw the free-body diagram of the beam. Label all relevant lengths and angles. (b) Determine the tension in the cable. (c) Determine the magnitude and direction of the force exerted on the beam at the pivot.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 So the three -belli diagram for this problem is shown here.

00:04 And also for this beam, our beam of free to be l, that would be its whole length.

00:17 Then we can now see that we can define here l.

00:22 Kousine of 60 as this length and l sign of 60 as this length.

00:26 And l sign of 60 as this length as well.

00:34 And for the other part, given that this angle is 60, so in turn this would be 30, which is right angle, right angle here 90 minus 60 equals 30.

00:44 So that means that this lens would be l sine of 30.

00:53 And this, of course, would be l over 2 as the weight of the beam will act in the middle as it was an uniform beam.

01:01 Okay, so now we are good to start solving the problem.

01:05 So this beam is an equilibrium which means that if we take the submission of moments at any point it would be equal to zero.

01:15 So if we consider this point it's called o.

01:18 Submission of moments at o should be equal to zero.

01:20 That means that our weight here, w times l over 2 times the cosine of 30, plus also if you consider the direction of the torque clockwise to be positive.

01:39 And for the other weight it would be w times l cosine of 30.

01:47 And we also have another force here t.

01:50 So it's minus t times this lens, which is l -cousine of 60, has to be equal to zero...

Question

Please give Ace some feedback