2. A uniform beam of mass M = 9.50 kg and length L = 15.0 m...

2. A uniform beam of mass M = 9.50 kg and length L = 15.0 m is resting on the point of a fulcrum support as shown. The fulcrum support point is situated a distance d = 5.00 m from the left end of the beam. Mass m1 is attached to the beam a distance x1 = 3.00 m to the left of the fulcrum support point. Mass m2 = 7.00 kg is attached to the beam a distance x2 = 7.00 m to the right of the fulcrum support point. a) Show all the forces acting on the beam above in an extended FBD for the beam. Recall that you can model the beam as a point particle located at its center of mass. b) Determine the magnitude of mass m1 that will keep the beam in static equilibrium. c) Determine the magnitude of the normal force of the fulcrum support point on the beam.

Transcript

00:01 So in this problem we need to start with our free body diagram of the beam.

00:05 And so we have the two masses which are going to cause some weight, effect as a weight acting on the beam.

00:13 M1, which we don't know, and m2, which is 7 kilograms.

00:22 Now there's going to be a force from the fulcrum.

00:25 Now obviously this is going to be upwards because the fulcrum needs to hold the beam up, otherwise the weight would just cause it to fall down forever.

00:32 The whole beam is 15 meters long.

00:41 Now the beam also has a weight of 9 .5 kilograms, so to the force multiplied by the acceleration to gravity g.

00:56 And these are also going to be m1g and m2g to be the forces.

00:59 Now the weight, if this is a uniform beam, we model to act on the center 7 .5 meters from the end.

01:09 Now for the dimensions that we're told, the fulcrum is 5 meters, which means this distance here 2 .5 meters.

01:17 And we're going to need that a bit later.

01:22 And the distances between the two masses are 3 meters and 7 meters to the fulcrum, respectively.

01:36 So let's pick an axis, and i picked my axis to be the fulcrum.

01:40 Pretty convenient place, we can get rid of the unknown end and get our one unknown m1 right away.

01:48 So that is pretty helpful.

01:51 So that is our free body diagram.

01:53 Now we want to look at b to find the mass 1 to hold the beam in equilibrium.

01:59 Well, the mass 1 is going to affect whether the beam rotates.

02:03 So we're going to look at sum of moments equal to 0 to be in equilibrium.

02:08 Counterclockwise positive by convention.

02:11 Now a moment is a force times a distance, and depending on the direction.

02:15 So m1 we see is a positive moment...

Question

Please give Ace some feedback