A 65.0-kg painter is on a uniform 25-kg scaffold supported from above by ropes (Fig. 9-84). Ther

step 1 So once again, welcome to a new problem. This time we have a painter that's standing on a unifor

A 65.0-kg painter is on a uniform 25-kg scaffold supported...

Key Concepts

Static Equilibrium

This concept involves ensuring that the net force and net moment (torque) on a system are zero, which is necessary for the system to remain at rest. In many physics problems, including those involving loads on beams or scaffolds, setting up equations for force and torque balance is essential to determine how different loads affect stability.

Torque Equilibrium

Torque or moment equilibrium refers to the requirement that the sum of all torques about any pivot point must equal zero for a system in static equilibrium. This idea is used to analyze how weights distributed along a beam or scaffold produce rotating effects, and to find the critical positions where an added weight might tip the balance.

Center of Mass

The center of mass is the weighted average location of mass in a system and is critical in determining how a structure responds to additional loads. By calculating shifts in the center of mass when an extra load is added, one can evaluate how far a person can move before the balance of forces causes instability.

Lever Arms

Lever arms are the perpendicular distances from the pivot or support point to the line of action of the force. They are key in calculating torques since a force’s ability to cause rotation increases with the length of its lever arm. This concept is crucial in determining safe positions for additional loads on extended bodies like scaffolds.

Transcript

00:01 So once again, welcome to a new problem.

00:05 This time we have a painter that's standing on a uniform scaffold.

00:13 So it goes all the way like that.

00:17 And the weight of the scaffold, we're going to call that ms, or rather the mass of the scaffold, is given us 25 kilograms.

00:33 And so, you know, the weight itself is going to be msg, where g is the acceleration due to gravity.

00:43 The other piece of information that's given is that the scaffold itself is being supported by two strings.

00:55 You know, one has a force on the left, and the other one has a force on the right.

01:05 So, fl and frr, they're supporting upwards.

01:11 The distance from the left edge up until the initial string support is 1 meter.

01:20 And there's a paint bucket that's sitting on the support right here.

01:30 And the paint bucket has an effective weight of, we're going to place it right here.

01:39 So the effective weight of the paint bucket is equivalent to, you know, we have to deal with the mass and then the weight.

01:51 So ms, oh, now, mpp is the paint bucket.

01:56 So mp is equivalent to four kilograms.

02:10 So the weight itself is mpg.

02:12 That's the one hanging from right there.

02:16 And then we have also a 65 kilogram painter.

02:23 So in the first case, the painter is going to stand towards the right edge, a specific distance x.

02:38 So it's going to stand on the right edge a distance x.

02:43 So let's just make sure that this distance is clarified.

02:47 So this distance is x.

02:54 And then also the same painter will stand on the left edge.

03:03 And again, you know, similar principles, but this time the distance of the painter from this edge will also be x.

03:12 We have another x from this position right here.

03:18 So these are two axes.

03:22 You know, maybe we could call this x right and this one x left.

03:29 So those are the two different units.

03:32 Also, the distance from the middle of the scaffold up until the right string is equivalent to two meters.

03:45 And then this gap between the paint bucket and the middle of the scaffold is one meter.

03:57 So those are pieces of information that's critical in solving the problem.

04:03 Also, it just happens that this distance from the right scaffold up until the right string is equivalent to 1 meter, or 1 .0 meters.

04:14 So that's the information given.

04:18 The main thing about the question is we want to find if the painter can walk safely on both edges.

04:43 And if not, if not, how close can he approach? the edges safely.

05:09 So that's what we're given.

05:11 We're going to go ahead and use torque.

05:13 The system is assumed to be in equilibrium and therefore the sum of torque around the right string is zero.

05:21 So we're going to have mp, that's the paint bucket mpg times three meters plus msg times 2 meters then minus the other thing is the weight of the painter so we're gonna call that m you know this weight right here i'm gonna call it m okay so then we have m we have m we have m g times x equals to zero so this is clockwise, so it's going to be negative.

06:21 That's why we have negative on the talk.

06:24 The painter, the weight of the painter, this is counterclockwise, so it's positive, and this one two is counterclockwise, so it's positive.

06:32 And this is relative to the right string right here.

06:36 That's where we compute our talk...

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