(II) How close to the edge of the 24.0-kg table shown in Fig. 9-54 can a 66.0-kg person sit with

step 1 So once again, welcome to a new problem. This time we have a table edge that's extending a dista

(II) How close to the edge of the 24.0-kg table shown in...

Key Concepts

Torque

Torque is a measure of the rotational effect of a force applied at a distance from a pivot point. It is calculated as the product of the force magnitude and the perpendicular distance (moment arm) from the line of action of the force to the pivot. In equilibrium problems, comparing the torques produced by different forces helps determine whether an object will rotate or tip.

Rotational Equilibrium

Rotational equilibrium occurs when the sum of the clockwise torques equals the sum of the counterclockwise torques around a chosen pivot point, resulting in no net angular motion. This principle is essential in stability analyses, such as determining how close a person can sit to the edge of a table without causing it to tip.

Center of Mass

The center of mass represents the average position of an object’s mass distribution. In problems involving stability, the location of the center of mass is crucial because it influences how gravitational forces produce torques about a pivot. When additional weight is added to a system, the combined center of mass must be considered to ensure that the system remains balanced.

Moment Arm

A moment arm is the perpendicular distance from the pivot point to the line along which a force acts. It determines how effectively a force can produce a torque. In balancing problems, adjusting the moment arm by shifting the point of force application can significantly affect whether the net torque will cause an object to tip or remain in equilibrium.

Transcript

00:02 So once again, welcome to a new problem.

00:05 This time we have a table edge that's extending a distance of 2 .2 meters.

00:14 So this is a table and it stretches from the left edge up until the right edge, a distance of 2 .20 meters.

00:26 And then also it's supported by two legs, 1 .2 meters.

00:33 Apart the you know the distance between the left leg and the right one happens to be 1 .2 meters so that just means that the weight of the table which is acting right in the middle is mg i'm just going to call it you know like mtg i'm gonna call it mtg i'm gonna call it mtg mass of table times g the distance between the center of gravity of the table up until the right leg would be half of 1 .2 which is 0 .6 meters and then also another piece of information that's given is the fact that from the right leg up until the edge of the table we have a distance of 0 .6 meters.

01:42 We have a distance of 0 .5 .5.

01:43 0 .5 meters.

01:48 The question, so this is the information that's given, the question for this problem is, if we have a person standing right here at this side of the table, we don't know what the distance is from the right leg of the table.

02:13 We're going to call that d, you know, that's their distance.

02:20 Oh let's just call it x the distance from the right leg of the table and we want to find out oh let's call that x1 and and then the distance their distance from the edge of the table let's call that x2 so we know that x1 plus x2 is equivalent to 0 .50 meters but we don't know what x1 is we can always find that the system is in equilibrium so we can get the torque, the sum of forces and the sum of talks around the right leg or right support.

03:10 So from this point, the sum of talks will be zero.

03:18 We're also given some other piece of information that was given was the fact that the weight or the mass of the table m .t.

03:28 Equals to 60 or 24 kilograms.

03:36 That's a piece of information that's given and another piece of information is that the mass of the person, we need to write this out, the mass of the table empty.

03:50 So, mt.

04:02 M .t equals to 24 kilograms and then the mass of the person, mp, equals to 66 kilograms.

04:17 That's the information that's given.

04:19 Some of the talks around this point is zero.

04:25 The person has their weight pointing downwards.

04:32 And that's mpg.

04:35 Just like the weight of the table is pointing downwards...

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