The masses of two children sitting at ends A and B of a...

The masses of two children sitting at ends $A$ and $B$ of a secsaw we 38 kg and 29 kg , respectively. Where should a third child sit so that the resulant of the weights of the three children will pass through $C$ if she has 2 mass of (a) 27 kg , (b) 24 kg .

Key Concepts

Torque

Torque is the tendency of a force to produce rotational motion about an axis or pivot. It is calculated as the product of the force and the perpendicular distance from the pivot to the line of action of the force. In problems involving seesaws or levers, torque helps in understanding how different weights at different distances affect the rotational balance.

Rotational Equilibrium

Rotational equilibrium occurs when the sum of all torques acting on a system about a pivot point is zero, meaning that there is no net rotational motion. This concept is fundamental when balancing objects on a lever, as it allows one to set up equations based on the torques from different forces to find balance conditions.

Lever Principle

The lever principle states that when two forces are applied to a lever, they produce torques that can balance each other if the product of one force and its distance from the pivot equals the product of the other force and its corresponding distance. This principle is essential for understanding how balance is achieved on a seesaw by adjusting the positions of weights.

Center of Mass

The center of mass is the point at which the entire mass of a system can be considered to be concentrated for the purpose of analysis of translational motion. When dealing with multiple weights on a lever, the effective location of the combined weights, or the center of mass, ensures that the overall gravitational force acts through a specific point, influencing the conditions required for equilibrium.

Transcript

00:01 Problem 3.105 in this problem, we have to find that where the third child should sit on the on this she saw so that the resultant of all those all those three forces passes through the point c so apart that let us draw a diagram first for the better understanding.

00:25 So this is the point c and one thing one can note from this diagram that this person a that is sitting at the end of a at the end a is heavier than the person that is sitting at point b.

00:41 So the third person shit at the right of the point c.

00:47 So let us say that the third person as sitting here and this was these two were already sitting.

00:55 So this was a and this was b, and its weight was £84 so it and its weight was £64.

01:05 So foreign first case, the weight of the person is £60.

01:10 So it's we did £60 since this way, these are the weights, so they will act vertically downward.

01:20 So let us say that this distance, uh, of the person see person that is sitting here from the point c is at a distance of a and this distance is concerned in the problem at 6 ft and this distance is mentioned the same, that is 6 ft.

01:46 So now we can apply the momentum balance, uh, momentum balance about the point c since the resultant forces passing through the point see, it means that there is no moment about point c so we can apply the moment of balance about point c in this case.

02:06 So if we write the moments about point c so this, uh, this, uh, the person sitting at the end a is going to cause a counter clockwise couple, so it will be positive.

02:18 So it will be 84 times 84 multiplied by six.

02:24 This £60 force is going to cause clockwise couple, so it will be minus 16 multiplied by e.

02:33 And this, uh, £64 person is again going to cause a clockwise couple...

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