How to figure out when a table will tip over

[ssnapier]

Homework Statement

How Close to the edge of a 20kg table, can a 66kg person sit without tipping it over?
The table is 2.2m long and there are two legs placed 0.5 m from each end of the table with 1.2 meters between the two legs and the top of the table is 0.80 m tall

Homework Equations

I am totally at a loss here, do I use r/R=Fd/gravity?

The Attempt at a Solution

 

[davo789]

The question you need to ask is why does the table tip up at all?

 

[ssnapier]

It tips because the guy sits on the edge and disturbs the balance (changes the center of gravity). I still have no idea how what equation I should be using.

 

[davo789]

The table is symmetric, and you can assume that its mass acts from the centre of the tabletop. If you draw yourself a diagram you should see what's going on. Let me know if you don't!

 

[rwisz]

As a scientist, the first step in solving this problem would be to gather all the necessary information and variables. In this case, we have a 20kg table, a 66kg person, and specific measurements for the table's dimensions and leg placement.

Next, we can use the equation for torque, which is force multiplied by the distance from the pivot point. In this case, the pivot point would be the edge of the table where the person is sitting. So, we can set up the equation as follows:

Torque = Force x Distance

We know that the force acting on the table is the weight of the person, which is 66kg multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, the force would be 647.28 N.

Now, we need to determine the distance from the edge of the table where the person is sitting to the pivot point. This can be calculated by subtracting the distance of the table's leg placement (0.5m) from the total length of the table (2.2m). This gives us a distance of 1.7m.

Plugging in these values into the equation, we get:

Torque = 647.28 N x 1.7m = 1100.736 Nm

We can compare this torque value to the torque that the table can withstand before tipping over. This can be calculated by using the equation for torque again, but this time with the force being the weight of the table itself (20kg x 9.8 m/s^2) and the distance being the height of the table (0.8m). This gives us a torque value of 156.8 Nm.

Since the torque exerted by the person sitting on the edge of the table (1100.736 Nm) is greater than the torque the table can withstand (156.8 Nm), the table will tip over. Therefore, the person sitting on the edge of the table will need to sit closer to the center in order to prevent it from tipping over.

In conclusion, by using the equation for torque and comparing the values, we can determine the maximum distance from the edge of the table that a person can sit without tipping it over.