Round Table Supported by 3 Legs

[Ckrueger11]

Homework Statement

A 36-kg round table is supported by three legs placed equal distances apart on the edge. What minimum mass, placed in the middle between two supports on the table's edge, will cause the table to overturn?

a) 12kg
b) 24kg
c) 36kg
d) 48kg

Homework Equations

Not sure of any equations

The Attempt at a Solution

I attached a diagram I drew, but I don't know how to do any of the calculations

 

[Borek]

I am not sure about math that will be best to solve the question, but first things first - do you know what condition must be fulfilled for the table to overturn?

 

[Ckrueger11]

I don't know the conditions

 

[Borek]

Something about center of mass and base...

 

[rwisz]

.

I would approach this problem by first considering the forces acting on the table and the minimum mass needed to cause it to overturn. We can use the principle of moments to determine the minimum mass required. The principle of moments states that the sum of the moments acting on a body must be equal to zero for it to be in equilibrium.

In this case, the three legs act as supports and create a clockwise moment, while the mass placed in the middle creates an anticlockwise moment. To prevent the table from overturning, the anticlockwise moment must be equal to the clockwise moment.

We can calculate the clockwise moment by multiplying the weight of the table (36kg) by the distance from the center of the table to the leg (half the diameter of the table). This gives us a clockwise moment of 18kg*m.

To calculate the anticlockwise moment, we need to consider the distance between the mass and the point where the table rests on the legs. From the diagram, we can see that this distance is equal to the distance between the two legs on the same side of the table, which is half the circumference of the table. This gives us an anticlockwise moment of 18kg*m.

Therefore, the minimum mass required to cause the table to overturn would be equal to the weight of the table (36kg). Any additional mass placed in the middle would create an anticlockwise moment greater than the clockwise moment, causing the table to overturn.

In conclusion, the correct answer is c) 36kg.