How far can the box be before it begins to tilt?

Question

A thin 3.00 kg box rests on a 7.00 kg board that hangs over the end of a table, as shown in the figure.

How far can the center of the box be from the end of the table before the board begins to tilt?

Answer 1

You want the center of gravity of the system to be at the edge of the table, also consider it to be your reference point.

Let the length at which the box can be placed be x,

So Equating weights to the right and left of that point,

Center of gravity of board + center of gravity of box = 0

7*(-5)+3*x = 0. Solve for x.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.

SHOW ANSWER

Answer 2

Let the box is a meter from the end of the table, Thus balancing the forces at the edge:-

=>[(7/0.50) x 0.3] x 0.15 = [(7/0.50) x 0.20] x 0.10 + 3 x a

=>0.63 = 0.28 + 3a

=>3a = 0.35

=>a = 0.35/3 = 0.1167m = 11.67cm

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.

SHOW ANSWER