Max Distance: Find Center of Box from Table End

[Dark Visitor]

I am unsure of how to go about this problem. So if anyone could help me by going step by step through it, showing all equations and numbers used, and then showing me the answers so I can make sure I get the same thing, I would appreciate it.


A thin 2.50 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?

http://session.masteringphysics.com/problemAsset/1013745/6/jfk.Figure.P08.13.jpg

 

[Andrew Mason]

I am unsure of how to go about this problem. So if anyone could help me by going step by step through it, showing all equations and numbers used, and then showing me the answers so I can make sure I get the same thing, I would appreciate it.


A thin 2.50 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?

http://session.masteringphysics.com/problemAsset/1013745/6/jfk.Figure.P08.13.jpg

Think of this as two masses the block and the centre of mass of the board applying torque about the fulcrum. What is the condition for tilting? (hint: it has to do with torque about the fulcrum).

AM

 

[Dark Visitor]

I am not sure what you mean by fulcrum. I don't think I have ever heard that word before. Sorry. Can you explain it please?

 

[chemtopper]

What he means by the fulcrum is the point of balance- Imagine a see-saw. The centre is the fulcrum.
Here the fulcrum is the edge of the table.
Since the block is 30 cm on the table and 20 cm outside it, you can take the downward force acting on the left hand side as 3/5 x 7 = 4.2 kg. This acts at the CG which is 15 cm away.
Hence moments on the left side = 4.2 x .15 = 0.63 kg-m.
Similarly moment on the right side = (2/5 x 7) x .1 = 0.28.
To this is added the moment due to the box with a weight of 2.5 kg at a dist of let's say S metres.
So moment on rt side = 0.28 + 2.5 x S.
when it is just about to fall,
0.63 = 0.28 + 2.5 x S.
Find out the value of S.

 

[Dark Visitor]

I got it to be .14 m, which turned out to be the right answer. Thanks a lot. You're explanation helped me understand what I was missing. I guess I was going about it all wrong.