My Math Forum Stuck with a multi-body problem

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April 9th, 2012, 10:20 AM   #1
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Stuck with a multi-body problem

[attachment=0:1exzofe3]IMG_20120409_111544.jpg[/attachment:1exzofe3]

I don't know why there's 3 different masses on that picture.
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 April 9th, 2012, 12:20 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 461 Math Focus: Calculus/ODEs Re: Stuck with a multi-body problem Let's assume block A has a mass of 6 kg and block B has a mass of 2 kg. Assuming no kinetic friction, the acceleration of the blocks, from Newton's 2nd law of motion is: $a=\frac{45\text{ N}}{(6+2)\text{ kg}}=\frac{45}{8}\:\text{\frac{m}{s^2}}$ Since the blocks are connected, their accelerations must be equal. Therefore, the force F block A must exert on block B is: $F=$$2\text{ kg}$$$$\frac{45}{8}\:\text{\frac{m}{s^2}}$$=\frac{ 45}{4}\:\text{N}=11.25\text{ N}$ A confusing diagram with the wrong result given. That's just wrong! If we average the two masses given for block A, then we get the result shown.
 April 9th, 2012, 01:23 PM #3 Newbie   Joined: Feb 2012 Posts: 22 Thanks: 0 Re: Stuck with a multi-body problem Yep, I had a feeling the answer's wrong. :P
 April 9th, 2012, 01:42 PM #4 Newbie   Joined: Feb 2012 Posts: 22 Thanks: 0 Re: Stuck with a multi-body problem Wait, on the second part, the mass isn't 6 kg? Isn't that block A's mass?
 April 9th, 2012, 01:58 PM #5 Newbie   Joined: Feb 2012 Posts: 22 Thanks: 0 Re: Stuck with a multi-body problem My friend said the total mass of block A is 8 kg.
April 9th, 2012, 03:11 PM   #6
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Re: Stuck with a multi-body problem

Quote:
 Originally Posted by shyronnie Wait, on the second part, the mass isn't 6 kg? Isn't that block A's mass?
We are finding what force must be exerted on block B to make it accelerate 45/8 m/sē. That's why, using F = ma, we use the mass of block B.

If the mass of block A is 8 kg then the force on Block B will be even smaller. It would be (mass of block B)/(mass of block A + mass of block B) * the applied force. If the mass of block A was 4 kg, then the force of block A onto block B would be 15 N.

 April 9th, 2012, 09:24 PM #7 Newbie   Joined: Feb 2012 Posts: 22 Thanks: 0 Re: Stuck with a multi-body problem That image is a really stupid one, in my opinion. My professor himself said that some of the questions in the book are wrong. I'll just think about what you said and what my friend said for now. He said that the 6 kg is like putting another item on top of block A, making the total mass of block A to be 8 kg. Which kinda doesn't make sense, considering that if I follow that logic, then that would mean the two blocks would have the same mass, but block A obviously looks bigger.
 April 9th, 2012, 09:31 PM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 461 Math Focus: Calculus/ODEs Re: Stuck with a multi-body problem Suppose there is a small insect in between the blocks. Would the bug be more likely to survive if force was exerted on the smaller block or on the larger block and why?
April 9th, 2012, 11:31 PM   #9
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Re: Stuck with a multi-body problem

Quote:
 Originally Posted by MarkFL Suppose there is a small insect in between the blocks. Would the bug be more likely to survive if force was exerted on the smaller block or on the larger block and why?
I'd say the larger block, since it would be harder to exert force on the larger block. It's easier to squash the bug with the smaller block.

 April 9th, 2012, 11:38 PM #10 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 461 Math Focus: Calculus/ODEs Re: Stuck with a multi-body problem Yes, since the larger block is 3 times as massive as the smaller block, the contact force would be 3 times as great if the force was exerted on the smaller block.

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