Mechanics - Connected particles problem

Skelly4444

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Apr 4, 2019
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I have 2 masses of 6kg and 4kg connected by a light inextensible coupling and sliding along a rough horizontal surface, being towed by a force of 40N. The masses are experiencing resistances to motion of 10N and 5N respectively. The towing force is then suddenly removed when the rope breaks. Calculate the new force in the coupling and state whether the system is in tension or compression.

When I set up my equations for the individual masses, I end up with differing values for T. I don't believe that this can be possible and I can't see where I'm going wrong. I have calculated the deceleration of the system to be -1.5ms-2.

Could someone please point me in the right direction for this problem, any advice would be greatly appreciated.
 
The 6 kg object was experiencing a net 40- 10= 30 N force so has acceleration 30/6= 5 m/s^2. The 4 kg object was experiencing a net 40- 5= 35N force so an acceleration of 35/4= 8.75 m/s^2. Those are different so that the coupling will quickly become taut. The tension in the coupling is 35- 20= 5 N.

While the coupling is taut we can treat the system as a single object of mass 10 kg. There is a towing force of 40N and total resistance of 15N so a net force of 40- 15= 25 N. That will result in an acceleration of 25/10= 2.5 m/s^2.

After the tow rope breaks, not the coupling, the 6 kg object experiences a retarding force of 10N so decelerates at 10/6= 5/3 m/s^3 and the 4 kg object experiences a retarding force of 5N so has acceleration 5/4= 1.25 m/s^2. Again those are different so the coupling will remain taut and and the tension will be 10- 5= 5N.
 
Thanks for your reply but I'm even more confused now.
When the rope breaks, surely the coupling goes into compression, not tension.
When calculating the individual decelerations of the particles, how can we just ignore the T force in the coupling?
We are required to calculate the new force in the coupling once the rope breaks, so how do we go about that?
If the particles decelerate at different rates as you suggest, no value of T appears to work correctly for the coupling calculation.
Please could you clarify why we ignore the T force when calculating the decelerations and why you have not made them both negative to indicate that they are indeed decelerations?
Many thanks in anticipation.
 
Did you give the entire problem? You say there is "a light inextensible coupling" and then talk about the "rope" breaking. Is that "light inextensible coupling" the rope? If so, after the rope breaks there is no coupling, to be in "compression" or "extension", at all! If there is some other "coupling" please tell us about it.
 
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