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M1 Statics: The difference between finding a force (P) and the maximum value

In questions when they ask you to find the maximum value of a vertical force on a slope (e.g. P- Psinx), how is that any different to finding the value of a force normally (Psinx)?
Original post by creativebuzz
In questions when they ask you to find the maximum value of a vertical force on a slope (e.g. P- Psinx), how is that any different to finding the value of a force normally (Psinx)?


The maximum force that can be applied which will keep the system in equilibrium, or keep the system in the same state.
Original post by lizard54142
The maximum force that can be applied which will keep the system in equilibrium, or keep the system in the same state.


Oh right, okay! Why is that true though?
Original post by creativebuzz
Oh right, okay! Why is that true though?


Consider a plank lying on an inclined plane, with a rope attached at one end. If the rope is in tension, you want to find the maximum value of this tension which doesn't lift the plank up; so if the tension was increased by even a small amount, say 0.1N, then the plank would be raised. It's basically the "tipping point" if that makes sense, where any extra force would cause the system to change and not be in equilibrium anymore. This is why they say maximum force.
Original post by lizard54142
Consider a plank lying on an inclined plane, with a rope attached at one end. If the rope is in tension, you want to find the maximum value of this tension which doesn't lift the plank up; so if the tension was increased by even a small amount, say 0.1N, then the plank would be raised. It's basically the "tipping point" if that makes sense, where any extra force would cause the system to change and not be in equilibrium anymore. This is why they say maximum force.



But I thought that, e.g. if the force P was pulling the particle up, then the maximum force would be when the particle is being pulled up. Because that's the largest P would ever be? If the particle stayed at one point then the force P would not be at its highest!
Original post by creativebuzz
But I thought that, e.g. if the force P was pulling the particle up, then the maximum force would be when the particle is being pulled up. Because that's the largest P would ever be? If the particle stayed at one point then the force P would not be at its highest!


The key point is equilibrium. The force isn't pulling the particle up, it is about to, given any increase in force; you want the system to remain in equilibrium. If you didn't care about equilibrium, then you could have an infinitely large force (in theory).
Original post by lizard54142
The key point is equilibrium. The force isn't pulling the particle up, it is about to, given any increase in force; you want the system to remain in equilibrium. If you didn't care about equilibrium, then you could have an infinitely large force (in theory).


Ah that makes sense!

So, mathematically, if the situation was still in equilibrium and we have Pcos30 - 15N=0 etc, then the method of finding the unknown force (P) is technically the same as finding the maximum force?
Original post by creativebuzz
Ah that makes sense!

So, mathematically, if the situation was still in equilibrium and we have Pcos30 - 15N=0 etc, then the method of finding the unknown force (P) is technically the same as finding the maximum force?


Yes.

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