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# Connected particles question watch

1. Two particles P and Q of mass 8kg and 2kg respectively, are connected by a light inextensible string. The particles are on a smooth horizontal plane. A horizontal force of magnitude F is applied to P in a direction away from Q and when the string is taut the particles move with acceleration 0.4ms^-2.

a) find the force F.
I've found F it is 4.

b) Find the tension in the string.
I've looked at the answer and get how it is 0.8, but isn't it entirely dependent on how you draw the diagram?
I drew the diagram so that P is behind Q, with T acting in the direction of motion for particle P. However, the answer shows T to be acting in the opposite direction to motion for P.

So my answer would be T-4=8(0.4) which means T would be 7.2N.
2. It doesn't depend how you draw the diagram.

The tension is the only force acting to accelerate the 2nd particle so it's F=ma for that one.

(It's also tthe difference between the force you apply and the F=ma on the 1st one, since in that case it's acting to hold the particle back.)
3. (Original post by dont know it)
Two particles P and Q of mass 8kg and 2kg respectively, are connected by a light inextensible string. The particles are on a smooth horizontal plane. A horizontal force of magnitude F is applied to P in a direction away from Q and when the string is taut the particles move with acceleration 0.4ms^-2.

a) find the force F.
I've found F it is 4.

b) Find the tension in the string.
I've looked at the answer and get how it is 0.8, but isn't it entirely dependent on how you draw the diagram?
I drew the diagram so that P is behind Q, with T acting in the direction of motion for particle P. However, the answer shows T to be acting in the opposite direction to motion for P.

So my answer would be T-4=8(0.4) which means T would be 7.2N.
If a force is applied to P in a direction away from Q then the system must be accelerating in the direction Q -> P. Does this make sense? There are no other external forces so it's impossible for it to be accelerating the other way.

This means that for particle P, the force F must be larger than the tension so you have

F - T = ma
4. Yes, you're pulling P and Q is following along behind.

Your equation is correct - either that or F=ma for Q should give you the same value for T
5. (Original post by phys981)
Yes, you're pulling P and Q is following along behind.

Your equation is correct - either that or F=ma for Q should give you the same value for T
I think my issue is when it says 'P away from Q', what does this mean exactly?
6. You're trying to pull P away from Q, but since they are connected Q comes along behind.
7. (Original post by dont know it)
I think my issue is when it says 'P away from Q', what does this mean exactly?
You can either pull P towards Q or away from Q e.g. if P and Q were like this

P ---------------- Q

Then pulling P away from Q means pulling P to the left since this is away from Q.

Or

Q ---------------- P

Pulling P away from Q would mean pulling P to the right.

If instead you pulled P towards Q then the string would become slack.
8. (Original post by Notnek)
You can either pull P towards Q or away from Q e.g. if P and Q were like this

P ---------------- Q

Then pulling P away from Q means pulling P to the left since this is away from Q.

Or

Q ---------------- P

Pulling P away from Q would mean pulling P to the right.

If instead you pulled P towards Q then the string would become slack.
Can't thank you enough!

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