# M1 Help - Difficult Exam Question

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#1
So the below is a question from the June 2007 Edexcel paper that I have a problem with.The only part I cannot do is the last part but I included the whole question so people can see it in context.
My problem is - how do you know when the string is taut again? I assumed the string would be taut again when Q stopped moving but according to the markscheme that is wrong :3
Two particles P and Q have mass 0.5 kg and m kg respectively, where m < 0.5. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially P is 3.15 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical, as shown in Figure 4. After P has been descending for 1.5 s, it strikes the ground. Particle P reaches the ground before Q has reached the pulley.

(a) Show that the acceleration of P as it descends is 2.8 m s–2.
(3)
(b) Find the tension in the string as P descends.
(3)
(c) Show that m = 5/18.
(4)
(d) State how you have used the information that the string is inextensible.
(1)
When P strikes the ground, P does not rebound and the string becomes slack. Particle Q then moves freely under gravity, without reaching the pulley, until the string becomes taut again.

(e) Find the time between the instant when P strikes the ground and the instant when the string becomes taut again.
(6)
0
7 years ago
#2
(Original post by bethanyyyy)
So the below is a question from the June 2007 Edexcel paper that I have a problem with.The only part I cannot do is the last part but I included the whole question so people can see it in context.
My problem is - how do you know when the string is taut again? I assumed the string would be taut again when Q stopped moving but according to the markscheme that is wrong :3
Two particles P and Q have mass 0.5 kg and m kg respectively, where m < 0.5. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially P is 3.15 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical, as shown in Figure 4. After P has been descending for 1.5 s, it strikes the ground. Particle P reaches the ground before Q has reached the pulley.

(a) Show that the acceleration of P as it descends is 2.8 m s–2.
(3)
(b) Find the tension in the string as P descends.
(3)
(c) Show that m = 5/18.
(4)
(d) State how you have used the information that the string is inextensible.
(1)
When P strikes the ground, P does not rebound and the string becomes slack. Particle Q then moves freely under gravity, without reaching the pulley, until the string becomes taut again.

(e) Find the time between the instant when P strikes the ground and the instant when the string becomes taut again.
(6)
The string goes slack when P hits the ground but Q is still moving upwards. The string will become taut again when Q returns to the point where it was when P hit the ground.
2
#3
Thank you
0
1 month ago
#4
(Original post by brianeverit)
The string goes slack when P hits the ground but Q is still moving upwards. The string will become taut again when Q returns to the point where it was when P hit the ground.
thanks this helps, so P stays on the ground and then the string will be not taut allowing Q to move up and then it will move down like a string when the string becomes taut and the time it goes up is the same as it goes down, my question is why does it act like a string? when its meant to be inextensible
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1 month ago
#5
(Original post by interlanken-fall)
thanks this helps, so P stays on the ground and then the string will be not taut allowing Q to move up and then it will move down like a string when the string becomes taut and the time it goes up is the same as it goes down, my question is why does it act like a string? when its meant to be inextensible
You've quoted someone who hasn't been online for several months from a thread that's 6 years old, so not sure you will get a response from him

What are those bold phrases above supposed to mean? Nothing is "moving like a string" or "acting like a string" - Q moves freely under gravity (first upwards then downwards) when the string is no longer taut, simply because nothing is constraining it do otherwise. Q still has a string attached to it, but the string is initially slack so does not influence the motion (being light).

However, when Q drops back to the point it was at when P hit the ground, then the string is now extended to its full length again (having been pulled by Q) and at this point it must become taut.
1
1 month ago
#6
(Original post by davros)
You've quoted someone who hasn't been online for several months from a thread that's 6 years old, so not sure you will get a response from him

What are those bold phrases above supposed to mean? Nothing is "moving like a string" or "acting like a string" - Q moves freely under gravity (first upwards then downwards) when the string is no longer taut, simply because nothing is constraining it do otherwise. Q still has a string attached to it, but the string is initially slack so does not influence the motion (being light).

However, when Q drops back to the point it was at when P hit the ground, then the string is now extended to its full length again (having been pulled by Q) and at this point it must become taut.
so the string from which Q moves up and down behaves like a spring in a way?, P will be on the floor with a flexible string and so this makes Q move up and down like a string?
0
1 month ago
#7
(Original post by interlanken-fall)
so the string from which Q moves up and down behaves like a spring in a way?,
No.
P will be on the floor with a flexible string and so this makes Q move up and down like a string?
What do you mean by *flexible* here? An inextensible string is "flexible" in the sense that it can bend (i.e. it doesn't have to be in a straight line), so you can have 2 points 1m apart connected by a 3m string, but it doesn't stretch (that's what inextensible means).

For the last part of the problem, the string will have no effect on the motion *until* the point where it goes taut. What happens after that is (in practical terms) problematic, but the question explicitly doesn't ask you about that.
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1 month ago
#8
(Original post by DFranklin)
No.
What do you mean by *flexible* here? An inextensible string is "flexible" in the sense that it can bend (i.e. it doesn't have to be in a straight line), so you can have 2 points 1m apart connected by a 3m string, but it doesn't stretch (that's what inextensible means).

For the last part of the problem, the string will have no effect on the motion *until* the point where it goes taut. What happens after that is (in practical terms) problematic, but the question explicitly doesn't ask you about that.
flexible as in its not tuat anymore, but I'm confused if the string is inextensible meaning it cant stretch, so how can Q move up and down when P hits the ground?
0
1 month ago
#9
(Original post by interlanken-fall)
flexible as in its not tuat anymore, but I'm confused if the string is inextensible meaning it cant stretch, so how can Q move up and down when P hits the ground?
It will move up (initially) when P hits the ground because it's already moving up - it has an upwards vertical velocity at that point.
It will decelerate and move down because gravity is acting on it.
(You basically have a projectile/SUVAT problem until the string goes taut again).
0
1 month ago
#10
are we assuming P remains on the floor so I'm having trouble seeing the string it will have to bend when 1 goes up and then relax when it goes down I thought it was meant to be inextensible
0
1 month ago
#11
(Original post by interlanken-fall)
are we assuming P remains on the floor so I'm having trouble seeing the string it will have to bend when 1 goes up and then relax when it goes down I thought it was meant to be inextensible
As I posted previously:

An inextensible string is "flexible" in the sense that it can bend (i.e. it doesn't have to be in a straight line), so you can have 2 points 1m apart connected by a 3m string, but it doesn't stretch (that's what inextensible means).
0
1 month ago
#12
(Original post by DFranklin)
As I posted previously:

An inextensible string is "flexible" in the sense that it can bend (i.e. it doesn't have to be in a straight line), so you can have 2 points 1m apart connected by a 3m string, but it doesn't stretch (that's what inextensible means).
thank you for you help!!
0
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