Pulley Mechanics Maths Alevel Question
I'm stuck on the last part of this question. If anyone could help that would be great, thanks. 😊
Two particles A and B, of masses 5kg and 2kg respectively, are connected by a light inextensible string, which is taut and passes over a smooth fixed pulley. The particles are released from rest.
a) Giving your answers in terms of g, find:
i) the acceleration of the system
ii) the tension in the string.
When A has descended for 2.5 seconds it strikes the ground and immediately comes to rest.
b) Find the speed of A when it hits the ground.
c) Assuming that B does not hit the pulley, find the greatest height that B reaches above its initial position.
I have the correct answers for parts a and b but can't work out part c. The correct answers are:
ai) 3/7g N
aii) 20/7g N
b) 10.5 ms^-1
c) 18.75 m
Two particles A and B, of masses 5kg and 2kg respectively, are connected by a light inextensible string, which is taut and passes over a smooth fixed pulley. The particles are released from rest.
a) Giving your answers in terms of g, find:
i) the acceleration of the system
ii) the tension in the string.
When A has descended for 2.5 seconds it strikes the ground and immediately comes to rest.
b) Find the speed of A when it hits the ground.
c) Assuming that B does not hit the pulley, find the greatest height that B reaches above its initial position.
I have the correct answers for parts a and b but can't work out part c. The correct answers are:
ai) 3/7g N
aii) 20/7g N
b) 10.5 ms^-1
c) 18.75 m
Original post by mqb2766
When A hits the ground, the string will become slack and B's motion will be determined solely by gravity. Can you finish it off?
It says the string is inextensible and taut, surely that means it won't go slack?
Original post by Purplellama25
It says the string is inextensible and taut, surely that means it won't go slack?
When A hits the floor and remains stationary, then B continues moving upwards so the distance between them decreases so the string will become slack as the distance between A and B is less than the string length.
When B returns to this position on the downwards trajectory, then the string would become taut again as the distance between A and B would be equal to the string length.
(edited 3 months ago)
Original post by mqb2766
When A hits the floor and remains stationary, then B continues moving upwards so the distance between them decreases so the string will become slack as the distance between A and B is less than the string length.
When B returns to this position on the downwards trajectory, then the string would become taut again as the distance between A and B would be equal to the string length.
When B returns to this position on the downwards trajectory, then the string would become taut again as the distance between A and B would be equal to the string length.
That makes sense but I think the question is asking for the distance B moves as A is falling towards the floor. So just the distance B moves upwards?
Original post by Purplellama25
That makes sense but I think the question is asking for the distance B moves as A is falling towards the floor. So just the distance B moves upwards?
Its a relatively common question so its worth being clear about it. There are two phases of motion
•
When the sting is taut which is question parts a and b. B moves up during this phase and it corresponds to the amount A moves down. You know the acceleration and the time so its relatively easy to work this out.
•
When A hits the ground and the string becomes slack and B moves up to its maximum height. This is determined by a second suvat phase and there is an initial velocity (part b) and the acceleration is g downwards.
Id get in the habit of sketching the two phases with the appropriate info marked on each sketch.
(edited 3 months ago)
Original post by mqb2766
Its a relatively common question so its worth being clear about it. There are two phases of motion
The total height above the initial position is the sum of these two displacements.
Id get in the habit of sketching the two phases with the appropriate info marked on each sketch.
•
When the sting is taut which is question parts a and b. B moves up during this phase and it corresponds to the amount A moves down. You know the acceleration and the time so its relatively easy to work this out.
•
When A hits the ground and the string becomes slack and B moves up to its maximum height. This is determined by a second suvat phase and there is an initial velocity (part b) and the acceleration is g downwards.
Id get in the habit of sketching the two phases with the appropriate info marked on each sketch.
Ah I understand now, thankyou. I've figured it out: 13.125 for the first phase and 5.625 for the second one. Thanks again 😊👍
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