Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

pulley

Two particles P and Q, of mass 3kg and 2kg respectively, are connected by a light inextensible string. Initally P is held at rest on a smooth fixed plane inclined at 30° to the horizontal. The string passes over a small smooth light pulley A fixed at the top of the plane. The part of the string from P to A is parallel to a line of greatest slope of the plane. The particle Q hangs freely below A. The system is released from rest with the string taut.

On release, Q is at height of 0.8m above the ground. When Q reaches the ground, it is brought to rest immediately by the impact with the ground and does not rebound. The initial distance of P from A is such that in the subsequent motion P does not reach A.

Find the time between the instant when Q reaches the ground and the instant when the string becomes taut again.

Sorry about the length...I just want to check my answer for this. I get 1.62 seconds...but it is very likely that I have made a mistake somewhere.

Thanks

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: pulley

Let the acceleration be a and the tension in the string T.

Considering the forces on P along the line of greatest slope:

And the forces on Q:

Now solve the two simultaneous equations for a and then use the equation of motion

And I got

.

Last edited by JaneFairfax (2007-11-28 06:35:40)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: pulley

on P:

on Q:

adding them together:

constant acceleration formula

taking g as 9.81

Last edited by luca-deltodesco (2007-11-28 07:45:59)

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Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: pulley

Hmm.. isn't 1.28s the time it takes for Q to hit the ground?

I worked out the velocity of Q when it hit the ground, and said it would be the same as the velocity of P the moment the string stops being taut. Then I found how long it would take for P to continue moving up the slope until it came to a stop, and doubled it to get how long it would take to get back to the point where the string was taut. :S

Edit: Why does it say I started this thread yesterday...?

Last edited by Daniel123 (2007-11-28 10:16:09)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: pulley

ah right, i didnt read the question properly. Well then what you would have is

forces acting on P are its weight and normal contact force, acceleration down slope is then

so total time, is t + 2t[sub]2[/sub]

taking g = 9.81

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The Beginning Of All Things To End.
The End Of All Things To Come.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: pulley

Ok.. I see where I made the mistake.

Thanks!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: pulley

Looks like I'm too late to answer the pulley question, but:

Why does it say I started this thread yesterday...?

I'd guess that's because your time settings are messed up. The forum puts the clock an hour forward when it should put it an hour back, so it's possibly displaying all times 2 hours later than they should be. Thus, it currently thinks that it's now tomorrow and hence that you posted yesterday.

You can fix this in your profile.

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Why did the vector cross the road?
It wanted to be normal.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: pulley

i had a quesiton similar to this in my Mech1 last january, except the slope was down not up (same situation basicly) the slope was not frictionless, and you were told to model it with a constant frictional force.

i.e. when Q  hit the ground, tension went to 0, you then had to calculate how much further P would travel before stopping due to friction, except ofcourse in the calculation you would see the particle slowing down due to friction on slope, and then reversing in direction because the friction is modelled as being constant i got 100% on that paper though, so i must have interpreted it correctly.

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The Beginning Of All Things To End.
The End Of All Things To Come.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: pulley

I've got my M1 this january... and if I can avoid making my usual silly mistakes I should be aiming for 100% as well. Where I went wrong in the above question was typing it into my calculator at the end... which is very annoying.. but at least its better than not being able to do the question.

And thanks mathsy.. I've fixed it now .

Last edited by Daniel123 (2007-11-29 09:10:40)