M1 Mechanics Help: Solve "P" Hitting Floor After String Breaks

[Darren]

Hi all, i have been really stuck with this question for hours now,


Two particles "P" and "Q" of masses 1Kg and 2Kg respectively are hanging vertically from the ends of a light inextensible string which passes over a smooth fixed pulley. The system is released from rest with both particles a distance of 1.5m above a floor. When the masses have been moving for 0.5s the string breaks.

Find the futher time that elapses before "P" hits the floor.


This has just got me totally confused, and to be honest i have no idea how to start, i have the picture drawn but am looking at it blankly. Any help is much appreciated.

Daz.

 

[Norman]

So you will need to find the distance P moves in 0.5s and its velocity at that point. Then when the string breaks, your velocity at the point becomes your initial velocity at a height 1.5 + D, where
D is the distance that P moved in the first part. P is now only subjected to the acceleration due to gravity and it is a simple kinematics problem.
Good luck,
Norm

 

[M98Ranger]

Hi Daz,

I can understand your confusion with this question. Let's break it down step by step to make it easier to understand.

First, we know that the system is released from rest, which means that both particles are initially at rest and have no velocity. The string breaks after 0.5 seconds, so we need to find the time it takes for particle P to hit the floor after the string breaks.

To solve this, we need to use the equations of motion for both particles. For particle P, we have the equation s = ut + 1/2at^2, where s is the displacement, u is the initial velocity (which is 0 since it was initially at rest), a is the acceleration (which is due to gravity and is equal to 9.8 m/s^2), and t is the time. We also know that the displacement s = 1.5m, since both particles were initially 1.5m above the floor.

For particle Q, we have the same equation, but with a different displacement (since it is 3m above the floor) and a different mass (2kg). However, since the string breaks, particle Q will continue to move downwards with a constant velocity of 9.8 m/s^2.

Now, to find the time it takes for particle P to hit the floor, we can equate the two equations for s and solve for t. This will give us the time it takes for particle Q to reach the floor, which is also the time it takes for particle P to reach the floor after the string breaks.

I hope this explanation helps you understand the problem better. If you need any further clarification, don't hesitate to ask. Best of luck with your studies!