- #1
Theodore Hodson
- 24
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Homework Statement
The diagram shows a particle P lying in contact with a smooth table top 1.5m above the floor. A light inextensible string of length 1m connects P to another particle Q hanging freely over a small smooth pulley at the edge of the table. The mass of each particle is 2 kg, and P is held at a point distant 0.5m from the edge of the table. When the system is released from rest find:
a) the speed of each particle when P reaches the edge of the table
b) the tension in the string
If P slips over the pulley without any change in its speed, find, for the subsequent motion:
c) the acceleration of the system
d) the tension in the string
Give the answers in terms of g.
2. Homework Equations
The Attempt at a Solution
Okay so I managed to figure out the first two parts of the problem. Using ##T## for tension and ##a## for acceleration and then setting up these simultaneous equations
##T-2a=0##
##2g-T=2a##
helped me get ##a=\frac{g}{2}## From here, finding the tension and speed was pretty straightforward (i.e rearranging for ##T## and using ##v^2-u^2=2as## for ##s=0.5## to get the speed)
so answer to part a) is ##\frac{\sqrt{g}}{\sqrt{2}}## and part b) is ##g## N.
Parts c) and d) of the problem are puzzling me though. "P slips over the pulley without any change in its speed" - Basically I'm getting confused about what's going on here visually and which bits of information I need to connect together. So is it saying that P is now falling downwards with the same speed as it had when it was at the edge of the table? But then I'm not sure how this can help me find the new tension/acceleration.
Would be very grateful for any hints here.