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Two particles A and B, of mass m and 2m respectively, are attached to the ends of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 7 - 2008 - Paper 1
Question 7
Two particles A and B, of mass m and 2m respectively, are attached to the ends of a light inextensible string. The particle A lies on a rough horizontal table. The s... show full transcript
Worked Solution & Example Answer:Two particles A and B, of mass m and 2m respectively, are attached to the ends of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 7 - 2008 - Paper 1
Step 1
a) find the tension in the string immediately after the particles begin to move
Answer
For particle B, we have the equation of motion:
[ 2mg - T = 2m g - 2m a ]
Since the acceleration is given by ( a = g - \frac{2}{3} \mu g ), we can substitute it in:
[ 2mg - T = 2mg - 2m \left( g - \frac{2}{3} \mu g \right) ]
Simplifying, we find that the tension ( T ) in the string is:
[ T = 10mg ]
Thus, the tension in the string is ( T = 10mg ).
Step 2
Step 3
c) Find the speed of A as it reaches P
Answer
When B hits the ground, A will have fallen a distance ( \frac{1}{3} h ). Using the energy principles, the velocity of A as it reaches P is given by:
[ v^2 = u^2 + 2as ]
where ( u = 0 ) and ( a = \frac{2}{3} g ) and ( s = \frac{1}{3}h ):
[ v^2 = 0 + 2 \cdot \frac{2}{3}g \cdot \frac{1}{3}h ]
Thus, we find that:
[ v = \sqrt{\frac{4gh}{9}} = \frac{2}{3} \sqrt{gh} ].
Step 4
d) State how you have used the information that the string is light.
Answer
The information that the string is light implies that it has negligible mass and does not affect the tension in the system. Therefore, the tension remains constant throughout, allowing us to treat the forces acting on each particle separately without considering the weight of the string itself.