A fixed rough plane is inclined at 30° to the horizontal - Edexcel - A-Level Maths Mechanics - Question 3 - 2013 - Paper 2
Question 3
A fixed rough plane is inclined at 30° to the horizontal. A small smooth pulley P is fixed at the top of the plane. Two particles A and B, of mass 2 kg and 4 kg resp... show full transcript
Worked Solution & Example Answer:A fixed rough plane is inclined at 30° to the horizontal - Edexcel - A-Level Maths Mechanics - Question 3 - 2013 - Paper 2
Step 1
Find the equation of motion for particle B
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Answer
For the particle B (mass 4 kg), the equation can be expressed as:
4g−T=4a
where g is the acceleration due to gravity, T is the tension in the string, and a is the acceleration of the system.
Step 2
Find the equation of motion for particle A
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Answer
For the particle A (mass 2 kg), the equation considering force resolution would be:
T−F−2gextsin(30°)=2a
Here, F is the frictional force, and the component of weight acting parallel to the plane is calculated as 2gextsin(30°).
Step 3
Resolve the forces acting on particle A
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Answer
The normal force R acting on particle A can be resolved perpendicular to the plane, resulting in:
R=2gextcos(30°)
Given that the coefficient of friction rac{1}{
oot{3}}, we can find the frictional force as:
oot{3}} R = rac{1}{
oot{3}} (2g ext{cos}(30°)) $$
Step 4
Substitute values to find tension T
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Answer
By substituting the equations from the previous steps, we can equate and solve for tension T. The equation simplifies to:
2T - 4g = 2a $$
After deriving the values on both equations, we can isolate T to find:
$$ T = rac{8g}{3} $$
This results in a specific tension immediately after release.
