A box of mass 1.5 kg is placed on a plane which is inclined at an angle of 30° to the horizontal - Edexcel - A-Level Maths: Mechanics - Question 5 - 2003 - Paper 1
Question 5
A box of mass 1.5 kg is placed on a plane which is inclined at an angle of 30° to the horizontal. The coefficient of friction between the box and plane is \( \frac{1... show full transcript
Worked Solution & Example Answer:A box of mass 1.5 kg is placed on a plane which is inclined at an angle of 30° to the horizontal - Edexcel - A-Level Maths: Mechanics - Question 5 - 2003 - Paper 1
Step 1
R(7): Find the normal reaction force R
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Answer
Using the resolving forces vertically, we have:
[ T \cos(20°) = F + 1.5g \sin(30°) ]
Where ( F ) is the frictional force.
Step 2
R(K): Find the horizontal component
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Answer
In the horizontal direction, the equation is:
[ T \sin(20°) + R = 1.5g \cos(30°) ]
Where ( g ) is the acceleration due to gravity, approximately ( 9.81 , \text{m/s}^2 ).
Step 3
Using F = \frac{1}{5}R: Relate the frictional force
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Answer
From the coefficient of friction, we know:
[ F = \frac{1}{5}R ]
Step 4
Eliminating R: Solve for T
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Answer
Substituting ( F ) into the equations to eliminate R, we can find ( T ). This results in:
