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
Establish the Forces Acting on the Box
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Answer
Identify the forces acting on the box:
Gravitational force acting downward, ( 1.5g ), where ( g \approx 9.81 , \text{m/s}^2 ).
Normal force ( R ) perpendicular to the inclined plane.
Tension ( T ) along the string at an angle of 20°.
Step 2
Resolve Forces Along the Plane
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Answer
For equilibrium along the plane (using components):
[ T \cos(20°) = F + 1.5g \sin(30°) ]
where ( F = \frac{1}{5} R ).
Step 3
Resolve Forces Perpendicular to the Plane
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Answer
For equilibrium perpendicular to the plane:
[ T \sin(20°) + R = 1.5g \cos(30°) ]
This sets the condition for normal force balance.
Step 4
Eliminate R and Solve for T
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Answer
Substitute ( R ) from the force equations:
[ R = \frac{5}{1} \left(T \cos (20°) - 1.5g \sin(30°)\right) ]
Substitute into perpendicular force equation, rearranging to derive ( T ):
[ T = 11 , \text{N} \text{ or } 11.0 , \text{N} ]
