Q227 · Practice questionComplex unfamiliar6 marks
QUESTION 227 (6 marks)
A block moves uphill on a incline. A rope pulls with force at above the incline. Friction has magnitude . The block remains on the plane. Use .
a)[3 marks]
Calculate the normal force.
b)[3 marks]
Determine the acceleration, taking uphill as positive, and state whether the block is speeding up.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
(a) . (b) ; it is slowing down.
Worked solution
(a) Normal to the plane, the weight component is into the plane and the rope component is outward. Thus , giving .
(b) Along the plane, . This gives . Its velocity is uphill and acceleration downhill, so it slows down.
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Resolve weight perpendicular to the incline.
Part a: Resolve the rope force away from the incline and balance normal components.
Part a: Calculate the normal force.
Part b: Resolve the rope parallel to the incline and include downhill weight and friction.
Part b: Calculate the signed acceleration.
Part b: Relate opposite velocity and acceleration directions to slowing down.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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