Q158 · Practice questionComplex familiar7 marks
QUESTION 158 (7 marks)
A crate is moving up a incline. A rope pulls parallel to the incline with tension . Friction has magnitude . Its initial speed is . Use and assume the forces remain constant until it first stops.
a)[2 marks]
Calculate the normal force and state its direction.
b)[3 marks]
Determine the acceleration, taking uphill as positive.
c)[2 marks]
Calculate the distance travelled up the incline before it first stops.
WORKED SOLUTION
7 marksPractice marking scheme
ANSWER
(a) , perpendicular to and away from the surface. (b) (downhill). (c) .
Worked solution
(a) There is no perpendicular acceleration, and the rope and friction are parallel to the slope. Thus .
(b) The weight component downhill is . Friction also acts downhill while the crate moves uphill. ; .
(c) gives , so . No assumption about friction after stopping is needed.
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: Balance forces perpendicular to the surface.
Part a: Calculate the normal force and give its outward perpendicular direction.
Part b: Resolve the weight down the slope.
Part b: Include downhill friction in a signed net force.
Part b: Calculate and interpret the acceleration.
Part c: Use a constant-acceleration equation with the correct sign.
Part c: Calculate a positive stopping distance.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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