OCTOBER 10.pdf - PHYS1015 October 8 2010 TOTAL MARKS 77...

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PHYS1015 October 8 2010 Page 1 of 5 TOTAL MARKS 77 FULL MARKS 70 INSTRUCTIONS Show your calculations. Marks are allocated for the way that calculations are done. Draw freebody diagrams for all questions where appropriate. Numerical algebra will be marked on the answer only. Symbolic algebra will be marked at each step and errors will not be carried forward. Useful equations : 2 3 2 2 2 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ 2 1 tan r z r z r z r ru zu v ru r u zu a r r u r r u zu dy dx d y dx r dr d
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PHYS1015 October 8 2010 Page 2 of 5 Question 1 [11 marks] An m = 800 kg car travels over a parabolic shaped hill. When the car is at point A , it is travelling at v = 10 ms -1 and increasing its speed at a rate of a = 2 ms -2 . (a) Show that the normal force decreases in magnitude with increasing speed. (b) Determine both the resultant normal force and the resultant frictional force that all the wheels of the car exert on the road at this instant. Neglect the size of the car. Question 2 [11 marks] Due to the constraint, the 0.5-kg cylinder C travels along the path described by ( ) . If arm OA rotates counter clockwise with an angular velocity ̇ and an angular acceleration of ̈ at the instant , determine the force exerted by the arm on the cylinder at this instant.The cylinder is in
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