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QTest #10-solutions - Version 096/ABCAA QTest#10...

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Version 096/ABCAA – QTest #10 – Antoniewicz – (56445) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points In a circus performance, a large 3 . 4 kg hoop of radius 5 . 4 m rolls without slipping. If the hoop is given an angular speed of 2 . 9 rad / s while rolling on the horizontal and is allowed to roll up a ramp inclined at 23 with the horizontal, how far (measured along the incline) does the hoop roll? The acceleration of gravity is 9 . 8 m / s 2 . 1. 42.962 2. 52.7332 3. 18.1376 4. 87.7965 5. 36.616 6. 23.1336 7. 64.0441 8. 18.8198 9. 27.9754 10. 40.5915 Correct answer: 64 . 0441 m. Explanation: Let : m = 3 . 4 kg , r = 5 . 4 m , ω i = 2 . 9 rad / s , θ = 23 , and g = 9 . 8 m / s 2 . By conservation of mechanical energy, U f = K i since v f = 0 m/s and h i = 0 m. U f = K trans,i + K rot,i mgh = 1 2 m v 2 i + 1 2 ( m r 2 ) ω 2 i m g d sin θ = 1 2 m ( r ω i ) 2 + 1 2 ( m r 2 ) ω 2 i = 1 2 m r 2 ω 2 i + 1 2 m r 2 ω 2 i g d sin θ = r 2 ω 2 i d = r 2 ω 2 i g sin θ = (5 . 4 m) 2 (2 . 9 rad / s) 2 (9 . 8 m / s 2 ) sin 23 = 64 . 0441 m .
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