5 5 Looping the loop Motion in a

5. 5 Looping the loop (Motion in a vertical circle) © Manhattan Press (H. K. ) Ltd. 1

5. 5 Looping the loop (Motion in a vertical circle (SB p. 185) Aircraft turning in flight 1. At the top At A, centripetal force is provided by mg and T 1 minimum speed at top © Manhattan Press (H. K. ) Ltd. 2

5. 5 Looping the loop (Motion in a vertical circle (SB p. 185) Aircraft turning in flight 2. At the bottom At B, centripetal force is provided by mg and T 2 minimum speed at bottom © Manhattan Press (H. K. ) Ltd. 3

5. 5 Looping the loop (Motion in a vertical circle (SB p. 186) Aircraft turning in flight 2. At the bottom T 2 = T 1 + 6 mg The tension at the bottom (T 2) is a maximum and the tension at the top (T 1) is a minimum. © Manhattan Press (H. K. ) Ltd. 4

5. 5 Looping the loop (Motion in a vertical circle (SB p. 186) Aircraft turning in flight E. g. (a) Roller coaster (b) Whirling a bucket of water Go to © Manhattan Press (H. K. ) Ltd. Example 6 5

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5. 5 Looping the loop (Motion in a vertical circle (SB p. 187) Q: The figure shows a toy runway. After being released from a point X, a small model car runs down the slope of height h, loops the loop, and travels towards point Z. The radius of the loop is r. (a) Ignoring the effect of friction, outline the energy changes as the model car moves from X to Z. Hence, find the speed of the car at P. © Manhattan Press (H. K. ) Ltd. 7

5. 5 Looping the loop (Motion in a vertical circle (SB p. 187) Q: (b) What is the minimum speed with which the car must pass point P at the top of the loop if it is to remain in contact with the runway? (c) What is the minimum value of h which allows the speed calculated in (b) to be attained? Solution © Manhattan Press (H. K. ) Ltd. 8

5. 5 Looping the loop (Motion in a vertical circle (SB p. 187) Solution: (a) Assume no energy is lost, PE �→ KE + PE �→ KE (at X) (at Y) (at P) (at Z) Let v be the speed of model car at point P. PE = KE + PE (at X) (at P) © Manhattan Press (H. K. ) Ltd. 9

5. 5 Looping the loop (Motion in a vertical circle (SB p. 187) Solution (cont’d): (b) Consider the free-body diagram of the model car at point P. mg: weight of model car, R: normal reaction acted on the model car by the runway (c) Compare the result of (b) with (1): 2 g ( h – 2 r) = gr h = 2. 5 r ∴ The minimum height h should be equal to 2. 5 r. © Manhattan Press (H. K. ) Ltd. Return to Text 10