(a) A block of mass m, initially at angular position 0 = 0, is sliding up...
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(a) A block of mass m, initially at angular position 0 = 0, is sliding up a frictionless circular arc of radius R with initial speed given by v = , as shown below. Gravity acts downwards. Show that, in order for the bilock to reach the top of the arc (8 = 180°) while remaining in contact with the arc, the initial velocity must be greater than tg = (5gR)/2 (8 marks). (b) Now, in addition to the conditions in part (a), a constant tension 0 <T < mg is applied in the radial direction through a pulley of negligible radius located at the centre of the circular are as shown below. In this situation, the block loses contact with the arc at 6 = 62 and v = v2. Show that vz = (TR/m -gR cos 62)/2 (4 marks). T const. R (c) Under the conditions in part (b), determine 02 in terms of T, m, g, vg and R (8 marks). (a) A block of mass m, initially at angular position 0 = 0, is sliding up a frictionless circular arc of radius R with initial speed given by v = , as shown below. Gravity acts downwards. Show that, in order for the bilock to reach the top of the arc (8 = 180°) while remaining in contact with the arc, the initial velocity must be greater than tg = (5gR)/2 (8 marks). (b) Now, in addition to the conditions in part (a), a constant tension 0 <T < mg is applied in the radial direction through a pulley of negligible radius located at the centre of the circular are as shown below. In this situation, the block loses contact with the arc at 6 = 62 and v = v2. Show that vz = (TR/m -gR cos 62)/2 (4 marks). T const. R (c) Under the conditions in part (b), determine 02 in terms of T, m, g, vg and R (8 marks).
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Related Book For
Fundamentals of Physics
ISBN: 978-0471758013
8th Extended edition
Authors: Jearl Walker, Halliday Resnick
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