rupinder midterm 2-B 2011 solns

rupinder midterm 2-B 2011 solns - by 7.7 cm as shown below...

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1. The picture shows a hoop of radius 37 cm and mass 12 kg with a string wrapped around the edge. One end of the string is attached to an unknown mass m1. Initially the system is at rest but then m1 is released causing it to drop and rotate the hoop around its center in the clockwise direction. In 7.9 revolutions the hoop reaches a speed of 5.4 rad/s. (a) What is the magnitude of the angular acceleration? (b) What is the mass of the block m1? (c) What is speed (in m/s) of the block 1.0 s after being released?
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2. You are designing the next great rollercoaster for Canada’s Wonderland. You want to add an upside loop to it (a vertical circle). If the top speed that the rollercoaster cars can generate is 135 km/h, what is the maximum radius that you can make the loop so that the roller coaster does not fall off the track during the loop? Your free-body diagram will be marked. 3. A block of mass 2.5 kg is used to compress a spring of spring constant 125 N/m
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Unformatted text preview: by 7.7 cm, as shown below. It is released and travels up the slope and stops right at the very top. From the beginning to the top of the slope there is no friction. (a) What is the height of the slope? It then starts moving down the far side of the slope which is a rough surface where the coefficient of kinetic friction between the block and slope is 0.35. At the end of the slope it ends up at the same height it started from. (b) What is the speed of the block right at the bottom of the slope? (c) How much further beyond the slope will it travel before coming to a stop? 4. You are playing marbles and flick marble A at 1.0 m/s toward stationary marble B which has half the mass of marble A. Marble A hits B and moves at 0.45 m/s, at an angle of 20.0° with respect to the original line of motion. Assuming no friction or rotation motion find marble B’s velocity (including direction) after the collision....
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