A penny (m = 2. 7g) rests on the edge of a turntable 8. 0 cm from the centre. Th

Question

A penny (m = 2. 7g) rests on the edge of a turntable 8. 0 cm from the centre. The turn-table starts from rest and accelerates at 0. 50 rad/s2. After 14 s the penny slide off. Pluto is the second largest dwarf planet*in the solar system, with a radius of 1, 200 km. In 2005 the Hubble space telescope discovered two new moons with a radius of approximately 50 km and a mass of 1. 0 x 1017kg. It takes Hydra 38 days to complete one orbit at a distance of 65. 000 km pluto. Bart the daredevil (m = 50 kg) is attempting to ride his skateboard around a loop-the-loop with a radius of 2. 0m. He starts at the top of a 5. 5m high ramp, with the loop-the -loop at the bottom. When Bart reaches the top of the loop, he has a tangential speed of 4. 9 m/s

Explanation / Answer

12 . a) a = alpha x r =0.50 x 0.08 = 0.04 m/s2

after 14 sec v = u +at = 0 + 0.04 x 14 =0.56 m/s

b) f = mv^2 / r = 0.0027 x 0.56^2 / 0.08 = 0.0106 N

c) u = f/mg = 0.0106 / (0.00207 x 9.8) = 0.4

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14)

a) initial p.e. = mgh = 50 x 9.8 x 5.5 = 2695 J

b) at top :

N +mg = mv^2 /r

N = 50 ( 4.9^2 / 2 - 9.8) = 110.25 N

c) work done by gravity + work done by friction = change in K.E>

50 x 9.8 x (5.5 - 4) + W = 50 ( 4.9^2 - 0) /2

W = -134.75 J

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