Arturo O. answered • 12/01/16
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I will set this up for you and you can crunch out the numbers.
(a)
At the top, the normal force FN points away from the center, and the weight mg points toward the center.
mg - FN = mv2/r
FN = mg - mv2/r
FN = m(g - v2/r)
You are given m, v, and r. Plug in the numbers, but first convert the speed to m/s. The apparent weight is lower than the true weight.
(b)
At the bottom, the normal force points inward toward the center while the weight points away from the center.
FN - mg = mv2/r
FN = mg + mv2/r
FN = m(g + v2/r)
Plug in the numbers, with v in m/s.
The apparent weight is higher than the true weight.
Arturo O.
(a)
v = 100 km/hr = 100,000 m /(3600 s) ≅ 27.78 m/s
FN = m(g - v2/r) = (75 kg)[9.81 m/s2 - (27.78 m/s)2/(500 m)] = 619.99 N
(b)
FN = m(g + v2/r) = (75 kg)[9.81 m/s2 + (27.78 m/s)2/(500 m)] = 851.51 N
Except for very small differences in round-off, I get the book answers. Did you correctly convert the velocity from km/hr to m/s?
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12/01/16
Jamie B.
12/01/16