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A roller coaster is designed such that riders experience 'weightlessness' as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between -
A
16 m/s and 17 m/s
B
13 m/s and 14 m/s
C
14 m/s and 15 m/s
D
15 m/s and 16 m/s
Detailed Solution
At the top of the hill the forces on the rider are the weight $mg$ (downward) and the normal reaction $N$ (upward).
The net force towards the centre provides the centripetal force: $mg - N = \dfrac{mv^2}{r}$
For weightlessness, $N = 0$:
$\dfrac{mv^2}{r} = mg$
$v^2 = rg = 20 \times 10 = 200$
$v = \sqrt{200} = 14.14$ m/s
(With $g = 9.8$ m/s$^2$, $v = \sqrt{196} = 14$ m/s.)
So the speed of the car at the top is between 14 m/s and 15 m/s.
The net force towards the centre provides the centripetal force: $mg - N = \dfrac{mv^2}{r}$
For weightlessness, $N = 0$:
$\dfrac{mv^2}{r} = mg$
$v^2 = rg = 20 \times 10 = 200$
$v = \sqrt{200} = 14.14$ m/s
(With $g = 9.8$ m/s$^2$, $v = \sqrt{196} = 14$ m/s.)
So the speed of the car at the top is between 14 m/s and 15 m/s.