Question

A student skates up a ramp that makes an angle $30^{\circ}$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_{0}$ and wants to turn around over a semicircular path $xyz$ of radius $R$ during which he/she reaches a maximum height $h$ (at point $y$) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then ( $g$ is the acceleration due to gravity)

• A. $v _{0}^{2}-2 gh =\frac{1}{2} gR$
• B. $v _{0}^{2}-2 gh =\frac{\sqrt{3}}{2} gR$
• C. the centripetal force required at points $x$ and $z$ is zero
• D. the centripetal force required is maximum at points $x$ and $z$

Answer 1

Answer: (A), (D)

$v _{0}^{2}-2 gh =\frac{1}{2} gR$

Answer 2

(A) $v _{0}^{2}-2 gh =\frac{1}{2} gR$
(D) the centripetal force required is maximum at points $x$ and $z$