Question
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.
$$14\,m/s$$ and $$15\,m/s$$
B.
$$15\,m/s$$ and $$16\,m/s$$
C.
$$16\,m/s$$ and $$17\,m/s$$
D.
$$13\,m/s$$ and $$14\,m/s$$
Answer :
$$14\,m/s$$ and $$15\,m/s$$
Solution :
The appearance of weightlessness occurs in space when the gravitational attraction of the earth on a body in space is equal to the centripetal force.
$$\eqalign{ & \therefore \frac{{m{v^2}}}{r} = mg \cr & {\text{or}}\,\,v = \sqrt {rg} = \sqrt {20 \times 10} = 14.14\,m/s \cr} $$
The appearance of weightlessness occurs in space when the gravitational attraction of the earth on a body in space is equal to the centripetal force.
$$\eqalign{ & \therefore \frac{{m{v^2}}}{r} = mg \cr & {\text{or}}\,\,v = \sqrt {rg} = \sqrt {20 \times 10} = 14.14\,m/s \cr} $$