Question

A roller coaster starting from rest descends 35 meters in its initial drop and then rises 23 meters when it goes over the first hill, which has a circular shape over the top. If a passenger at the top of the hill feels an apparent weight equal to one-half of her normal weight, what is the radius of curvature of the first hill? Neglect any frictional losses.

Answer 1

Answer:

Radius of hill = r = 48 m

Explanation:

Given data:

Initial height = $h_{1}$ = 35 m

Final height =  $h_{2}$ = 23m

Radius = r = ?

We know that

Change in potential energy = ΔP.E = mg(Δh)

ΔP.E = mg($h_{2}$ - $h_{1}$)

ΔP.E = mg(35 - 23)

ΔP.E = 12 mg

We know that

Change in Kinetic Energy = ΔK.E = 0.5 mv²

According to energy of conservation

ΔK.E = ΔP.E

0.5 mv² = 12 mg

v² = 24 g  Eq 1

As she feels an apparent weight which is one-half of her normal weight

So,

Apparent weight = 0.5 normal weight

mg - mv²/r = 0.5 mg

0.5 g = v²/r

v² = 0.5 gr   Eq 2

Compare Eq 1 and Eq 2

0.5 gr = 24 g

r = 48 m