Posted by R on Wednesday, May 8, 2013 at 12:01am.
The roller coaster starts with a velocity of 16 m/s. One of the riders is a small girl of mass 26 kg. Find her apparent weight when the roller coaster is at locations B and C. At these two locations, the track is circular, with the radii of curvature given.
rB = 10 m,
rC = 20 m,
The heights at points A, B, and C are
hA = 22 m,
hB = 32 m,
and
hC = 0.
Assume friction is negligible and ignore the kinetic energy of the wheels. (The figure is not necessarily drawn to scale.)
What is the weight at B?

Physics  Elena, Wednesday, May 8, 2013 at 6:10am
Point A: h₁= 22 m, v₁=16 m/s;
Point B: h₂= 32 m, r₂= 10 m, v₂=?;
Δh₁₂ = h₂h₁=3222 = 10 m;
Point C: h₃=0, r₃= 20 m, v₃=?;
Δh₂₃ = h₂h₃ = 32 – 0 = 32 m.
KE₁+PE₁=PE₂ + KE₂,
mv₁²/2 +mgh₁=mgh₂ +mv₂²/2,
mv₁²/2= mv₂²/2+ mgh₂  mgh₁=
=mv₂²/2+ mg Δh₁₂.
v₂ = sqrt{ v₁² 2gΔh₁₂} =
=sqrt{16²  2•9.8•10} =7.75 m/s.
For point B:
ma₂=mgN₂,
N₂=mgma₂=m[g (v₂²/r₂)]=
= 26[ 9.8 – (7.75²/10)]= 98.8 N,
N₂ (normal force) = W₂ (weight)
W₂= 98.8 N.
PE₂ +KE₂ = PE₃+KE₃,
mgh₂ +mv₂²/2 = mgh₃ +mv₃²/2,
mv₃²/2 = mgh₂ +mv₂²/2  mgh₃=
=mv₂²/2 + mg Δh₂₃ ,
v₃ = sqrt{v₂² +2g Δh₂₃}=
=sqrt{ 7.75² + 2•9.8•32) = 26.2 m/s.
For point C:
ma₃= N₃ – mg,
N₃= mg+ma₃=m[g+ (v₃²/r₃)]=
= 26[ 9.8 + (26.2²/20)]= 1148.2 N.
N₃ (normal force) = W₃ (weight)
W₃= 1148.2 N.
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