Question

A roller coaster starts with a velocity of 17 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 in the figure. The heights at points A, B, and C are

h_A = 13 m,

h_B = 23 m,

and

h_C = 0.

Assume friction is negligible and ignore the kinetic energy of the wheels.

Weight at B- __________

Weight at C-___________

Answer 1

Here initial energy = 0.5*m*v0² + m*g*hA (Assuming she is starting at A.)

Her energy at point B = 0.5*m*vB² + m*g*hB

Using Energy Conservation.

0.5*m*v0² + m*g*hA = 0.5*m*vB² + m*g*hB
v0² + 2*g*hA = vB² + 2*g*hB
solve for vB:
vB² = v0² + 2*g*(hA - hB)

The centrifugal force on the girl, FcB = m*vB²/r
The apparent weight of the girl is W(B) = m*g - FcB

W(B) = m*(g - vB²/r)
W(B) = 26*(9.8 - [17^2 + 2*9.8*(13 - 23)] /10)
W(B) = 13 N
Weight at B = 13 N

Apparent Weight at Point C =
At point C -
0.5*m*v0² + m*g*hA = 0.5*m*vC^2
vC^2 = v0² + 2*g*hA

The centrifugal force on the girl, FcC = m*vC²/r
The apparent weight of the girl is W(C) = m*g + FcC

W(C) = m*(g + [v0² + 2*g*hA]/r)
W(C) = 26*(9.8 + [17^2 + 2*9.8*13]/20)
W(C) = 961.7 N
Weight at C = 961.7 N