Question

The roller coaster in Figure P6.36 starts with a velocity of 15.3 m/s. One of the riders is a small girl of mass 39 kg. At points B and C, the track is circular with the radii of curvature given in the figure. The heights at points A, B, and C are h_A= 24.55 m, h_B = 34.65 m, and h_C=0 m. You may assume the track is frictionless.

1) Find the velocity of the roller coaster at point B.

2) Find the velocity of the roller coaster at point C.

3) Find her apparent weight at B

4) Find her apparent weight at C

Answer 1

In this problem the student has not enclosed diagram . So I am assuming figures for the radiai of the path at points B and C to be 10m and 20m respectively and that following diagram represnts this case.

are respectively equal to 25.55m , 34.65m and 0m

1.

velocity at B = ?

Initially the Kinetic energy of the girl is = 1/2 x 39 Kg X 15.3m/s X 15.3 m/s =4564.8 J

Initial Potential energy of girl at A = 39 Kg X 9.8 m/sec2 X 24.55 m = 9383.0 J

Total Energy of girl at A = 13947.8 J

The potential Energy at B = 39 Kg X 9.8 m/sec2 X 34.65 m = 13243.23 J

The Kinetic Energy at B = 13947.8 J - 13243.2 J = 704.6 J

velocity of girl at B = Sqrt (704.6 J X 2 /39 Kg ) = 6.0 m/s

Velocity of roller coaster at B = 6.0 m/s

2 . Kinetic energy of girl at C = 13947.8 J

Velocity of girl at C = velocity of R/C at C = Sqrt ( 13947.8J X 2 / 39 Kg) = 26.7 m/s

3. apparent weight at B = Actual wt - centrifugal force = 39 Kg X 9.8 m/s2 - 39 kg X 6m/s X 6m/s/10 m

= 382.2 - 140.4 = 241.8 N

4 . apparent weight at c = Actual weight + centrifugal force = 39 Kg X 9.8m/s2 + 39 kg x 26.7 m/s x 26.7 m/s/20 m

= 382.2 + 1390.1 = 1772.3 N