8) A roller coaster of mass 225 kg is moving with a speed of 8.00 m/s on top of

Question

8) A roller coaster of mass 225 kg is moving with a speed of 8.00 m/s on top of the track at position A as shown in the figure. The vertical height above ground level at position A is 200 m and is 160m at point C. Neglect friction and define the potential energy to be 0 at point B 200 m 100 m -Prncial Energy a) What is the total mechanical energy of the roller coaster at point A? 4.46x10 2a.1 b) What is the speed of the roller coaster at point C? e) Assume that the track at point C is circular and has a radius of 60.0 m. Draw a FBD for the roller coaster at point C. Make sure your vector lengths make sensc d) Use your FBD to determine the maximum speed the roller coaster can have at C to stay on the track. u.3 e) Is this ride safe? Explain quantitatively why or why not.

Explanation / Answer

8)Given,

M = 225 kg ; va = 8 m/s ; h = 200 m ; Hc = 160 m

a)Ea = KE + PE

Ea = 1/2 m va^2 + m g h

Ea = 0.5 x 225 x 8^2 + 225 x 9.81 x 300 = 6.7 x 10^5 J

Hence, Ea = 6.7 x 10^5 J

b)Ec = KE + PE

Ec = Ea = 6.7 x 10^5 = 1/2 m vc^2 + m g hc

0.5 x 225 x vc^2 + 225 x 9.81 x 160 = 6.7 x 10^5

vc = 53 m/s

c)for the stated condition to occur, the gravity should balance the centripital force.

d)At point C, r = 60 m

m v^2/r = mg => v = sqrt(gR)

v = sqrt(9.81 x 60) = 24.3 m/s

Hence, v = 24.3 m/s

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