The roller coaster car has a mass of 550 kg. including its passenger. It is rele

Question

The roller coaster car has a mass of 550 kg. including its passenger. It is released from rest at the top of the hill A. Neglect friction, the mass of the wheels, and the size of the car. Take h_B = 19 m rho_D = 9.5 m. h_c = 13 m. and rho c =6.5 m (Figure 1) Determine the minimum height h of the hill crest so that the car travels around both inside the loops without leaving the track. Express your answer to three significant figures and include the appropriate units. What is the normal reaction on the car when the it is at B? Express your answer to three significant figures and include the appropriate units. What is the normal reaction on the car when the it is at C? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Given that,

mass = 550 kg ; hB = 19 m ; hC = 13 m ; pC = 6.5 m

A) Applying conservation of energy at loop B.

1/2 m vB2 = m g (h - hB)

0.5 vB2 = g (h - 19) (1)

We know that, F= mg and F = mv2/r equating the forces we get, v = sqrt (r g)

vB = sqrt (19/2 x 9.8) = 9.65 m/s

putting this value in 1, we get

0.5 x (9.65)2 = 9.8( h - 19)

h = 23.75 meters

Hence h = 23.75 meters.

B)Normal reaction at B, NB = 0.

C)Applying conservation of energy at loop C

1/2 m vC2 = m g (h - hC)

0.5 vC2 = g(23.75 - 13)

0.5  vC2 = g (10.75)

vC = sqrt (9.8 x 10.75 / 0.5) = 14.52 m/s

Now, NC = Fc - mg = m vc2 / r - mg = 550 x (14.52)2 / 6.5 - 550 x 9.8 = 12449.5 N

Hence, Nc = 12449.5 N

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