A rollercoaster car starts from rest at point A which is at a height of 16.53 m

Question

A rollercoaster car starts from rest at point A which is at a height of 16.53 m and proceeds with a 120kg mass. The car travels through point B which is at a height of 0 m and then through point C which is at a height if 7 m.

If 20% of total mechanical energy would be lost due to friction between points A and B, what would be the speed at point B?

If 20% of total mechanical energy would be lost due to friction between points B and C, what would be the speed at point C?

If 20% of total mechanical energy would be lost due to friction between points A and C, what would be the speed at point C?

Explanation / Answer

at A, Ea = m*g*h

at B Eb = 0.5*m*vb^2

from A to B

Ea - 0.2*Ea = 0.5*m*vb^2

(16.53*9.8) - (0.2*16.53*9.8) = 0.5*Vb^2

Vb = 16.1 m/s

from B to C

Eb = 0.5*m*Vb^2

Ec = m*g*h2 + 0.5*m*Vc^2

Eloss = -0.2*Eb =

Eb + Eloss = Ec

0.5*m*Vb^2 - 0.2*0.5m*Vb^2 = 0.5*m*Vc^2 + m*g*h2

(16.1*16.1) - (0.2*16.1*16.1) = Vc^2 + (2*9.8*7)

Vc =8.37 m/s (nearly)

------------------

Ea - 0.2*Ea = 0.5*m*Vc^2

(16.53*9.8) - (0.2*16.53*9.8) = 0.5*Vc^2

Vc = 16.1 m/s

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