A single frictionless roller-coaster car of mass m = 825 kg tops the first hill

Question

A single frictionless roller-coaster car of mass m = 825 kg tops the first hill with speed v_0 = 16.0 m/s at height 28.0 m. (a) What is the speed of the car at point A? m/s (b) What is the speed of the car at point B? m/s (c) What is the speed of the car at point C? m/s (d) How high will it go on the last hill, which is too high to cross? m (e) If we substitute a second car with twice the mass, what is the speed of this car at point A? m/s What is the speed of this car at point B? m/s What is the speed of this car at point C? m/s How high will it go on the last hill? m.

Explanation / Answer

here,

v0 = 16 m/s

h = 28 m

m = 825 kg

a)

let the speed at A be vA

as the height of A is same as initial point

vA = 16 m/s

b)

let the speed at B be vB

using conservation of energy

0.5 * m * (vB^2 - v0^2) = m * g * (h - h/2)

0.5 * ( vB^2 - 16^2) = 9.81 * ( 14)

vB = 23.04 m/s

c)

let the speed at C be vC

using conservation of energy

0.5 * m * (vC^2 - v0^2) = m * g * (h - 0)

0.5 * ( vB^2 - 16^2) = 9.81 * (28)

vC = 28.4 m/s

d)

let the final height be h'

using conservation of energy

m * g * (h' - h) = 0.5 * m * v0^2

9.81 * ( h' - 28) = 0.5 * 16^2

h' = 41.05 m

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