Consider the roller coaster car pictured [ignore air resistance and friction] a)

Question

Consider the roller coaster car pictured [ignore air resistance and friction]

a) Write an algebraic expression for the total energy of the car at point B, before its release (vb=0 m/s)

b) Write an algebraic expression for the total energy of the car at point C, where y=0

c) Calculate the velocity of the car at point C.Let hB=20m, m car=400 kg

Consider the roller coaster car pictured [ignore air resistance and friction] a) Write an algebraic expression for the total energy of the car at point B, before its release (vb=0 m/s) b) Write an algebraic expression for the total energy of the car at point C, where y=0 c) Calculate the velocity of the car at point C.Let hB=20m, m car=400 kg

Explanation / Answer

Solution:

a) The total energy of the car at the point B = potential energy + kinetic energy

Potential energy at the point B which is at a height hB = mghB =mass x gravity x height of point B

Kinetic energy at the point B =1/2mvb^2=0 since vb = 0

Therefore , total energy at the point B= mghB

b) Since point C is at the height y=0, its potential energy =0

The total energy at the point C= kinetic energy at C= 1/2mvC2

c) From the conservation of energy ,

The total energy of the car at C =Total energy of the car at B

=> 1/2mvC2 = mghB

=> vC = squareroot (2ghB)

           =2 x 9.8 x 20

          = 19.8 m/s = velocity of the car at C

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