A 4357 kg roller coaster starts from rest at the top of a 36.5 m high track. Determine its speed of the car at the top of a loop that is 10.8 m high.    

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The roller coaster with mass 4357 kg is initially at rest at a height 36.5 m. It moves down and reaches the top of a loop where its height is 10.8 m. To determine the speed of the roller coaster at the top of the loop assume that the roller coaster is a closed system and the total energy in a closed system remains the same, this is also referred to as the law of conservation of energy.

Let the velocity of the roller coaster at the top of the loop equal V. Equating the total energy of the roller coaster at the top of the high track with that at the top of the loop gives:

m*g*36.5 + 0 = m*g*10.8 + (1/2)*m*V^2

=> V^2 = 9.8*2*(36.5 - 10.8)

=> `V ~~ 22.44` m/s

The speed of the roller coaster at the top of the loop is approximately 22.44 m/s

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