A single frictionless roller-coaster car of mass m2 = 800 kg tops the first hill

Question

A single frictionless roller-coaster car of mass m2 = 800 kg tops the first hill with kinetic energy of 60,000 J at height h = 30 m. Ignore friction and air resistance. Set gravitational potential energy of the car-Earth system equal to zero at the ground (i.e. at point C). Last hill 0 First hill b. The last hill is too high for the car to cross. What is the potential energy of the car-Earth system when the car reaches its maximum height on the last hill? How high above the ground will the car go on the last hill? In other words, find the maximum height reached by the car on the last hil c.

Explanation / Answer

Given m = 800 kg , Kinetic energy at first hill(KE1) = 60000J ,

h = 30 m

At first hill,

Total energy(E) = PE + KE1

E = mgh + KE1

E = (800*9.8*30) + 60,000

E = 235200 + 60000 = 295200 J

Part b) since the energy is conserved , as no external forces are acting

Potential energy when the car reaches maximum height on the last hill (PE1)= 295200 joules

Part c) m*g*h1 = 295200

h1 = 295200/9.8*800

h1 = 37.653 m

Therefore, maximum height = 37.653 m

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