Physics

Problem

A roller-coaster car of mass

500\,\text{kg}

starts from rest at point

A

, which is

25\,\text{m}

above ground level. It moves down a frictionless track and climbs up to point

B

, which is

10\,\text{m}

above ground level. Air resistance and friction are negligible. Take

g = 9.8\,\text{m}\,\text{s}^{-2}

. a. (i) Define mechanical energy of a system. b. (ii) Calculate the speed of the car at point

B

using conservation of mechanical energy. c. (iii) The car next encounters a loop of radius

5.0\,\text{m}

whose highest point

C

20\,\text{m}

above ground level. Find the minimum speed the car must have at point

C

so that it just maintains contact with the track (consider the condition for contact at the top of a vertical circle). d. (iv) Show, with calculations, whether the car will have sufficient speed to maintain contact at point

C

without any additional propulsion between

B

and

C

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