A roller coaster ride begins with a chainpulling the coaster to the top of hill.

Question

A roller coaster ride begins with a chainpulling the coaster to the top of hill. The top of the Hill is 25 mabove the ground and as the coaster passes the top, it is moving at8.0 m/s. During the ride the coaster goes through loops and turnsbefore finally reaching the end. The end is gorund level and is thecoaster reaches it moving at 22 m/s. if it is determined that 40 kJof mechanical energy is lost air resistance and friction during theride, what is the mass of the roller coaster? A roller coaster ride begins with a chainpulling the coaster to the top of hill. The top of the Hill is 25 mabove the ground and as the coaster passes the top, it is moving at8.0 m/s. During the ride the coaster goes through loops and turnsbefore finally reaching the end. The end is gorund level and is thecoaster reaches it moving at 22 m/s. if it is determined that 40 kJof mechanical energy is lost air resistance and friction during theride, what is the mass of the roller coaster? A roller coaster ride begins with a chainpulling the coaster to the top of hill. The top of the Hill is 25 mabove the ground and as the coaster passes the top, it is moving at8.0 m/s. During the ride the coaster goes through loops and turnsbefore finally reaching the end. The end is gorund level and is thecoaster reaches it moving at 22 m/s. if it is determined that 40 kJof mechanical energy is lost air resistance and friction during theride, what is the mass of the roller coaster?

Explanation / Answer

Let m kg be the mass of coaster and potential energy at groundlevel is zero. Initial energy - Final energy = energy loss Initial energy (when it is at the top) = (1/2)(m kg)(8m/s)2 + (m kg)(10 m/s2)(25m) (taking g = 10m/s2) Final energy (at the bottom) = (1/2)(m kg)(22 m/s)2 Given energy loss = 40 kJ = 40,000 J Given energy loss = 40 kJ = 40,000 J Equating, we get, 32m + 250m - 242m = 40,000 m = 1000 Answer - mass of the coaster is 1000 kg

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