On a roller coaster ride the total mass of the cart - with passengers included -

Question

On a roller coaster ride the total mass of the cart - with passengers included - is 305 kg. Peak K is at 45.0 m above the ground, peak L is at 25.0 m. The speed of the cart at K is 15.7 m/s, at L it is 13.4 m/s. (The wheel mechanism on roller coaster carts always keeps the carts safely on the rail.)

https://s4.lite.msu.edu/enc/61/715b0c213c4b97cb8ac83d52b560f018ea367a939f326f531270ce7e8ecabcbcd19ee590428e4004f7d379e4855c90d357d60d2777c2063a139b2b54d2b19fba0c8f92d8a88399ddce7c6c565033294a.gif

How much energy is lost due to friction between the two peaks?

Explanation / Answer

Energy lost = (potential energy at K + kinetic energy at K)- ( Potential energy at L + kinetic energy at L)

= m*(gHk + .5*Vk^2) -  m*(gHl+ .5*Vl^2) = 61 Kj + 10.206 Kj = 71.206 KIlo joules

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