Mechanical energy into thermal energy

AI Thread Summary
The discussion revolves around calculating the percentage of mechanical energy lost to thermal energy due to friction in a roller coaster scenario. The roller coaster's maximum height is 94.5m, leading to a theoretical maximum speed of 43.1 m/s, while the actual maximum speed is only 4.1 m/s. The user attempts to apply the work-energy principle but struggles to arrive at the correct percentage of energy loss. The correct calculation involves determining the work done against friction and comparing it to the initial gravitational potential energy. Ultimately, the expected energy loss due to friction is 8.9%.
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Homework Statement


the roller coaster is 94.5m high at its highest point. what is the maximum possible speed of the roller coaster? the roller coaster's actual maximum speed is 4.1m/s.what percentage is lost to thermal energy due to friction?

Homework Equations


Wnc= Efinal-Eintial
the part i didnt get is highlighted in red.
please help me


The Attempt at a Solution


Wnc= Efinal- Eintial
Efinal= Ek
Einitial=Eg
after i got the numbers i said (Wnc/Einitial)*100 to get the percentage. but it did not get me to the answer.
the answer on the book is = 8.9%
and its maximum speed is = 43.1 m/s
 
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divide Wnc by the energy that it should've had (with the 43.1 m/s velocity, .5m(43.1)^2)
and then multiply by 100
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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