The title could be: Calculating Energy Loss and Conservation in Falling Objects

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AI Thread Summary
A discussion on calculating energy loss and conservation in falling objects focuses on two problems involving a pine cone and a roller coaster. The first problem involves determining the energy lost to entropy when a 2kg pine cone drops from 41 meters and hits the ground at 10 m/s. The second problem asks for the height at which an 1800kg roller coaster traveling at 24 m/s will have its kinetic energy calculated at 10 meters above the ground. Participants apply the equations for gravitational potential energy and kinetic energy, emphasizing the relationship between initial and final energy states. The conversation highlights the need for clarity in calculations and understanding energy conservation principles.
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Homework Statement


So, I need a little help with a few problems
So, say a 2kg pine cone drops from a tree 41 meters high. If it hits the ground at 10m/s then how much was lost to entropy?
Or
A 1800kg roller coaster begins at the top of 190m hill, at what height will the velocity be 24m/s and what will be its kinetic energy when it reaches a height of 10m above the ground.?
Thanks for any or all help.

Homework Equations


Energy of work = Force times distance
Gravitational potential = mgy
Kinetic Energy = .5 time mass time velocity squared

The Attempt at a Solution


For the 2nd one, I used mgy= .5 time mass time velocity squared but submitted 24 for the velocity to find y but I don't think it's right.
For the 1st, I used mgy+.5 time mass time velocity squared to find the energy but don't know where to go from there.
 
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Energy initial = energy final

potential energy of pine cone up in tree =

kinetic energy of pine cone before it hits + energy "lost" on the way down

You can figure out two of those to find the third.

For the second part,

Energy initial = energy at some intermediate step

potential energy up high =

potential energy up not so high + kinetic energy at that not so high place
 
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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