Efficiency of a Cart Rolling Down an Inclined Plane

AI Thread Summary
The discussion focuses on calculating the efficiency of a cart rolling down an inclined plane. The user provides specific measurements, including the height of the incline, the length of the board, the mass of the cart, and the force applied to pull it up. They calculate the energy input as 1.694 J using the work formula W = Fd. There is uncertainty about calculating energy output, with a suggestion to use kinetic energy but concerns about double counting losses. The conversation emphasizes the need to determine the energy the cart has at the top of the incline for accurate efficiency calculations.
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Homework Statement



Alright for this thing, we had to pull a cart up a inclined plane and time how long it took to get to the bottom.

Distance from ground to top of inclined plane is - 0.125m
Length of Board is - 1.21m
Mass of cart - 1.09kg
Force to pull cart up - 1.4N
Time it took for cart to roll down board - 1.92s

So I need to calculate:
Energy Input (pulling cart up)
Energy Output
Efficiency

Homework Equations




W = Fd

Eff = Useful output energy/Input Energy x 100%


The Attempt at a Solution



So I am guessing Energy Input is
W=FD
W=(1.4)(1.21)
W = 1.694 J

Would Energy output be
E = 1/2mv^2?
 
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I don't think so, wouldn't that be counting your losses twice? It takes 1.7 joules of input energy (Work) to pull the cart up to the top of the plane. How much energy does it have when it gets there?
 
Last edited:
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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