What Is the Required Power for a Cable Car on a Slope?

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To determine the required power for a cable car on a slope, first calculate the change in height, which is essential for understanding energy changes. The cable car, moving up a 1000 m slope at a 30-degree angle and a speed of 3.5 m/s, carries 20 persons with an average weight of 600 N each. Work is needed to lift the cable car, and this can be calculated using the height change and the total weight. The time taken to ascend the slope can be derived from the speed and distance, allowing for the calculation of power using the formula Power = Work/Time. Overall, the problem emphasizes the relationship between work, energy changes, and the required power for the cable car operation.
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A cable car is operated on a slope 1000 m long making an angle of 30deg. with the horizontal. The cable car moves up the slope with a speed of 3.5 m/s and carries 20 persons of average weight 600 N. What power is needed?
 
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first of all

SHOW US YOU ACTUALLY TRIED TO SOLVE THIS!

secondly draw a free body diagram

what is the change is height of the cable car ? If there is a change in height what else can change (in energy terms)

In order to take something up a height what is needed? To bring about the change in energy we need work.

Figure out the time needed for the cable car to go up that incline.

Now you have work and time thus you have power
 
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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