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I'm completing an assignment about roller coaster physics, however, I'm having difficulty understanding a concept. The image depicts a rollercoaster with a motor, however, I am not sure what it means when it says to determine "the energy that must be put in to reach point 2". I can determine the energy specifically at points 1 and 2, but I'm not sure if that's of any use. Where did I go wrong?

enter image description here

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The Energy given by the motor between point 1 and point 2 would be equal to the difference in Energy between point 1 and 2.

In the second part as you have been given Power of motor, you can use P=dE/dt to determine the time taken.

For third and fourth part you simply have to conserve energy as the motor is only between point 1 and 2.

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  • $\begingroup$ Thank you so much for the clarification for each part of the question! Just a thought, are you supposed to use the change in energy you calculate in part A for part B in the power formula? $\endgroup$
    – Megan Dime
    May 26 at 23:05
  • $\begingroup$ @MeganDime Yes as the power is constant, it provides constant energy in unit time and it will you the time required to give the energy change between point 1 and 2. $\endgroup$ May 27 at 6:56
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Well, if you can determine the value of the mechanical energy (potential+kinetic) at those two points, then their difference must be equal to the energy that the motor supplied to the cart. for part b) you want to use $P=\frac{dE}{dt}$ to determine the amount of time it takes for the motor to output the energy that you found in part a)

If you cannot figure out part c) and d) feel free to reply and I can help you out.

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  • $\begingroup$ hey! thank you so much for the clarification. for part 3, i was thinking of using the equation Em = mv^2/2 (because mgh cancels out) and then plugging in the mechanical energy on the left side of the equation according to the law of conservation of energy. but would i need to use the mechanical energy at point 1 or 2? because isn't the mechanical energy at those 2 points different, so i would get 2 different answers? I'm not sure what I should do :/ $\endgroup$
    – Megan Dime
    May 26 at 23:55
  • $\begingroup$ Change in energy is 0 because the motor is not doing work past point 2. This implies that the gravitational potential energy at the top of the hill is converted to kinetic energy at the bottom of the hill. mgh+KE(initial)=KE(final) so you must add the gravitational potential energy of 124.5 meters to the kinetic energy it has at the top of the hill and that will give you the kinetic energy at the bottom of the hill. To answer your question about which one of the two points, you want to use the last point that you know the carts energy, point 2. $\endgroup$
    – Azerack
    May 27 at 3:07
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You are going in the right direction; after calculating mechanical energies at points 2 and 1, you calculate the difference, $ E_2 - E_1 = \Delta E = \Delta K + \Delta U = (K_2 - K_1) + (U_2 - U_1)$, which is exactly the extra energy you put in, to go from point 1 to point 2.

Notice that both $\Delta K$ and $\Delta U$ comes out to be positive (non zero), so there must be non conservative force acting on it, that's exactly what the motor is doing, so,

Work done by motor is $$\int_1 ^2 P dt = \Delta E$$

this gives you the time taken $\Delta t=t_2 - t_1$.

The third and fourth parts are the easier ones, as for them, $\Delta E = 0$.

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  • $\begingroup$ this is great, thank you! $\endgroup$
    – Megan Dime
    May 26 at 23:57
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Consider that the roller coaster is at point 1. The roller coaster has some kinetic energy as depicted in the figure and some potential energy if we consider ground as a zero reference point.

As the roller coaster is moving the point 2 we can see that the velocity of the roller coaster has been shown to increase from 5.24m/s to 8.86m/s and there has been an increase in the gravitational potential energy of the roller coaster. This simply implies that there has been some additional energy supplied to the body which caused its total mechanical energy to increase.

Now, coming to the solution the energy that must be supplied should be just the difference between the total mechanical energy between point 2 and point 1. (At this point I am just assuming that there is no friction on the hill as there has been no mention about any energy losses in the question).

The 3000W motor will do the work for the roller coaster cart to reach the mechanical energy mentioned in position 2.

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  • $\begingroup$ thank you for clearing up some of my questions! :) $\endgroup$
    – Megan Dime
    May 26 at 23:56

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