A roller coaster starts from rest at the top of a hill with 1000J of potential e

Question

A roller coaster starts from rest at the top of a hill with 1000J of potential energy. How much kinetic energy does it have? How much total mechanical energy? How much total, kinetic, and potential energy does the can have after it has travelled halfway down the hill? How much total, kinetic, and potential energy does the cart have after it has travelled all of the way down the hill? A block is compressed a distance x against a spring such that the system now has a total mechanical energy of 100J. Assume there are no frictional forces. How many joules of energy is in the form of potential energy at this position? How-much energy is in the form of kinetic energy? The block is released, and the spring has expanded to half the original compression (the new position is at x' = x/2). How much energy is in the form of potential and kinetic energy? Note we are not asking for the velocity. What is the Potential Energy of the spring when x" = 0, the un-stretched position? What is the Kinetic Energy of the block at x" = 0? A 100kg roller coaster can starts from rest atop a 60 meter tall hill and rolls down at 45 degree. What is the speed of the coaster at the bottom of the hill if there is no friction? What is the speed if there is a constant 120N retarding force?

Explanation / Answer

According to the given porblem,

1)From the conservation of energy law, we know that TE = ke + pe = 0 + 1000 = 1000 J = mgH = PE at the top of the big plunge. ke = 0 because the car is not moving. So all the TE is PE at that point, T.E = P.E = 1000J

2) When h = H/2, the car is 1/2 way down the plunge, we have TE = ke + mgH = mgH = ke + mgH/2 = TE Keep in mind TE = 1000 J no matter where that car is. so,ke = TE - mgH/2 = TE - PE/2 So ke = 1000 - 1000/2 = 500 J kinetic energy. The rest is potential energy or 500 J. The total remains at 1000 J.

3)At the bottom of the plunge, where h = 0, there is no pe. So TE = ke + pe = ke + 0 = 1000 J = KE. The total and kinetic are 1000 J and the PE = 0. ANS.

4) Same as the above problem, Using the energy conservation principal,

Total energy remains same. So, at the intial compressed state P.E = S.P.E = =1/2kx2 = 100J

And K.E = 0 J and total T.M.E = 100J

5.) At half the distance,

T.M.E = 100J = P.E` + K.E

so, K.E = 100J - 1/2k (x/2)2 = 100J - P.E/4 = 100J -25 J = 75J, P.E` = P.E/4 = 25J

6.) Here the x = 0 therefore, P.E = 0 and T.M.E = K.E = 100J

Only 4 Sub-parts in a question as per chegg rules.

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