Need Help? Aroler coaster car of mass 1.60 103 kg is initially at the top of a r

Question

Need Help? Aroler coaster car of mass 1.60 103 kg is initially at the top of a rise at point Itthen moves 335 m at an angle of 60 ge below the horizontal to a lowe pet® and®and the change in potential energy as the car moesfer (a Find both the potentialenergy o the system when the car is at pots assuming y 0 at point port ® to port® potential energy at 52528 Your response differs from the correct answer by more than 10%. Double check your calculations. J potential energy at 52511 change in potential energy The response you Your response differs significantly from the correct answer Rework your solution from the beginning and check each step carefully. 3 172 submitted has the wrong sign.3 O at point which is another 15.0 m d in the same slope from point ® (b) Repeat part (a), this time choosing y potential energy at potential energy at change in potential energy Need Help? Resd Type here to search

Explanation / Answer

(a)

Radius of point A,

rA = 33.5*cos60 = 16.75 m

potential energy at point A,

PEA = mg*2(rA)

PEA  = 1.6*10^3*9.8*2*16.75

PEA = 5.25*10^5 J

Potential energy at point B-

From energy consertvation,

PEB = KE = (1/2)mv^2

where v = sqrt (2gh)

v = sqrt (2*9.8*33.5) = 25.62 m/s

PEB = (1/2)*1.6*10^3*(25.62)^2

PEB = 5.25*10^5 J

Change in PE = 0

(b)

y = 0 at point C which is 15 m down,

PEA = mgh

PEA = 1.6*10^3*9.8*(33.5 + 15)*cos60

PEA = 3.8*10^5 J

potential energy at point B,

PEB = mgh'

PEB = 1.6*10^3*9.8*15*cos60

PEB = 1.17*10^5 J

Change in PE = PEA - PEB

Change in PE = 2.63 * 10^5 J

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