Question

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A roller-coaster car of mass 1.80 x 102 kg is initially at the top of a rise at point. It then moves 31.9 m at an angle of 55.00 below the horizontal to a lower point ® (a) Find both the potential energy of the system when the car is at points and and the change in potential energy as the car moves from point to point ®, assuming y = 0 at point ®. potential energy at Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. J 4.61000 X potential energy at 0 change in potential energy -4.61 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.) (b) Repeat part (a), this time choosing y = 0 at point ©, which is another 15.0 m down the same slope from point potential energy at potential energy at ® change in potential energy Need Help? Read it

Answer 1

A 55° According to the question, the horizontal displacements AB = 31.9 m Now, we have to know the vertical displacement : AC- ,حراNO we know, Sin 55° AC AB or, AC ABX Sin 55° 31.9 X Sin 55° 26°13 m 26:13 m kq at A Now, vertical height of point a Potential energy m xg xu = (1'8x10°x 98 26:13)) 461 X1033 m=18x109 q? . 9.8 m/s2 në 26'13 m

... vertical height of B. m: 19x10'ng 9. 9.8 m/s2 • Potential energy at B : mxgxu hom OU change in potential energy Final PE Initial PE [o - (961 *10')] 461 x 103 AB = 31.9 am BC 150 m 55: D E Now, the distance between B and c 150 m and, we have to know the vertical heights of points A and B. vertical neight of A AD BE 91 Now, we know, sin 550 BE BC (From A BFC) BE = BC X sin 55 1229 m and , sin 550 AD AC (From A ADC) NOW, AC AB + BC (319 + 150 m 46.9 m AD = AC X Sin 55° 469 X Sin 55° 38.42 m ma 18x10°kg 9:9.8 misa 39'42 m Now, Potential A energy at = ('8 x 109 x 9.8 x 38'42) J 677'73 x103 g Potential energy at B mxgx BE BE = 12:29 m =(18 X10% x 9'8 x 12'29) 216.79 X10

change in potential energy Final PE Initial PE [(216°79 x 10) - (677.73 X10')] 3 460°94 x103 J 461 x 103 Important Note:- change in potential energy between two points does't depend on the reference plane to measure the heights of the points .