A 100.0 kg cart is initially moving at 200 m/\'s at the top of a hill A of a rol

Question

A 100.0 kg cart is initially moving at 200 m/'s at the top of a hill A of a roller coaster. The s 10.0 m. The cart moves down a very low friction (can neglect) hill past points 8 and C and horizontal and has substantial friction f-80.4N. The cart stops when it reaches G. Giver is w.-8.00 m/s and h . 2.00 m. The drawing on scale-approaimate. The height ha from the ground track is he 5.00m, speed at he )what is the total mechanical energy ME (sum of kinetic and potential energies) at A ,000 (ii) what is the speed of the cart at B, 19ooo , V. (iii) what is the height orRetractuenn 000o 1 10000 may (iv) what is the length d of the track from D to G?

Explanation / Answer

i)

TA = Total mechanical energy at A = (0.5) m va2 + mg ha = (0.5) (100) (2)2 + (100) (9.8) (10) = 10000 J

ii)

using conservation of energy

TB = TA = 10000 J

(0.5) m vb2 + mg hb = 10000

(0.5) (100) vb2 + (100) (9.8) (5)= 10000

vb = 10.1 m/s

iii)

using conservation of energy

TC = TA = 10000 J

(0.5) m vc2 + mg hc = 10000

(0.5) (100) (8)2 + (100) (9.8) hc = 10000

hc = 6.94 m

iv)

using conservation of energy

TD = TA = 10000 J

(0.5) m vd2 + mg hd = 10000

(0.5) (100) vd2 + (100) (9.8) (2)= 10000

vd = 12.7 m/s

using work-change in kinetic energy theorem

- f d = (0.5) m (vg2 - vd2)

- 80.4 d = (0.5) (100) ((0)2 - (12.7)2)

d = 100.3 m

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