A roller coaster starts at position A with speedv D 1m=sasitgoesoverthe initial hill, height h1 D 100 m, as shown in the diagram. Assuming no loss in Energy (i.e. no friction), determine the speed at the following locations: a. (3 Points) Position B at height h2 D50m b. (3 Points) Position C at height h3 D75m c. (3 Points) Position D at ground level, height h D 0 m
a)
m = mass of the roller coaster
At position A :
v1 = 1 m/s
h1 = 100 m
At position B :
v2 = ?
h2 = 50 m
Using conservation of energy between A and B
KE at B + PE at B = KE at A + PE at A
(0.5) m v22 + mg h2 = (0.5) m v12 + mg h1
(0.5) v22 + g h2 = (0.5) v12 + g h1
(0.5) v22 + (9.8 x 50) = (0.5) (1)2 + (9.8 x 100)
v2 = 31.3 m/s
b)
m = mass of the roller coaster
At position A :
v1 = 1 m/s
h1 = 100 m
At position C :
v3 = ?
h3 = 75 m
Using conservation of energy between A and C
KE at C + PE at C = KE at A + PE at A
(0.5) m v32 + mg h3 = (0.5) m v12 + mg h1
(0.5) v32 + g h3 = (0.5) v12 + g h1
(0.5) v32 + (9.8 x 75) = (0.5) (1)2 + (9.8 x 100)
v3 = 22.2 m/s
c)
m = mass of the roller coaster
At position A :
v1 = 1 m/s
h1 = 100 m
At position D :
v4 = ?
h4 = 0 m
Using conservation of energy between A and D
KE at D + PE at D = KE at A + PE at A
(0.5) m v42 + mg h4 = (0.5) m v12 + mg h1
(0.5) v42 + g h4 = (0.5) v12 + g h1
(0.5) v32 + (9.8 x 0) = (0.5) (1)2 + (9.8 x 100)
v4 = 44.3 m/s
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