Question

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

Answer 1

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