Conservation of Energy 5

Question

A roller coaster begins at 6 m/s at the top of a 25 m hill. Find the velocity at a point 10 m above the bottom of the hill.

Answer 1

Conservation of energy says the total energy at point 1 equals the total energy at point 2.

Total Energy at Point 1 (E₁) includes both kinetic and potential energy. Kinetic energy (KE₁) = 1/2mv₁². Potential energy (PE₁) = mgh₁ So E₁ = 1/2mv₁² + mgh₁ = 1/2m(6²) + m(9.81)(25) = m(18 + 245.25) = 263.25m

Total Energy at Point 2 (E₂) also includes both kinetic and potential energy. Kinetic energy (KE₂) = 1/2mv₂². Potential energy (PE₂) = mgh₂ So E₂ = 1/2mv₂² + mgh₂ = 1/2mv₂² + m(9.81)(10) = m(1/2v₂² + 98.1)

E₁ = E₂ so 263.25m = m(1/2v₂² + 98.1)

Dividing both sides by m gives us: 263.25 = 1/2v₂² + 98.1

Sutracting 98.1 from both sides the multiplying by 2 gives us: v₂² = 330.3

Taking the square root of both sides gives v₂ = 18.17 m/s. There is really only one significant figure in the givens, so I guess we would need to round this to 20 m/s but I'm not sure how fussy your teacher is about sig figs.