Question-165791

Question Number 165791 by aurpeyz last updated on 08/Feb/22

Answered by ghchoi0707 last updated on 08/Feb/22

m = Mass of roller coaster (any unit)

g = Acceleration by Gravity ≒ 9 . 8 m / s^{2}

z = Position of roller coaster (m)

v_{i} / v_{f} = Initial / Final velocity of roller coaster (m / s)

E = Mechanical Energy

K = Kinetic Energy

U = Potential Energy (By Gravity)

We have to find v_{f} .

Let [Initial U] = 0 J .

Then Δ U = m g Δ z = m g \times (- 20) = - 20 m g

(∵ U is path independent .

In other words, you just have to check only initial and final condition .)

as Δ E = 0, Δ K = \frac{m}{2} \times (v_{f}^{2} - v_{i}^{2}) = - Δ U = 20 m g .

as v_{i} = 0, v_{f} = \sqrt{40 g} ≒ 19.8 (m / s) .

Answered by MJS_new last updated on 09/Feb/22

ignoring friction and air resistance {it}^{'} s equal

to a free fall of 20 m :

s = \frac{{g t}^{2}}{2} \Rightarrow t = \sqrt{\frac{2 s}{g}}

v = g t = \sqrt{2 g s} = \sqrt{2 \times 9.81 \times 20} \approx 19.8 \frac{m}{s}

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