A particle starts sliding down a frictionless inclined plane

Asked by admin @ 20/08/2021 in Physics viewed by 277 People

A particle starts sliding down a frictionless inclined plane .If Sn is the distance travelled by it from t=n-1 to t=n seconds .Find the ratio Sn/Sn-1

Answered by admin @ 20/08/2021

We have the formula,

s = ut + (at²) / 2

Here the particle starts sliding down, so it was in rest, hence the initial velocity, u = 0.

Here a = mg sin θ, where m is the mass of the particle, g acceleration due to gravity and θ the angle of inclination of the inclined plane. But we take it as 'a' only.

So, for 'n - 1' seconds,

s = a(n - 1)² / 2

And for 'n' seconds,

s = an² / 2

Given that S_n = s(n) - s(n - 1), i.e.,

S_n = [n² - (n - 1)²] a / 2

S_n = (2n - 1) a / 2

So we can have S_(n - 1) = (2n - 3) a / 2

Hence the ratio will be,

S_n / S_(n - 1) = (2n - 1) / (2n - 3)

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