Question

Thr kinetic energy of the particle moving along a cirlce with radius R depends on the distance covered S as K=αS^2, where α is constant find the force acting on the particle as a function of S​

Answer 1

[_]______________?

F tangential = mat = m dv/dt

F radial = mac = mv^2/R

•K = αS^2

•K = 1/2 mv^2

So we have: 1/2 mv^2 = αS^2

v^2 = 2αS^2 /m

Differentiating wrt time,we get :

=>2v × dv/dt = [ 2α/m ] • 2S ds/dt

Now, ds/dt = v (speed )

So we have dv/dt = 2αS/m

∴F tangential = mdv/ dt = 2αS _[i]

∴F radial = mac = mv^2 /R = 2αS^2/R _[ii]

From [i] and [ii],

Net force = [√F^2 tangential + F^2 radial]

= 2αS √1+S^2/R^2

Answer :

The Net Force acting on the particle is

2αS (√1+S^2/R^2) N

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Answer 2

Explanation:

Net Force acting on the particle is 2as(√1+s^2 2/R^2) N... is the correct answer!!