A particle executing Simple Harmonic Motion comes to rest at the extreme positions. Is the resultant force on the particle zero at these positions according to Newton's First Law?
Answers
Answer ⇒ No.
Explanation ⇒ A Particle following the Simple Harmonic Motion, will be having the zero velocity at the extreme position.
This is because, As per as the Formula of the velocity,
v² = ω²(A² - x²)
where, ω is the angular frequency of the S.H.M. and A is the Amplitude and x is the distance which the particle in S.H.M Travels from the mean position.
Now, x = A, at extreme.
∴ v² = ω²(A² - A²)
∴ v = 0
This means, it comes to rest at the extreme positions.
Now, The Velocity zero, does not accompany that the Acceleration and Hence force will be zero. Also, Newton's First law does not says this in any way.
Newton's First law say, if no net force is acting on ab body then the state of the body in motion or in rest will not change. But, the Net Force is not zero in the case of the S.H.M.
Magnitude of the Force is given by,
F = -kx , negative sign shows that the force is acting opposite to the displacement.
where, k is the spring constant or Force constant or also called as the constant pf the Simple Harmonic Motion (S.H.M.)
When, the x = A, At Extremes,
then F = -kA , which is non-zero.
Thus, Resultant Force is non-zero at this position.
Hope it helps.