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Question

a pendulem is swinging in a semi circular path and the maximum speed of bob at the lowest position is 7m/s. If g= 9.8 m/s2, the lenght of the pendulem is


Solution

Ui + Ki = Uf + Kf
Initial kinetic energy Ki = 0 because the ball is released from rest.
Final potential energy Uf = 0 by definition.
Conclusion: Ui = Kf or mgh = ½ mvf2,
where h is the height from which the ball is released.
Cancel the m's to give: vf = (2gh)½
Determine h from geometry: h = L - Lcos θ = L (1-cos θ)= L(1-cos90)=L,
where theta= angle made with vertical
With Vf=7m/s and θ = 90°, h = L,
vf = (2gL)½
=>L=2.5m

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