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

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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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