The bob of the pendulum has a mass of m and is released from rest when it is in

Question

The bob of the pendulum has a mass of m and is released from rest when it is in the vertical position shown (Position 1). The bar that is holding the mass is stiff but has no mass.

(1) Derive equations of the speed of the bob and the tension in the bar at the instant the bob passes through its lowest position (Position 2).

Use the method of energy conservation assuming that the diameter of the bob is much less than the length of the bar.

Start with equations in the equation sheets and show all work.

Explanation / Answer

initially bob has no kinetic energy...lets take our origin at lowest position of bob
therefore initial energy= potential energy=m*g*(2l) where l is the length of the bob.
finally bob has no potential energy,but it has kinetic energy=.5*m*v2

final energy = initial energy

m*g*(2l)=.5*m*v2

v2=4gl

v=2(gl)

force equation is

t-mg=m*v2/l

t=mg+m*v2/l=mg+4mg=5mg

t=5mg

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