A pendulum consists of a point mass swinging back and forth at the end of a mass

Question

A pendulum consists of a point mass swinging back and forth at the end of a massless string of length R. The motion is in a vertical plane. The string makes a maximum angle of 90 degree with respect to the vertical direction. You can use energy conservation to relate the velocity to the angle, as discussed in class. (a) Find the angle at which the acceleration vector is horizontal. (b) Find the magnitude of the acceleration at that angle. (c) Find the angle at which the horizontal component of the acceleration is maximum. (d) Find the magnitude of the acceleration at that angle.

Explanation / Answer

energy conservation theorem=

T-mgcos (theta)=mv2 /R

because given theta=90

so T=mv2/R

the horizontal component of T provides centriprtal acceleration.

the acceleration vector is horizontal when the angle is 90.

and value of a is

a =v2 /r

a= sqrt(at2 +ar2 )

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