A pendulum is held with its string (length 2.0 meters) horizontal and is then re

Question

A pendulum is held with its string (length 2.0 meters) horizontal and is then released from rest. The mass (m = 0.5 kg) swings down and on its way back up, the string is cut when the pendulum makes an angle theta with the vertical.

1. What is the expression for the speed of the mass when the string is cut?

2. What should theta be so that the mass has the largest vertical component of momentum when it reaches the vertical position equal to the lowest point in the swing (y = -2.0 m)?

3. Confirm your results in questions 6 & 7 using MATLAB and Euler's Method.

Explanation / Answer

when it makes angle @ with vertical.

I have come down Rcos@ = 2cos@

so change in gravitational p.E. = mgh = 2mgcos@

it will convert into K.E.

2mgcos@ = mv^2 /2

v = sqrt(4gcos@) = 2sqrt(gcos@)

2.

as it comes down , its potential energy converted in kinetic energy .

More it will come down, it will more K.E. , thus more speed .

So at lowet point it have most k>e. Thus most speed.

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