Kinetic & Potential Energy of a Pendulum

[VicGong]

Homework Statement

Assume a pendulum of length L is released from angle theta. When it swings to its lowest point (at the point where the string is vertical). the string hits a rod that is perpendicular to the plane of the swing and positioned at 1/2 L. Find an expression for the angle to which the pendulum will swing after hitting the bar.

Relevant Equations

PE = mgh
KE = 1/2 mv^2
TME = PE + KE

When the pendulum is released, the Kinetic Energy should be 0. When the pendulum is at the bottom/hits the rod, it should have 0 potential energy. However, I don't quite understand what happens after it hits the rod.

 

[Orodruin]

When the pendulum is at the bottom/hits the rod, it should have 0 potential energy.

This depends on where you put the reference level for your potential.

What conservation laws are applicable?

 

[BvU]

Hello @VicGong,

$\qquad$ !​

what happens after it hits the rod

Can you describe it in words ?
Perhaps do the experiment ?

Note that "it should have 0 potential energy" defines a zero-point for the potential energy.

[edit] Ah! Oro was a fraction of a second faster

$\$

 

[kuruman]

However, I don't quite understand what happens after it hits the rod.

When the string hits the rod, the pendulum bob is moving at some speed $v_0$ which you can easily calculate. The subsequent motion will be that of a pendulum of length $\frac{1}{2}L$ that has speed $v_0$ at the lowest point of its motion.