# Pendulum's maximum momentum?

## Homework Statement

A pendulum hung by a string that is 90m (simplicity's sake) can come a maximum of 72m leftward or right ward. Where does it feel it's maximum momentum?

m=meters M=mass

PE=mgh
KE=.5(M)(v)^2
Mv= momentum

## The Attempt at a Solution

My question is: will a pendulum always have its maximum momentum right underneath its point of attachment (0 restoring force)? This is when Potential Energy is zero, so it should have it's maximum kinetic energy, meaning it's maximum speed and thus it's maximum momentum. Right?

So in finding the ball's maximum height, 90^2-72^2=54^2

Meaning it's 36 (90-54) meters above it's lowest point.

Mgh=M(9.8)(36)=353M

if we take the mass out of all equations (and still call it joules) then:

PE=353J

353J=.5(v)^2

v=26.6 m/s

Is this how you would find this kind of answer?

Simon Bridge
Homework Helper
Reasoning from conservation of energy is the usual approach, yeah.
You cannot take the mass out of the equations and still call it joules though - it has to be called "square speed" or "meters per second all squared".

$$mgh = \frac{p^2}{2m} \implies p=m\sqrt{2gh}$$ ... so you cannot do it without knowing the mass.

so you cannot do it without knowing the mass.

Right, but in this case since the mass doesn't change it doesn't change where the ball feels its maximum momentum.

Simon Bridge