Conservation of Momentum
Prelab:
Please write the conservation equations in your derivation.
1) From the conservation equations for momentum and energy,
,
you will get
.
2) From
,
we get
.
3) For inelastic motion, the equation for conservation of momentum is,
.
Thus, the energy loss fraction is,
.
Lab:
Don't forget answering the questions in the assignment!
Uncertainty Sources:
1. Tilting of the track;
2. Rubber band is not perfectly converting the energy;
3. etc.
Bonus:
Google "linearize data" to discover more!
From
,
we let
,
then the first equation becomes
.
Take natural logarithm of both side, then you will get
.
If we take the transformation
,
then the relationship becomes
,
which is a linear relationship! Then you can use LINEST to estimate the coefficient.
(Note: Natural Logarithm can only be applied to non-negative values. In this case, when there's negative value, you can add a negative sign on both sides to make them non-negative!)