thanks for the help. I have one final question: (δT)1 is the random error of a single measurement but what if I wanted to include systematic error? Would I need to take the square of both errors and then take the square root of the sum since the above equations assumes only statistical...
Homework Statement
This has been bothering me for quite a while. I'm trying to work out how many measurements I will need to make to get my uncertainty under a predetermined value. If say I want the a fractional uncertainty \frac{\delta T}{T} to be equal to or under some value for some timed...
Okay I understand now from here: http://en.wikipedia.org/wiki/Kinetic_energy#Derivation
But I've never seen differentials like d(\vec{v}\cdot\vec{v}) before. Why am I not allowed to say d(\vec{v}\cdot\vec{v}) = dv^2 ?
For anyone else wondering about this see here also...
Homework Statement
I'm working through a derivation for work in Thornton's Classical Dynamics but I'm stuck at one step.
\begin{align}
\vec{F} \cdot d\vec{r} &= m\frac{d\vec{v}}{dt} \cdot \frac{d\vec{r}}{dt}dt = m\frac{d\vec{v}}{dt} \cdot \vec{v}dt \\ &= \frac{m}{2}\frac{d}{dt}(\vec{v}\cdot...
Homework Statement
If I have a solid sphere of radius R and charge density +\rho \, C/m^3 and I then remove a smaller sphere of radius b and is a distance a from the center of the larger sphere, what is the electric field inside the cavity?
I get an answer which I think is right. I've look...
Homework Statement
A truck moving at 36 m/s is overtaken by a police car moving at 45 m/s in the same direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck as the police car approaches the truck? (The speed of...