- #1
slingboi
- 8
- 0
I have tried it and the units end up being Nm^-2 (the unit of stress) however the unit for joules is Nm.
Calculating Stress in Joules: My Experience
- Thread starter slingboi
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- Experience Joules Stress
AI Thread Summary
The discussion focuses on the relationship between stress and energy calculations in joules. Stress is defined as force per unit area (Nm^-2), while joules represent energy as force times distance (Nm). By multiplying stress by volume, the units effectively convert to energy, clarifying the connection. Participants confirm understanding of this relationship, indicating successful comprehension of the calculations involved. The explanation resolves initial confusion about unit conversions in stress and energy.
- #2
Studiot
- 5,440
- 10
How do you work this out?
Strain is length/length ie dimensionless.
Stress is force/area. ie force/m2. Multiply this by volume (m3) and you get force time distance ie work (energy).
It does work out
- #3
slingboi
- 8
- 0
Ohhh, thanks! i get it now!
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire.
We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges.
By using the Lorenz gauge condition:
$$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$
we find the following retarded solutions to the Maxwell equations
If we assume that...
Maxwell’s equations imply the following wave equation for the electric field
$$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2}
= \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$
I wonder if eqn.##(1)## can be split into the following transverse part
$$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2}
= \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$
and longitudinal part...
The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing.
The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##.
But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
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