That is complete bull****. Microwave radiation is not stored anywhere in cooked food, the waves simply move the water molecules up and down as they follow the sinusoidal changing electric field so that they warm up through friction. The food cannot become a source of microwaves itself.
It is...
Then you'll have to solve the differential equation:
\displaystyle F_{motor} - \mu m g = m \ddot{x}\qquad \text{(Newton's II Law)}
\displaystyle \ddot{x} + \mu g - a_0 = 0
Where a_0 is F/m.
In this case, it is clear that the acceleration \ddot{x} of the body will be zero if and only if \mu g...
Please use LaTeX.
Friction force dissipates a power:
\displaystyle P_f = \frac{F\cdot \mathrm{d}s}{\mathrm{d}t} = \mu m g v
Drag force:
\displaystyle P_d = c_1v^2 + c_2 v^3
For some drag coefficients c_1 and c_2
Therefore the limit speed is the real solution of:
\displaystyle...
Gee! You're using the wrong equations for energy! A photon carries a momentum
p = h/\lambda.
According to special relativity:
\displaystyle E^2 = p^2 c^2 + m_0^2 c^4. But photons have no mass! Therefore, no \frac 1 2 mv^2!
\displaystyle \vec{B} = (56\,\mathrm{mT})\hat{\i} + (46\,\mathrm{mT})\hat{\j}
\displaystyle \vec{v} = (2.6\,\mathrm{km/s})\hat{k}
When you have components, it is often wasier to calculate the cross product by finding the determinant of the matrix:
\displaystyle \vec{v}\times\vec{B} =...
The star is approaching the Earth with a speed v \approx 52\ \mathrm{km/s}, which you can calculate by solving:
\displaystyle \lambda^{\prime} = \lambda \left( \frac{1+\beta}{1-\beta}\right)^{1/2} \quad \text{ where } \quad \beta = \frac{v}{c}
You probably overlooked that 6.561 is smaller...
I think Ohm's Law and Faraday's Law would help:
\displaystyle V = iR
\displaystyle \oint\vec{E}\cdot d\vec{l} = \mathcal{E}_{ind} = -\frac{d\Phi_B}{dt}