Answer:
momentum formula = Mass × Velocity
Answer:
If conditions are just right, you can see Polaris from just south of the equator. Although Polaris is also known as the North Star, it doesn't lie precisely above Earth's North Pole. If it did, Polaris would have a declination of exactly 90 degree.
Explanation:
Answer:
the bending moment will be W from either sides
Explanation:
bending moment= force (load) * perpendicular distance, if I understand the question the distance will be 1/2 of the length
=> f x 1/2(l) =W*1/2(2) =W
Answer:
I think the answer is
C) iron nails are attracted towards all materials
Answer:
From the question we are told that
The length of the rod is ![L_o](https://tex.z-dn.net/?f=L_o)
The speed is v
The angle made by the rod is ![\theta](https://tex.z-dn.net/?f=%5Ctheta)
Generally the x-component of the rod's length is
![L_x = L_o cos (\theta )](https://tex.z-dn.net/?f=L_x%20%3D%20%20L_o%20cos%20%28%5Ctheta%20%29)
Generally the length of the rod along the x-axis as seen by the observer, is mathematically defined by the theory of relativity as
![L_xo = L_x \sqrt{1 - \frac{v^2}{c^2} }](https://tex.z-dn.net/?f=L_xo%20%20%3D%20%20L_x%20%20%5Csqrt%7B1%20%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D)
=> ![L_xo = [L_o cos (\theta )] \sqrt{1 - \frac{v^2}{c^2} }](https://tex.z-dn.net/?f=L_xo%20%20%3D%20%20%5BL_o%20cos%20%28%5Ctheta%20%29%5D%20%20%5Csqrt%7B1%20%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D)
Generally the y-component of the rods length is mathematically represented as
![L_y = L_o sin (\theta)](https://tex.z-dn.net/?f=L_y%20%20%3D%20%20L_o%20%20sin%20%28%5Ctheta%29)
Generally the length of the rod along the y-axis as seen by the observer, is also equivalent to the actual length of the rod along the y-axis i.e
Generally the resultant length of the rod as seen by the observer is mathematically represented as
![L_r = \sqrt{ L_{xo} ^2 + L_y^2}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%20%5Csqrt%7B%20L_%7Bxo%7D%20%5E2%20%2B%20L_y%5E2%7D)
=> ![L_r = \sqrt{[ (L_o cos(\theta) [\sqrt{1 - \frac{v^2}{c^2} }\ \ ]^2+ L_o sin(\theta )^2)}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%5Csqrt%7B%5B%20%28L_o%20cos%28%5Ctheta%29%20%5B%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%5C%20%5C%20%5D%5E2%2B%20L_o%20sin%28%5Ctheta%20%29%5E2%29%7D)
=> ![L_r= \sqrt{ (L_o cos(\theta)^2 * [ \sqrt{1 - \frac{v^2}{c^2} } ]^2 + (L_o sin(\theta))^2}](https://tex.z-dn.net/?f=L_r%3D%20%5Csqrt%7B%20%28L_o%20cos%28%5Ctheta%29%5E2%20%2A%20%5B%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%5D%5E2%20%2B%20%28L_o%20sin%28%5Ctheta%29%29%5E2%7D)
=> ![L_r = \sqrt{(L_o cos(\theta) ^2 [1 - \frac{v^2}{c^2} ] +(L_o sin(\theta))^2}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%5Csqrt%7B%28L_o%20cos%28%5Ctheta%29%20%5E2%20%5B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%5D%20%2B%28L_o%20sin%28%5Ctheta%29%29%5E2%7D)
=> ![L_r = \sqrt{L_o^2 * cos^2(\theta) [1 - \frac{v^2 }{c^2} ]+ L_o^2 * sin(\theta)^2}](https://tex.z-dn.net/?f=L_r%20%3D%20%20%5Csqrt%7BL_o%5E2%20%2A%20cos%5E2%28%5Ctheta%29%20%20%5B1%20-%20%5Cfrac%7Bv%5E2%20%7D%7Bc%5E2%7D%20%5D%2B%20L_o%5E2%20%2A%20sin%28%5Ctheta%29%5E2%7D)
=> ![L_r = \sqrt{ [cos^2\theta +sin^2\theta ]- \frac{v^2 }{c^2}cos^2 \theta }](https://tex.z-dn.net/?f=L_r%20%20%3D%20%20%5Csqrt%7B%20%5Bcos%5E2%5Ctheta%20%2Bsin%5E2%5Ctheta%20%5D-%20%5Cfrac%7Bv%5E2%20%7D%7Bc%5E2%7Dcos%5E2%20%5Ctheta%20%7D)
=> ![L_o \sqrt{1 - \frac{v^2}{c^2 } cos^2(\theta ) }](https://tex.z-dn.net/?f=L_o%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%20%7D%20cos%5E2%28%5Ctheta%20%29%20%7D)
Hence the length of the rod as measured by a stationary observer is
![L_r = L_o \sqrt{1 - \frac{v^2}{c^2 } cos^2(\theta ) }](https://tex.z-dn.net/?f=%20L_r%20%3D%20L_o%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%20%7D%20cos%5E2%28%5Ctheta%20%29%20%7D)
Generally the angle made is mathematically represented
![tan(\theta) = \frac{L_y}{L_x}](https://tex.z-dn.net/?f=tan%28%5Ctheta%29%20%3D%20%20%5Cfrac%7BL_y%7D%7BL_x%7D)
=> ![tan {\theta } = \frac{L_o sin(\theta )}{ (L_o cos(\theta ))\sqrt{ 1 -\frac{v^2}{c^2} } }](https://tex.z-dn.net/?f=tan%20%7B%5Ctheta%20%7D%20%3D%20%20%5Cfrac%7BL_o%20sin%28%5Ctheta%20%29%7D%7B%20%28L_o%20cos%28%5Ctheta%20%29%29%5Csqrt%7B%201%20-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%7D)
=>
Explanation: