Think of it this way:
-- Any time you have something that means (some number) PER UNIT,
it doesn't matter how many units there are on the table or in the bucket,
because that amount doesn't change the (number) PER UNIT.
-- If oranges cost $1 PER POUND, it doesn't matter how many pounds
you buy, the whole bagful is still $1 PER POUND.
-- If a certain salad dressing has 40 calories PER Tablespoon, it doesn't
matter whether you eat a drop of it or drink the whole jar. You still get
40 calories PER Tablespoon.
-- Density means '(mass) PER unit of volume'. Whether you have a tiny
chip of the substance or a whole truckload of it, there's still the same
amount of mass IN EACH unit of volume.
Answer:
It cancels recoil.
Explanation:
For each action there is an equal an opposite reaction.
The principle of conservation of momentum tell us that if a single spore were ejected the fern would suffer a recoil from it. This recoil would take energy and speed from the spore. But if they are ejected in pairs the recoil is canceled and all the energy is transferred to the spores resulting in higher speeds.
Answer:
Explanation:
Given
speed of Electron ![u=2\times 10^7\ m/s](https://tex.z-dn.net/?f=u%3D2%5Ctimes%2010%5E7%5C%20m%2Fs)
final speed of Electron ![v=4\times 10^7\ m/s](https://tex.z-dn.net/?f=v%3D4%5Ctimes%2010%5E7%5C%20m%2Fs)
distance traveled ![d=1.2\ cm](https://tex.z-dn.net/?f=d%3D1.2%5C%20cm)
using equation of motion
![v^2-u^2=2as](https://tex.z-dn.net/?f=v%5E2-u%5E2%3D2as)
where v=Final velocity
u=initial velocity
a=acceleration
s=displacement
![(4\times 10^7)^2-(2\times 10^7)^2=2\times a\times 1.2\times 10^{-2}](https://tex.z-dn.net/?f=%284%5Ctimes%2010%5E7%29%5E2-%282%5Ctimes%2010%5E7%29%5E2%3D2%5Ctimes%20a%5Ctimes%201.2%5Ctimes%2010%5E%7B-2%7D)
![a=5\times 10^{16}\ m/s^2](https://tex.z-dn.net/?f=a%3D5%5Ctimes%2010%5E%7B16%7D%5C%20m%2Fs%5E2)
acceleration is given by ![a=\frac{qE}{m}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7BqE%7D%7Bm%7D)
where q=charge of electron
m=mass of electron
E=electric Field strength
![5\times 10^{16}=\frac{1.6\times 10^{-19}\cdot E}{9.1\times 10^{-31}}](https://tex.z-dn.net/?f=5%5Ctimes%2010%5E%7B16%7D%3D%5Cfrac%7B1.6%5Ctimes%2010%5E%7B-19%7D%5Ccdot%20E%7D%7B9.1%5Ctimes%2010%5E%7B-31%7D%7D)
Answer:
Im pretty sure 1 is gravity, 2 is force
Explanation:
Answer:
![q=1.95*10^{-7}C](https://tex.z-dn.net/?f=q%3D1.95%2A10%5E%7B-7%7DC)
Explanation:
According to the free-body diagram of the system, we have:
![\sum F_y: Tcos(15^\circ)-mg=0(1)\\\sum F_x: Tsin(15^\circ)-F_e=0(2)](https://tex.z-dn.net/?f=%5Csum%20F_y%3A%20Tcos%2815%5E%5Ccirc%29-mg%3D0%281%29%5C%5C%5Csum%20F_x%3A%20Tsin%2815%5E%5Ccirc%29-F_e%3D0%282%29)
So, we can solve for T from (1):
![T=\frac{mg}{cos(15^\circ)}(3)](https://tex.z-dn.net/?f=T%3D%5Cfrac%7Bmg%7D%7Bcos%2815%5E%5Ccirc%29%7D%283%29)
Replacing (3) in (2):
![(\frac{mg}{cos(15^\circ)})sin(15^\circ)=F_e](https://tex.z-dn.net/?f=%28%5Cfrac%7Bmg%7D%7Bcos%2815%5E%5Ccirc%29%7D%29sin%2815%5E%5Ccirc%29%3DF_e)
The electric force (
) is given by the Coulomb's law. Recall that the charge q is the same in both spheres:
![(\frac{mg}{cos(15^\circ)})sin(15^\circ)=\frac{kq^2}{r^2}(4)](https://tex.z-dn.net/?f=%28%5Cfrac%7Bmg%7D%7Bcos%2815%5E%5Ccirc%29%7D%29sin%2815%5E%5Ccirc%29%3D%5Cfrac%7Bkq%5E2%7D%7Br%5E2%7D%284%29)
According to pythagoras theorem, the distance of separation (r) of the spheres are given by:
![sin(15^\circ)=\frac{\frac{r}{2}}{L}\\r=2Lsin(15^\circ)(5)](https://tex.z-dn.net/?f=sin%2815%5E%5Ccirc%29%3D%5Cfrac%7B%5Cfrac%7Br%7D%7B2%7D%7D%7BL%7D%5C%5Cr%3D2Lsin%2815%5E%5Ccirc%29%285%29)
Finally, we replace (5) in (4) and solving for q:
![mgtan(15^\circ)=\frac{kq^2}{(2Lsin(15^\circ))^2}\\q=\sqrt{\frac{mgtan(15^\circ)(2Lsin(15^\circ))^2}{k}}\\q=\sqrt{\frac{10*10^{-3}kg(9.8\frac{m}{s^2})tan(15^\circ)(2(0.22m)sin(15^\circ))^2}{8.98*10^{9}\frac{N\cdot m^2}{C^2}}}\\q=1.95*10^{-7}C](https://tex.z-dn.net/?f=mgtan%2815%5E%5Ccirc%29%3D%5Cfrac%7Bkq%5E2%7D%7B%282Lsin%2815%5E%5Ccirc%29%29%5E2%7D%5C%5Cq%3D%5Csqrt%7B%5Cfrac%7Bmgtan%2815%5E%5Ccirc%29%282Lsin%2815%5E%5Ccirc%29%29%5E2%7D%7Bk%7D%7D%5C%5Cq%3D%5Csqrt%7B%5Cfrac%7B10%2A10%5E%7B-3%7Dkg%289.8%5Cfrac%7Bm%7D%7Bs%5E2%7D%29tan%2815%5E%5Ccirc%29%282%280.22m%29sin%2815%5E%5Ccirc%29%29%5E2%7D%7B8.98%2A10%5E%7B9%7D%5Cfrac%7BN%5Ccdot%20m%5E2%7D%7BC%5E2%7D%7D%7D%5C%5Cq%3D1.95%2A10%5E%7B-7%7DC)