Answer:
The number of protons in the atom!
Explanation:
Answer:
<em>The final speed of the second package is twice as much as the final speed of the first package.</em>
Explanation:
<u>Free Fall Motion</u>
If an object is dropped in the air, it starts a vertical movement with an acceleration equal to g=9.8 m/s^2. The speed of the object after a time t is:
![v=gt](https://tex.z-dn.net/?f=v%3Dgt)
And the distance traveled downwards is:
![\displaystyle y=\frac{gt^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7Bgt%5E2%7D%7B2%7D)
If we know the height at which the object was dropped, we can calculate the time it takes to reach the ground by solving the last equation for t:
![\displaystyle t=\sqrt{\frac{2y}{g}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%3D%5Csqrt%7B%5Cfrac%7B2y%7D%7Bg%7D%7D)
Replacing into the first equation:
![\displaystyle v=g\sqrt{\frac{2y}{g}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v%3Dg%5Csqrt%7B%5Cfrac%7B2y%7D%7Bg%7D%7D)
Rationalizing:
![\displaystyle v=\sqrt{2gy}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v%3D%5Csqrt%7B2gy%7D)
Let's call v1 the final speed of the package dropped from a height H. Thus:
![\displaystyle v_1=\sqrt{2gH}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v_1%3D%5Csqrt%7B2gH%7D)
Let v2 be the final speed of the package dropped from a height 4H. Thus:
![\displaystyle v_2=\sqrt{2g(4H)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v_2%3D%5Csqrt%7B2g%284H%29%7D)
Taking out the square root of 4:
![\displaystyle v_2=2\sqrt{2gH}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v_2%3D2%5Csqrt%7B2gH%7D)
Dividing v2/v1 we can compare the final speeds:
![\displaystyle v_2/v_1=\frac{2\sqrt{2gH}}{\sqrt{2gH}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v_2%2Fv_1%3D%5Cfrac%7B2%5Csqrt%7B2gH%7D%7D%7B%5Csqrt%7B2gH%7D%7D)
Simplifying:
![\displaystyle v_2/v_1=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v_2%2Fv_1%3D2)
The final speed of the second package is twice as much as the final speed of the first package.
Answer:
(a) 89 m/s
(b) 11000 N
Explanation:
Note that answers are given to 2 significant figures which is what we have in the values in the question.
(a) Speed is given by the ratio of distance to time. In the question, the time given was the time it took the pulse to travel the length of the cable twice. Thus, the distance travelled is twice the length of the cable.
![v=\dfrac{2\times 620 \text{ m}}{14\text{ s}} = \dfrac{1240\text{ m}}{14\text{ s}}=88.571428\ldots \text{ m/s}= 89\text{ m/s}](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7B2%5Ctimes%20620%20%5Ctext%7B%20m%7D%7D%7B14%5Ctext%7B%20s%7D%7D%20%3D%20%5Cdfrac%7B1240%5Ctext%7B%20m%7D%7D%7B14%5Ctext%7B%20s%7D%7D%3D88.571428%5Cldots%20%5Ctext%7B%20m%2Fs%7D%3D%2089%5Ctext%7B%20m%2Fs%7D)
(b) The tension,
, is given by
![v =\sqrt{\dfrac{T}{\mu}}](https://tex.z-dn.net/?f=v%20%3D%5Csqrt%7B%5Cdfrac%7BT%7D%7B%5Cmu%7D%7D)
where
is the speed,
is the tension and
is the mass per unit length.
Hence,
![T = \mu\cdot v^{2}](https://tex.z-dn.net/?f=T%20%3D%20%5Cmu%5Ccdot%20v%5E%7B2%7D)
To determine
, we need to know the mass of the cable. We use the density formula:
![\rho = \dfrac{m}{V}](https://tex.z-dn.net/?f=%5Crho%20%3D%20%5Cdfrac%7Bm%7D%7BV%7D)
where
is the mass and
is the volume.
![m=\rho\cdot V](https://tex.z-dn.net/?f=m%3D%5Crho%5Ccdot%20V)
If the length is denoted by
, then
![\mu = \dfrac{m}{l} = \dfrac{\rho\cdot V}{l}](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%5Cdfrac%7Bm%7D%7Bl%7D%20%3D%20%5Cdfrac%7B%5Crho%5Ccdot%20V%7D%7Bl%7D)
![T = \dfrac{\rho\cdot V}{l} v^{2}](https://tex.z-dn.net/?f=T%20%3D%20%5Cdfrac%7B%5Crho%5Ccdot%20V%7D%7Bl%7D%20v%5E%7B2%7D)
The density of steel = 8050 kg/m3
The cable is approximately a cylinder with diameter 1.5 cm and length or height of 620 m. Its volume is
![V = \pi \dfrac{d^{2}}{4} l](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Cdfrac%7Bd%5E%7B2%7D%7D%7B4%7D%20l)
![T = \dfrac{\rho\cdot\pi d^2 l}{4l}v^2 = \dfrac{\rho\cdot\pi d^2}{4}v^2](https://tex.z-dn.net/?f=T%20%3D%20%5Cdfrac%7B%5Crho%5Ccdot%5Cpi%20d%5E2%20l%7D%7B4l%7Dv%5E2%20%3D%20%5Cdfrac%7B%5Crho%5Ccdot%5Cpi%20d%5E2%7D%7B4%7Dv%5E2)
![T = \dfrac{8050\times\pi\times0.015^2}{4} \times 88.57^2](https://tex.z-dn.net/?f=T%20%3D%20%5Cdfrac%7B8050%5Ctimes%5Cpi%5Ctimes0.015%5E2%7D%7B4%7D%20%5Ctimes%2088.57%5E2)
![T = 11159.4186\ldots \text{ N} = 11000 \text{ N}](https://tex.z-dn.net/?f=T%20%3D%2011159.4186%5Cldots%20%5Ctext%7B%20N%7D%20%3D%2011000%20%5Ctext%7B%20N%7D)
<span>CorrectThe direction of the electric field stays the same regardless of the sign of the charges that are free to move in theconductor.Mathematically, you can see that this must be true since the expression you derived for the electric field isindependent of .Physically, this is because the force due to the magnetic field changes sign as well and causes positive charges tomove in the direction (as opposed to pushing negative charges in the direction). Therefore the result isalways the same: positive charges on the side and negative charges on the side. Because the electric fieldgoes from positive to negative charges will always point in the direction (given the original directions of</span>