Answer:
a) x = (0.0114 ± 0.0001) in
, b) the number of decks is 5
Explanation:
a) The thickness of the deck of cards (d) is measured and the thickness of a card (x) is calculated
x = d / 52
x = 0.590 / 52
x = 0.011346 in
Let's look for uncertainty
Δx = dx /dd Δd
Δx = 1/52 Δd
Δx = 1/52 0.005
Δx = 0.0001 in
The result of the calculation is
x = (0.0114 ± 0.0001) in
b) You want to reduce the error to Δx = 0.00002, the number of cards to be measured is
#_cards = n 52
The formula for thickness is
x = d / n 52
Uncertainty
Δx = 1 / n 52 Δd
n = 1/52 Δd / Δx
n = 1/52 0.005 / 0.00002
n = 4.8
Since the number of decks must be an integer the number of decks is 5
The nervous system is responsible for sending, receiving, and interpreting information from all parts of the body. The nervous system monitors and coordinates internal organ function and responds to changes in the external environment. (The role) The central nervous system consists of the brain and the spinal cord. It is part of the overall nervous system that also includes a complex network of neurons, known as the peripheral nervous system. (Central nervous system)
Answer:
It would be hard to test scientifically since it's subjective and can only be proven true if you conducted some experimentations and observations.
Weight in water = mass of block - mass of volume of displaced water
Answer:
![\Delta t=(\frac{20}{g'}+\sqrt{\frac{400}{g'^2}+\frac{100}{g'} } )-(\frac{20}{g}+\sqrt{\frac{400}{g^2}+\frac{100}{g} } )](https://tex.z-dn.net/?f=%5CDelta%20t%3D%28%5Cfrac%7B20%7D%7Bg%27%7D%2B%5Csqrt%7B%5Cfrac%7B400%7D%7Bg%27%5E2%7D%2B%5Cfrac%7B100%7D%7Bg%27%7D%20%20%7D%20%20%29-%28%5Cfrac%7B20%7D%7Bg%7D%2B%5Csqrt%7B%5Cfrac%7B400%7D%7Bg%5E2%7D%2B%5Cfrac%7B100%7D%7Bg%7D%20%20%7D%20%20%29)
Explanation:
Given:
height above which the rock is thrown up, ![\Delta h=50\ m](https://tex.z-dn.net/?f=%5CDelta%20h%3D50%5C%20m)
initial velocity of projection, ![u=20\ m.s^{-1}](https://tex.z-dn.net/?f=u%3D20%5C%20m.s%5E%7B-1%7D)
let the gravity on the other planet be g'
The time taken by the rock to reach the top height on the exoplanet:
where:
final velocity at the top height = 0 ![m.s^{-1}](https://tex.z-dn.net/?f=m.s%5E%7B-1%7D)
(-ve sign to indicate that acceleration acts opposite to the velocity)
![t'=\frac{20}{g'}\ s](https://tex.z-dn.net/?f=t%27%3D%5Cfrac%7B20%7D%7Bg%27%7D%5C%20s)
The time taken by the rock to reach the top height on the earth:
![v=u+g.t](https://tex.z-dn.net/?f=v%3Du%2Bg.t)
![0=20-g.t](https://tex.z-dn.net/?f=0%3D20-g.t)
![t=\frac{20}{g} \ s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B20%7D%7Bg%7D%20%5C%20s)
Height reached by the rock above the point of throwing on the exoplanet:
![v^2=u^2+2g'.h'](https://tex.z-dn.net/?f=v%5E2%3Du%5E2%2B2g%27.h%27)
where:
final velocity at the top height = 0 ![m.s^{-1}](https://tex.z-dn.net/?f=m.s%5E%7B-1%7D)
![0^2=20^2-2\times g'.h'](https://tex.z-dn.net/?f=0%5E2%3D20%5E2-2%5Ctimes%20g%27.h%27)
![h'=\frac{200}{g'}\ m](https://tex.z-dn.net/?f=h%27%3D%5Cfrac%7B200%7D%7Bg%27%7D%5C%20m)
Height reached by the rock above the point of throwing on the earth:
![v^2=u^2+2g.h](https://tex.z-dn.net/?f=v%5E2%3Du%5E2%2B2g.h)
![0^2=20^2-2g.h](https://tex.z-dn.net/?f=0%5E2%3D20%5E2-2g.h)
![h=\frac{200}{g}\ m](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B200%7D%7Bg%7D%5C%20m)
The time taken by the rock to fall from the highest point to the ground on the exoplanet:
(during falling it falls below the cliff)
here:
initial velocity= 0 ![m.s^{-1}](https://tex.z-dn.net/?f=m.s%5E%7B-1%7D)
![\frac{200}{g'}+50 =0+\frac{1}{2} g'.t_f'^2](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7Bg%27%7D%2B50%20%3D0%2B%5Cfrac%7B1%7D%7B2%7D%20g%27.t_f%27%5E2)
![t_f'^2=\frac{400}{g'^2}+\frac{100}{g'}](https://tex.z-dn.net/?f=t_f%27%5E2%3D%5Cfrac%7B400%7D%7Bg%27%5E2%7D%2B%5Cfrac%7B100%7D%7Bg%27%7D)
![t_f'=\sqrt{\frac{400}{g'^2}+\frac{100}{g'} }](https://tex.z-dn.net/?f=t_f%27%3D%5Csqrt%7B%5Cfrac%7B400%7D%7Bg%27%5E2%7D%2B%5Cfrac%7B100%7D%7Bg%27%7D%20%20%7D)
Similarly on earth:
![t_f=\sqrt{\frac{400}{g^2}+\frac{100}{g} }](https://tex.z-dn.net/?f=t_f%3D%5Csqrt%7B%5Cfrac%7B400%7D%7Bg%5E2%7D%2B%5Cfrac%7B100%7D%7Bg%7D%20%20%7D)
Now the required time difference:
![\Delta t=(t'+t_f')-(t+t_f)](https://tex.z-dn.net/?f=%5CDelta%20t%3D%28t%27%2Bt_f%27%29-%28t%2Bt_f%29)
![\Delta t=(\frac{20}{g'}+\sqrt{\frac{400}{g'^2}+\frac{100}{g'} } )-(\frac{20}{g}+\sqrt{\frac{400}{g^2}+\frac{100}{g} } )](https://tex.z-dn.net/?f=%5CDelta%20t%3D%28%5Cfrac%7B20%7D%7Bg%27%7D%2B%5Csqrt%7B%5Cfrac%7B400%7D%7Bg%27%5E2%7D%2B%5Cfrac%7B100%7D%7Bg%27%7D%20%20%7D%20%20%29-%28%5Cfrac%7B20%7D%7Bg%7D%2B%5Csqrt%7B%5Cfrac%7B400%7D%7Bg%5E2%7D%2B%5Cfrac%7B100%7D%7Bg%7D%20%20%7D%20%20%29)