Answer:
Bananas go through a unique process known as negative geotropism. Instead of continuing to grow towards the ground, they start to turn towards the sun. The fruit grows against gravity, giving the banana its familiar curved shape.
Answer:
I = 2172.46 A
Explanation:
Given that,
The length of a solenoid, l = 2.1 m
The inner radius of the solenoid, r = 28 cm = 0.28 m
The number of turns in the wire, N = 1000
The magnetic field in the solenoid, B = 1.3 T
We need to find the current carried by it. We know that, the magnetic field in a solenoid is given by :
![B=\mu_o nI\\\\or\\\\B=\mu_o \dfrac{N}{L}I\\\\I=\dfrac{BL}{\mu_o N}](https://tex.z-dn.net/?f=B%3D%5Cmu_o%20nI%5C%5C%5C%5Cor%5C%5C%5C%5CB%3D%5Cmu_o%20%5Cdfrac%7BN%7D%7BL%7DI%5C%5C%5C%5CI%3D%5Cdfrac%7BBL%7D%7B%5Cmu_o%20N%7D)
Put all the values,
![I=\dfrac{1.3\times 2.1}{4\pi \times 10^{-7}\times 1000}\\\\I=2172.46\ A](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7B1.3%5Ctimes%202.1%7D%7B4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5Ctimes%201000%7D%5C%5C%5C%5CI%3D2172.46%5C%20A)
So, it carry current of 2172.46 A.
Answer:
a. The station is rotating at ![1.496 \frac{rev}{min}](https://tex.z-dn.net/?f=%201.496%20%5Cfrac%7Brev%7D%7Bmin%7D)
b. the rotation needed is ![2.8502 \frac{rev}{min}](https://tex.z-dn.net/?f=%202.8502%20%5Cfrac%7Brev%7D%7Bmin%7D)
Explanation:
We know that the centripetal acceleration is
![a_{c}= \omega ^2 r](https://tex.z-dn.net/?f=a_%7Bc%7D%3D%20%5Comega%20%5E2%20r)
where
is the rotational speed and r is the radius. As the centripetal acceleration is feel like an centrifugal acceleration in the rotating frame of reference (be careful, as the rotating frame of reference is <u>NOT INERTIAL,</u> the centrifugal force is a fictitious force, the real force is the centripetal).
<h3>a. </h3>
The rotational speed is :
![2.7 \frac{m}{s^2} = \omega ^2 * 110 \ m](https://tex.z-dn.net/?f=2.7%20%5Cfrac%7Bm%7D%7Bs%5E2%7D%20%3D%20%5Comega%20%5E2%20%2A%20110%20%20%5C%20m)
![\omega ^2 = \frac{2.7 \frac{m}{s^2}} {110 \ m}](https://tex.z-dn.net/?f=%20%5Comega%20%5E2%20%3D%20%5Cfrac%7B2.7%20%5Cfrac%7Bm%7D%7Bs%5E2%7D%7D%20%7B110%20%5C%20m%7D%20)
![\omega = \sqrt{ 0.02454 \frac{rad^2}{s^2} }](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%20%5Csqrt%7B%200.02454%20%5Cfrac%7Brad%5E2%7D%7Bs%5E2%7D%20%7D%20)
![\omega = 0.1567 \frac{rad}{s}](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%200.1567%20%5Cfrac%7Brad%7D%7Bs%7D%20%20)
Knowing that there are
in a revolution and 60 seconds in a minute.
![\omega = 0.1567 \frac{rad}{s} \frac{1 \ rev}{2\pi \ rad} \frac{60 \ s}{1 \ min}](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%200.1567%20%5Cfrac%7Brad%7D%7Bs%7D%20%20%5Cfrac%7B1%20%5C%20rev%7D%7B2%5Cpi%20%5C%20rad%7D%20%5Cfrac%7B60%20%5C%20s%7D%7B1%20%5C%20min%7D)
![\omega = 1.496 \frac{rev}{min}](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%201.496%20%5Cfrac%7Brev%7D%7Bmin%7D)
<h3>b. </h3>
The rotational speed needed is :
![9.8 \frac{m}{s^2} = \omega ^2 * 110 \ m](https://tex.z-dn.net/?f=9.8%20%5Cfrac%7Bm%7D%7Bs%5E2%7D%20%3D%20%5Comega%20%5E2%20%2A%20110%20%20%5C%20m)
![\omega ^2 = \frac{9.8 \frac{m}{s^2}} {110 \ m}](https://tex.z-dn.net/?f=%20%5Comega%20%5E2%20%3D%20%5Cfrac%7B9.8%20%5Cfrac%7Bm%7D%7Bs%5E2%7D%7D%20%7B110%20%5C%20m%7D%20)
![\omega = \sqrt{ 0.08909 \frac{rad^2}{s^2} }](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%20%5Csqrt%7B%200.08909%20%5Cfrac%7Brad%5E2%7D%7Bs%5E2%7D%20%7D%20)
![\omega = 0.2985 \frac{rad}{s}](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%200.2985%20%5Cfrac%7Brad%7D%7Bs%7D%20%20)
Knowing that there are
in a revolution and 60 seconds in a minute.
![\omega = 0.2985 \frac{rev}{min} \frac{1 \ rev}{2\pi \ rad} \frac{60 \ s}{1 \ min}](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%200.2985%20%5Cfrac%7Brev%7D%7Bmin%7D%20%20%5Cfrac%7B1%20%5C%20rev%7D%7B2%5Cpi%20%5C%20rad%7D%20%5Cfrac%7B60%20%5C%20s%7D%7B1%20%5C%20min%7D%20)
![\omega = 2.8502 \frac{rev}{min}](https://tex.z-dn.net/?f=%20%5Comega%20%20%3D%202.8502%20%5Cfrac%7Brev%7D%7Bmin%7D)