Answer:
![f=81.96 \ Hz](https://tex.z-dn.net/?f=f%3D81.96%20%5C%20Hz)
Explanation:
Givens
![L=95cm](https://tex.z-dn.net/?f=L%3D95cm)
![m_{sculpture} =13kg](https://tex.z-dn.net/?f=m_%7Bsculpture%7D%20%3D13kg)
![m_{wire}=5g](https://tex.z-dn.net/?f=m_%7Bwire%7D%3D5g)
The frequency is defined by
![f=\frac{v}{\lambda}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7Bv%7D%7B%5Clambda%7D)
Where
is the speed of the wave in the string and
is its wave length.
The wave length is defined as ![\lambda = 2L = 2(0.95m)=1.9m](https://tex.z-dn.net/?f=%5Clambda%20%3D%202L%20%3D%202%280.95m%29%3D1.9m)
Now, to find the speed, we need the tension of the wire and its linear mass density
![v=\sqrt{\frac{T}{\mu} }](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7BT%7D%7B%5Cmu%7D%20%7D)
Where
and the tension is defined as ![T=m_{sculpture} g=13kg(9.81 m/s^{2} )=127.53N](https://tex.z-dn.net/?f=T%3Dm_%7Bsculpture%7D%20g%3D13kg%289.81%20m%2Fs%5E%7B2%7D%20%29%3D127.53N)
Replacing this value, the speed is
![v=\sqrt{\frac{127.53N}{5.26 \times 10^{-3} } }=155.71 m/s](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7B127.53N%7D%7B5.26%20%5Ctimes%2010%5E%7B-3%7D%20%7D%20%7D%3D155.71%20m%2Fs)
Then, we replace the speed and the wave length in the first equation
![f=\frac{v}{\lambda}\\f=\frac{155.71 m/s}{1.9m}\\ f=81.96Hz](https://tex.z-dn.net/?f=f%3D%5Cfrac%7Bv%7D%7B%5Clambda%7D%5C%5Cf%3D%5Cfrac%7B155.71%20m%2Fs%7D%7B1.9m%7D%5C%5C%20f%3D81.96Hz)
Therefore, the frequency is ![f=81.96 \ Hz](https://tex.z-dn.net/?f=f%3D81.96%20%5C%20Hz)
Answer:
1.2cm
Explanation:
V=(2ev/m)^1/2
=(2*1.6*10^19 x2500/ 1.67*10^27)^1/2
=6.2x10^5m/s
Radius of resulting path= MV/qB
= 1.67*10^-27x6.92*10^6/1.6*10^-16 x0.6
=0.012m
=1.2cm
Solution :
a). B at the center :
![$=\frac{u\times I}{2R}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7Bu%5Ctimes%20I%7D%7B2R%7D%24)
Here, one of the current is in the clockwise direction and therefore, the other current must be in the clockwise direction in order to cancel out the effect of the magnetic field that is produced by the other.
Therefore, the answer is ANTICLOCKWISE or COUNTERCLOCKWISE
b). Also, the sum of the fields must be zero.
Therefore,
![$\left(\frac{u\times I_1}{2R_1}\right) + \left(\frac{u\times I_2}{2R_2}\right) = 0$](https://tex.z-dn.net/?f=%24%5Cleft%28%5Cfrac%7Bu%5Ctimes%20I_1%7D%7B2R_1%7D%5Cright%29%20%2B%20%5Cleft%28%5Cfrac%7Bu%5Ctimes%20I_2%7D%7B2R_2%7D%5Cright%29%20%3D%200%24)
So,
![$\frac{I_1}{d_1}= \frac{I_2}{d_2}$](https://tex.z-dn.net/?f=%24%5Cfrac%7BI_1%7D%7Bd_1%7D%3D%20%5Cfrac%7BI_2%7D%7Bd_2%7D%24)
![$=\frac{16}{21}=\frac{I_2}{32}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B16%7D%7B21%7D%3D%5Cfrac%7BI_2%7D%7B32%7D%24)
A
Therefore, the current in the outer wire is 24.38 ampere.
Answer:
<u>The magnitude of the friction force is 8197.60 N</u>
Explanation:
Using the definition of the centripetal force we have:
![\Sigma F=ma_{c}=m\frac{v^{2}}{R}](https://tex.z-dn.net/?f=%5CSigma%20F%3Dma_%7Bc%7D%3Dm%5Cfrac%7Bv%5E%7B2%7D%7D%7BR%7D)
Where:
- m is the mass of the car
- v is the speed
- R is the radius of the curvature
Now, the force acting in the motion is just the friction force, so we have:
<u>Therefore the magnitude of the friction force is 8197.60 N</u>
I hope it helps you!