Answer:
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Explanation:
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Answer:
Please find the answer in the explanation.
Explanation:
When you try to move the magnet back and forth between the two coils, the motion of the magnet will be oscillatory and this action will cause current and EMF to induce
According to law of Faraday, current or EMF will be induced when a magnet is moved in the presence of coils
If the magnet continues to move back and forth between the two coils, what might be causing this will be the presence of the induced electromagnetic force between the two coils.
To solve this problem, it is necessary to use the concepts related to the Force given in Newton's second law as well as the use of the kinematic equations of movement description. For this case I specifically use the acceleration as a function of speed and time.
Finally, we will describe the calculation of stress, as the Force produced on unit area.
By definition we know that the Force can be expressed as
F= ma
Where,
m= mass
a = Acceleration
The acceleration described as a function of speed is given by
![a = \frac{\Delta v}{\Delta t}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%5CDelta%20v%7D%7B%5CDelta%20t%7D)
Where,
Change in velocity
Change in time
The expression to find the stress can be defined as
![\sigma=\frac{F}{A}](https://tex.z-dn.net/?f=%5Csigma%3D%5Cfrac%7BF%7D%7BA%7D)
Where,
F = Force
A = Cross-sectional Area
Our values are given as
![v= 80km/h\\t=5.8*10^3s\\m = 3kg \\A = 2.3*10^{-4}m^2](https://tex.z-dn.net/?f=v%3D%2080km%2Fh%5C%5Ct%3D5.8%2A10%5E3s%5C%5Cm%20%3D%203kg%20%5C%5CA%20%3D%202.3%2A10%5E%7B-4%7Dm%5E2)
Replacing at the values we have that the acceleration is
![a = \frac{\Delta v}{\Delta t}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%5CDelta%20v%7D%7B%5CDelta%20t%7D)
![a = \frac{80km/h(\frac{1h}{3600s})(\frac{1000m}{1km})}{5.8*10^3}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B80km%2Fh%28%5Cfrac%7B1h%7D%7B3600s%7D%29%28%5Cfrac%7B1000m%7D%7B1km%7D%29%7D%7B5.8%2A10%5E3%7D)
![a = 3831.41m/s^2](https://tex.z-dn.net/?f=a%20%3D%203831.41m%2Fs%5E2)
Therefore the force expected is
![F = ma\\F = 3*3831.41m/s^2 \\F = 11494.25N](https://tex.z-dn.net/?f=F%20%3D%20ma%5C%5CF%20%3D%203%2A3831.41m%2Fs%5E2%20%5C%5CF%20%3D%2011494.25N)
Finally the stress would be
![\sigma = \frac{F}{A}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Cfrac%7BF%7D%7BA%7D)
![\sigma = \frac{11494.25N}{2.3*10^{-4}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Cfrac%7B11494.25N%7D%7B2.3%2A10%5E%7B-4%7D%7D)
![\sigma = 49.97*10^6 Pa = 49.97Mpa](https://tex.z-dn.net/?f=%5Csigma%20%3D%2049.97%2A10%5E6%20Pa%20%3D%2049.97Mpa)
Therefore the compressional stress that the arm withstands during the crash is 49.97Mpa
Answer:
Steel is almost 2.9 times heavier the aluminium.