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
[tex]a = \frac{\Delta v}{\Delta t}[/tex]
Where,
[tex]\Delta v =[/tex] Change in velocity
[tex]\Delta t =[/tex]Change in time
The expression to find the stress can be defined as
[tex]\sigma=\frac{F}{A}[/tex]
Where,
F = Force
A = Cross-sectional Area
Our values are given as
[tex]v= 80km/h\\t=5.8*10^3s\\m = 3kg \\A = 2.3*10^{-4}m^2[/tex]
Replacing at the values we have that the acceleration is
[tex]a = \frac{\Delta v}{\Delta t}[/tex]
[tex]a = \frac{80km/h(\frac{1h}{3600s})(\frac{1000m}{1km})}{5.8*10^3}[/tex]
[tex]a = 3831.41m/s^2[/tex]
Therefore the force expected is
[tex]F = ma\\F = 3*3831.41m/s^2 \\F = 11494.25N[/tex]
Finally the stress would be
[tex]\sigma = \frac{F}{A}[/tex]
[tex]\sigma = \frac{11494.25N}{2.3*10^{-4}}[/tex]
[tex]\sigma = 49.97*10^6 Pa = 49.97Mpa[/tex]
Therefore the compressional stress that the arm withstands during the crash is 49.97Mpa
