To calculate the compressional stress that the arm withstands during the crash, we can use the formula:
Stress = Force / Area
First, let's calculate the force exerted on the arm during the crash. We can use Newton's second law, which states that force is equal to mass multiplied by acceleration:
Force = mass * acceleration
The acceleration can be calculated using the formula for average acceleration:
Acceleration = (final velocity - initial velocity) / time
Convert the initial velocity from km/h to m/s:
Initial velocity = 80 km/h * (1000 m/1 km) * (1 h/3600 s) = 22.22 m/s
Substituting the values into the formula:
Acceleration = (0 - 22.22 m/s) / 4.2 ms = -5276.19 m/s^2
Now, substitute the values for mass and acceleration into the formula for force:
Force = 3.0 kg * -5276.19 m/s^2 = -15828.57 N
Since the compressional stress refers to force per unit area, we can substitute force and area into the formula for stress:
Stress = -15828.57 N / 2.5 cm^2 = -6331.43 Pa
The compressional stress that the arm withstands during the crash is approximately -6331.43 Pa. Note that stress is a scalar quantity, so the negative sign indicates a compressional stress.