Question

The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately 2.5 cm². During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of 80 km/h in 5.5 ms. If the arm has an effective mass of 3.0 kg, what is the compressional stress that the arm withstands during the crash?

Answer 1

initial speed = 80 km/h

= 80 * 5/18 = 22.22 m/s

final speed = 0 m/s

time taken = 5.5 ms

using fomula, acceleration = (final speed - initial speed)/time

= (0 - 22.22)/0.0055

= -4040.4 m/s^2

therefore, magnitude of force = m *a

= 3 * 4040.4

= 12121.212 N

compressional stress of arm = Force / area

= 12121.212/(2.5 * 10^[-4])

= 48484848.48 N/m^2

= 4.85 * 10 ^ 7 N/m^2

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