An equestrian rider wearing a helmet falls off her horse and strikes her head on

Question

An equestrian rider wearing a helmet falls off her horse and strikes her head on the ground. At the first instant of impact the vertical velocity of the rider's head is 5.8 m/s towards the ground. The mass of the rider's head is 5 kg. The helmet is lined with energy-absorbing material that is 3.0 cm thick. The thickness of the hard outer shell of the helmet, as well as the innermost padding, allows the head to displace 1.5 cm during the impact while crushing and compressing part of the energy-absorbing material and padding as well as the dirt that her head hits. Assume there is only vertical movement at impact. A) What is the average net force exerted on the rider's head during the impact from the fall? B) Estimate the average deceleration during this impact in g's. C) Assuming the threshold for a concussion is 100 g's, what is her risk of sustaining a concussion?

Explanation / Answer

A)

All the KE is converted to work done against the average net force(Favg)

So, 0.5*mv^2 = Favg*d

So, 0.5*5*5.8^2 = Favg*0.015

So, Favg = 5607 N <-----answer

B)

average deceleration, a = Favg/m = 5607/5 = 1121.4 m/s2

In terms of g, a = 1121.4/9.8 = 114.4 g

C)

As the deceleration is greater than 100g , the risk of concussion is high

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