Question

8. A horse rider falls off her horse and strikes her head on the ground. Luckily, she is wearing a helmet. At the first instant of impact the vertical velocity of the rider’s head is 5.8 m/s. The mass of the rider’s head is 5 kg. The helmet is lined with energy absorbing material that is 3.0cm thick. The thickness of the hard outer shell of the helmet, as well as the innermost padding used for fit and comfort allow the head to displace 1.5 cm during the impact. The crushing and compressing of the helmet’s the energy absorbing material and padding as well as the displacement of the dirt her head hits accounts for this 1.5cm displacement. What is the average force exerted by the helmet on the rider’s head during the impact from the fall?

9. What is the peak force exerted by the helmet on the rider’s head during the impact from the fall?

10. The criteria for a catastrophic head injury are often expressed in terms of the peak acceleration of the head. This acceleration is expressed in terms of the acceleration due to gravity, or g. A peak acceleration above 300 g will cause a catastrophic head injury or death. Use your answer from question 9 and Newton’s 2nd Law of Motion to estimate the peak acceleration (expressed as g’s) of the head during this impact. The mass of the head is 5 kg.

Answer 1

Initial veloctiy of the head is , mass of the head

Thus the kinectic energy of the mass and helmet system is

by putting all the quantities in the above equaiton, we get

Given is that the head is displced 1.5 cm or 0.015m during the impact

therefore the work done by the helmet and padding to secure the head is

we know that the energy never lost, it just changes from one form to other. In the final position the head is in rest, therfore the kinetic energy is converted into the work done by the helmet to stop the head

thus

Hence the average force exerted by the helmet on the rider's head duting the impact from the fall is 5606.67 N