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Risk Analysis Exercise (25 points): US women’s lacrosse ranks second only to American football in the incidence rate of concussions and has high rates of face and eye injuries. Unlike men’s lacrosse, hemlets are not required in women’s lacrosse, which has a no-contact rule. Whether allowing or requiring hemet use will decrease head injury in women’s lacrosse remains controversial. Read the article and write a one to twopage plan for performing of detailed risk assessment of helmet use or non-use in women’s lacrosse: a) Summarize the main evidence for and against requiring or allowing but not requiring helmets. b) Identify the important governing biomechanical principles and forces that are likely to be most important in determining head injury in women’s lacrosse. c) Identify issues or questions on which more data need to be obtained. d) Describe how existing and new data can be analyzed to assess risk. e) Describe one or more biomechanical experiments and corresponding mathematical analyses that would help to inform a rigorous risk assessments. 2. The equation of the trajectory of a volleyball player’s hand was found to follow: (angles in radians) (a) Prove that this motion is constrained to a spherical surface (b) Find the velocity of her hand as a function of time (c) Find the tangent vector of the hand motion as a function of time (15 points) 3. A gymnast on the high bar is performing giant circles in a uniform circular motion with a constant tangential velocity of 4 m/s. The gymnast’s center of gravity is 0.8 m from the bar. Determine the angular velocity and acceleration and the tangential and normal components of the linear acceleration of the gymnast’s center of gravity. If the gymnast releases the bar at an instant when his center of gravity is beneath the bar, how far from the bar will the gymnast land if the gymnast’s center of gravity is 2.5 m above the floor at the instant of release and 1 m above his feet when he lands? (15 points) 4. The rotation of the rod OA about O is defined by the relation: � = 0.5�'(.)* sin(3��) where � is in radians and � is in seconds. The collar B slides along the rod so that its distance in meters from O is given by � = 1 + 2� − 6�9 + 8�;. When � = 0.5� determine: (a) the velocity of the collar, (b) the acceleration of the collar, and (c) the acceleration of the collar relative to the rod. (15 points)

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1 a. There are several arguments against the use of helmets for women players, which are as follows:
1. The risk of concussions in women lacrosse is not known
2. Men wear helmets but still have concussions and so helmets do not prevent concussions
3. Concussions can be prevented by proper education and rules
4. When protective gear is used, the games may become rougher
5. The women’s game does not involve physical contact and is about finesse and precision
6. Women lacrosse players did not wear helmets in the past and the tradition should be honored
7. Players will lose the respect of their peers
These arguments can be countered using proper evidence. The following are the counter-arguments that justify the use of helmets in women lacrosse:
1. These are several collected from emergency rooms and other data sources that indicate that there is a lot of risk in women’s lacrosse due to concussion
2. Concussions in men lacrosse players is due to collisions unlike head injuries caused due to contact with sticks or balls, as is the case with women players
3. Even though there is education and emphasis on rules, there is inherent risk due to the nature of the game. Swinging sticks and balls flying are a part of the game and protective helmets are needed to avoid them.
4. The increased aggressiveness should be mitigated by proper enforcement of proper laws by the referees.
5. Even though there is no-contact rule in women’s game, it does not save from head injuries caused due to contact with the stick or the ball. It is found that stick or ball contact is the primary reason for head injury in women players, especially for goalies.
6. In the past there was not much awareness and the games were not as competitive as they are now. There is much awareness, athleticism has increased and even the stick designs have changes. So, the risk for head injuries has increased when compared with the past.
7. The claim that players will lack respect from peers by using protective helmets does not lack evidence. Some players may try to show-off others but they are risking their life by doing this.
b. There are two main causes of head injuries, one due to collisions and other due to the contact of sticks or high speed balls. Collisions among players may cause high amount of rotational forces on the head. These rotational forces cause the tissues of the brain to move at different speed causing shear forces, which in turn axonal damage to the brain’s midline internal structures of the, particularly the corpus callosum...

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