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Traumatic brain injury (TBI) while riding roller coasters can occur when external forces cause the brain to accelerate or decelerate rapidly, damaging the brain tissue. TBI is a major cause of death and disability, but the extent to which riding a roller coaster poses an increased risk for TBI is unclear.Riders of coasters experience gravitational forces that may be too large for their body to withstand. Yet, gravitational forces alone cannot predict TBI. The body can endure large gravitational forces if they occur over periods of less than 25 seconds. Predicting the probability of a TBI requires the identification of kinematic parameters such as ride duration, coaster velocity, and acceleration, as well as those forces experienced by the body as a result.Measures such as the Head Injury Criterion (HIC) and Head Impact Power (HIP) are used to aid in TBI predictions. HIC is calculated using acceleration over a certain time interval (usually t = 15 ms) to estimate the likelihood of injury arising from an impact. HIC evaluates only linear acceleration, while HIP accounts for both linear and rotational acceleration. To compare the TBI risk of different activities, scientists often use the following equation:HIC = F x ∆tEquation 1where F is the average linear force and ∆t is the time interval. Scientists conducted an experiment to test the TBI risk of several activities in comparison to roller coasters. The linear accelerations, linear velocities, angular accelerations, and angular velocities of participants’ heads were measured and averaged for four participants across five activities: three roller coaster rides, a pillow fight, and a five m/s bumper hit (see Table 1). The linear acceleration of a pillow fight's results is graphed in Figure 2. Finally, the probability of a concussion, the most common and the least serious type of TBI, was graphed as a function of HIC. Participants 1, 2, 3, and 4 weigh 800, 350, 400, and 750 N, respectively.Table 1 Study resultsFigure 1 Head linear acceleration during pillow fightFigure 2 Predicted risk of concussionQuestion 40Which of the following situations would present Participant 3 with the greatest risk for TBI? A.A linear acceleration of 10 m/s2 for 2 ms in a car crashB.A single punch to the head causing acceleration of 100 m/s2 for 3 msC.Riding a roller coaster of 9 m/s2 sustained for 40 sD.Total body acceleration of 15 m/s2 for 1 ms

Question

Traumatic brain injury (TBI) while riding roller coasters can occur when external forces cause the brain to accelerate or decelerate rapidly, damaging the brain tissue. TBI is a major cause of death and disability, but the extent to which riding a roller coaster poses an increased risk for TBI is unclear.Riders of coasters experience gravitational forces that may be too large for their body to withstand. Yet, gravitational forces alone cannot predict TBI. The body can endure large gravitational forces if they occur over periods of less than 25 seconds. Predicting the probability of a TBI requires the identification of kinematic parameters such as ride duration, coaster velocity, and acceleration, as well as those forces experienced by the body as a result.Measures such as the Head Injury Criterion (HIC) and Head Impact Power (HIP) are used to aid in TBI predictions. HIC is calculated using acceleration over a certain time interval (usually t = 15 ms) to estimate the likelihood of injury arising from an impact. HIC evaluates only linear acceleration, while HIP accounts for both linear and rotational acceleration. To compare the TBI risk of different activities, scientists often use the following equation:HIC = F x ∆tEquation 1where F is the average linear force and ∆t is the time interval. Scientists conducted an experiment to test the TBI risk of several activities in comparison to roller coasters. The linear accelerations, linear velocities, angular accelerations, and angular velocities of participants’ heads were measured and averaged for four participants across five activities: three roller coaster rides, a pillow fight, and a five m/s bumper hit (see Table 1). The linear acceleration of a pillow fight's results is graphed in Figure 2. Finally, the probability of a concussion, the most common and the least serious type of TBI, was graphed as a function of HIC. Participants 1, 2, 3, and 4 weigh 800, 350, 400, and 750 N, respectively.Table 1 Study resultsFigure 1 Head linear acceleration during pillow fightFigure 2 Predicted risk of concussionQuestion 40Which of the following situations would present Participant 3 with the greatest risk for TBI? A.A linear acceleration of 10 m/s2 for 2 ms in a car crashB.A single punch to the head causing acceleration of 100 m/s2 for 3 msC.Riding a roller coaster of 9 m/s2 sustained for 40 sD.Total body acceleration of 15 m/s2 for 1 ms

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Solution

To determine which situation presents the greatest risk for TBI for Participant 3, we need to calculate the Head Injury Criterion (HIC) for each situation using the formula provided: HIC = F x ∆t.

However, we need to remember that F is the average linear force, which is mass x acceleration. Since force is given in Newtons (N), we need to convert the weight of Participant 3 (400N) to mass. We can do this using the formula weight = mass x gravity. Assuming gravity is 9.8 m/s², the mass of Participant 3 is approximately 40.8 kg.

Now we can calculate the HIC for each situation:

A. Car crash: F = mass x acceleration = 40.8 kg x 10 m/s² = 408 N. HIC = F x ∆t = 408 N x 2 ms = 816.

B. Punch: F = mass x acceleration = 40.8 kg x 100 m/s² = 4080 N. HIC = F x ∆t = 4080 N x 3 ms = 12240.

C. Roller coaster: F = mass x acceleration = 40.8 kg x 9 m/s² = 367.2 N. HIC = F x ∆t = 367.2 N x 40 s = 14688.

D. Total body acceleration: F = mass x acceleration = 40.8 kg x 15 m/s² = 612 N. HIC = F x ∆t = 612 N x 1 ms = 612.

Therefore, the situation that would present Participant 3 with the greatest risk for TBI is C. Riding a roller coaster of 9 m/s² sustained for 40 s.

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