Question

A cyclist in the Tour de France hits an unmarked curb in the race, gets launched from her bike and hits her head on the pavement. Fortunately she is wearing a helmet and at the momen of impact the vertical velocity of her head is 5.3 m/s. The Giro helmet she is wearing is lined with energy-absorbing material that is 2.3 cm thick and the thickness of the hard outer shell along with the innermost padding allows the 4.5 kg head to displace 1.3 cm while coming to a stop and crushing and compressing the energy-absorbing material and padding during the impact with the ground. a) What is the average force exerted by the helmet on the cyclist's head during the impact from the crash? (2 pt) b) If the maximum force exerted by the helmet on the cyclist's head is approximately twice the average force determined in partya), what is the maximum or peak acceleration in m/s²

experienced by the head during the crash? ( 2pt) c) Research has found that a concussion can be sustained when the head sustains an impact of 80 g (acceleration due to gravity) and a catastrophic head injury or death can occur when the head experiences 300 g or greater. Determine how many times greater than g this maximum acceleration is due to the crash and indicate if the rider was most likely to i) not sustain a concussion, ii) did sustain a concussion or iii) sustained a catastrophic head injury.

Answer 1

The average force exerted by the helmet on the cyclist's head during the impact is 23.85 N. The maximum acceleration experienced by the head during the crash is 10.6 m/s². The rider most likely sustained a concussion from the crash.

Step-by-step explanation:

In order to calculate the average force exerted by the helmet on the cyclist's head during the impact from the crash, we can use the formula:

average force = mass × acceleration

The mass of the head is given as 4.5 kg and the change in velocity is given as 5.3 m/s. Therefore, the average force can be calculated as:

average force = 4.5 kg × 5.3 m/s = 23.85 N

To calculate the maximum or peak acceleration experienced by the head during the crash, we can use the formula:

peak acceleration = maximum force / mass

We already know the mass is 4.5 kg and the maximum force is approximately twice the average force, which means:

maximum force = 2 × 23.85 N = 47.7 N

Now we can calculate the peak acceleration as:

peak acceleration = 47.7 N / 4.5 kg = 10.6 m/s²

To determine how many times greater than g this maximum acceleration is due to the crash, we can use the formula:

acceleration in multiples of g = (peak acceleration / g)

Given that acceleration due to gravity, g, is 9.8 m/s², we can calculate:

acceleration in multiples of g = (10.6 m/s² / 9.8 m/s²) = 1.08

Since the maximum acceleration is less than 300 g, but greater than 80 g, the rider most likely sustained a concussion from the crash.