During an Olympic bobsled run, the Jamaican team makes a turn of radius 7.9 m at a speed of 97.4 km/h. What is their accelaration in g-units?
To find the acceleration of the Jamaican team in g-units, we need to convert their speed from km/h to m/s and then use the centripetal acceleration formula:
1. First, we need to convert the speed from km/h to m/s. We can do this by multiplying the given speed by 1000/3600, since there are 1000 meters in a kilometer and 3600 seconds in an hour:
Speed in m/s = 97.4 km/h × (1000 m / 3600 s)
≈ 27.1 m/s
2. Next, we can calculate the centripetal acceleration using the formula:
Ac = v^2 / r
where "Ac" is the centripetal acceleration, "v" is the velocity, and "r" is the radius.
Plugging in the values we have:
Ac = (27.1 m/s)^2 / 7.9 m
= 734.41 m^2/s^2 / 7.9 m
≈ 92.93 m/s^2
3. Finally, we can convert the centripetal acceleration to g-units. One g-unit is equal to the acceleration due to gravity, approximately 9.8 m/s^2. We can divide the centripetal acceleration by 9.8 to find the acceleration in g-units:
Acceleration in g-units = 92.93 m/s^2 / 9.8 m/s^2
≈ 9.49 g-units (rounded to two decimal places)
Therefore, the acceleration of the Jamaican team during the bobsled run is approximately 9.49 g-units.