A g (pronounced "gee") is a unit of acceleration. Notice it is italicized. This is so it won't be confused with g (grams). 1 g = 9.8 m/s2. Typically a person will black out if they experience an acceleration of 4 to 6 g for more than a few seconds.
Determine how fast an object must be going if it is to experience a centripetal acceleration of 5.1 g while moving in a circular path of radius 11 m.
To determine how fast an object must be going to experience a centripetal acceleration of 5.1 g while moving in a circular path of radius 11 m, we can use the formula for centripetal acceleration:
a = v^2/r
Where:
a = centripetal acceleration
v = velocity
r = radius
We know that 1 g = 9.8 m/s^2, so we can convert the centripetal acceleration from g to m/s^2:
a = 5.1 g * 9.8 m/s^2 = 49.98 m/s^2
Now, we can rearrange the formula to solve for v:
v = sqrt(a * r)
Substituting the values:
v = sqrt(49.98 m/s^2 * 11 m)
Simplifying:
v = sqrt(549.78 m^2/s^2)
Finally, we take the square root of 549.78 to find the velocity:
v ≈ 23.47 m/s
Therefore, the object must be moving at approximately 23.47 m/s to experience a centripetal acceleration of 5.1 g while moving in a circular path of radius 11 m.