If the jet is moving at a speed of 1800 at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.4 's
The jet is moving in a verticle loop
You did not give units so I assume 1800 m/s and 6.4 m/s^2
Ac = v^2/r
6.4 = 1800^2/r
r = 1800^2/6.4 in meters if you gave me metric units
To determine the minimum radius of the circle, we can use the equation for centripetal acceleration:
Centripetal acceleration (a) = (v^2) / r
Where:
a is the centripetal acceleration,
v is the velocity of the jet, and
r is the radius of the circle.
We are given that the velocity of the jet at the lowest point is 1800 m/s, and we need to find the minimum radius that ensures the centripetal acceleration does not exceed 6.4 m/s^2.
Let's plug in the values and solve for the radius:
6.4 = (1800^2) / r
To isolate the variable r, let's rearrange the equation:
r = (1800^2) / 6.4
Now, we can calculate the radius by substituting the given values into the equation:
r = (1800^2) / 6.4
r = 3240000 / 6.4
r ≈ 506250 m
Therefore, the minimum radius of the circle to ensure that the centripetal acceleration at the lowest point does not exceed 6.4 m/s^2 is approximately 506250 m.