If the jet is moving at a speed of 1500 km/h 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 6.0 g's.
To determine the minimum radius of the circle, we need to first calculate the centripetal acceleration at the lowest point. Centripetal acceleration is given by the formula:
a = (v^2) / r
Where:
a = centripetal acceleration
v = velocity
r = radius
Given:
v = 1500 km/h
a = 6.0 g's = 6.0 * 9.8 m/s^2 (converting g's to m/s^2)
Let's start by converting the velocity from km/h to m/s:
1500 km/h * (1000 m/km) * (1/3600 h/s) = v m/s
Simplifying the conversion, we have:
1500 * (1000/3600) = v m/s
v ≈ 416.67 m/s
Now, let's substitute the values into the centripetal acceleration formula:
6.0 * 9.8 = (416.67^2) / r
Let's solve for r:
6.0 * 9.8 * r = 416.67^2
r = (416.67^2) / (6.0 * 9.8)
Calculating the value of r:
r ≈ (416.67^2) / (6.0 * 9.8)
r ≈ 1801.70 meters
Therefore, the minimum radius of the circle should be approximately 1801.70 meters to ensure that the centripetal acceleration at the lowest point does not exceed 6.0 g's.