An aerobatic airplane pilot experiences
weightlessness as she passes over the top of
a loop-the-loop maneuver.
the acceleration of gravity is 9.8 m/s^2
if her speed is 440 m/s at this time, find the
radius of the loop.
answer in units of km.

20 km

Explanation:

Draw a free body diagram.  Weightlessness means there's no normal force.

Sum of forces in the centripetal direction (-y):

∑F = ma

mg = m v² / r

g = v² / r

r = v² / g

r = (440 m/s)² / (9.8 m/s²)

r = 20,000 m

r = 20 km

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2