Answer: F = ma = 1000 * 6.25 = 6,250 N.
Step-by-step explanation:
The centripetal acceleration (a) of an object moving in a circular path is given by:
a = v^2 / r
where v is the tangential velocity and r is the radius of the loop.
The force factor, or centripetal force (F), required to keep an object moving in a circular path is given by:
F = ma
where m is the mass of the object.
At the bottom of the loop, where the tangential velocity is 10 m/s, the centripetal acceleration is:
a = v^2 / r = 10^2 / 9 = 100 / 9 m/s^2
The force factor required to maintain this acceleration depends on the mass of the object. For example, if the mass of the roller coaster car is 1000 kg, then the force factor required would be:
F = ma = 1000 * (100 / 9) = 11,111 N
At the top of the loop, where the tangential velocity is 7.5 m/s, the centripetal acceleration is:
a = v^2 / r = 7.5^2 / 9 = 6.25 m/s^2
Using the same mass of 1000 kg, the force factor required would be:
F = ma = 1000 * 6.25 = 6,250 N.