A string can withstand a force of 135 N before breaking. A 2.0 kg mass is tied to the string and whirled in a horizontal circle with a radius of 1.10 m. What is the maximum speed that the mass can be whirled at before
the string breaks?

The mass would have centripetal acceleration a given by

a = v ² / R

where

v = tangential speed of the mass

R = length of the string

By Newton's second law, a maximum tension of F = 135 N would apply an acceleration of

135 N = (2.0 kg) a   →   a = 67.5 m/s²

which requires a tangential speed v of

67.5 m/s² = v ² / (1.10 m)   →   v = √((67.5 m/s²) (1.10 m)) ≈ 8.62 m/s

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

at right angles to each other