"A 0.4 kg mass, attached to the end of a 0.75 m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum velocity can the mass have if the string is not to break?"

The maximum velocity the mass can have if the string is not to break = 29.05 m/s

Explanation:

The force balance in the mass:

The tension in the string must always be equal to the force keeping the mass in horizontal circular motion.

The force keeping the mass in circular motion is given by

F = mv²/r

m = mass of body = 0.4 kg

v = speed of the body in circular motion

r = radius of the circular motion = 0.75 m

Maximum tension the string can withstand will correspond to the maximum velocity of the body in horizontal circular motion

T = F = mv²/r

450 = (0.4)(v²)/(0.75)

v² = 450×0.75/0.4 = 843.75

v = 29.05 m/s

Explanation:

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when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.