You swing a bucket full of water in a vertical circle at the end of a rope. The mass of the bucket plus the water is 1.2 kg. The center of mass of the bucket plus the water moves in a circle of radius 1.4 m. At the instant that the bucket is at the top of the circle, the speed of the bucket is 7.2 m/s. What is the tension in the rope at this instant

Given Information:  

Radius = r = 1.4 m  

Mass of bucket = m = 1.2 kg  

Speed of bucket = 7.2 m/s

Required Information:  

Tension in the rope = Fstring = ?

Tension in the rope = 32.67 N

Explanation:  

So we have a bucket of water which is attached to a rope and the bucket is going through a circular motion.

There are two forces acting on the bucket; tension force of the rope and the weight of the bucket so we can write

Fnet = Fstring + W

Fnet = Fstring + mg

Since the bucket is going through a circular motion,

F = mv²/r

mv²/r = Fstring + mg

Fstring = mv²/r - mg

Fstring = 1.2*(7.2)²/1.4 - 1.2*9.8

Fstring = 44.43 - 11.76

Fstring = 32.67 N

Therefore, at the instant that the bucket is at the top of the circle with speed of 7.2 m/s, the tension in the rope at this instant is 32.67 N.

i wanna say it’s between b and d, leaning more towards b.