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 = ?
Answer:
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.