long (a guess), how with what frequency should you spin the bucket to prevent yo

Question

long (a guess), how with what frequency should you spin the bucket to prevent yourself from getting wet? Consider the following diagram for problems 9 and 10.

9. A 0.73 ball on the end of a string is spun at a constant speed of 6m/s. If the string is 1.2m long, what is the tension in the string at the top of the circle? What is the tension at the bottom of the circle?

10. A ball is spun around in a uniform vertical circle of r = 2.37m, as shown in the diagram. If the tension at the bottom is twice that at the top, how fast is the ball going

Explanation / Answer

Here,

Guessing the frequency for moving the bucket ,

the frequency should be more than 2 Hz.

9)

m = 0.73 Kg

v = 6 m/s

L = 1.2 m

Tension at the top of circle = m* v^2/L - m * g

Tension at the top of circle = 0.73 * (6^2/1.2 - 9.8)

Tension at the top of circle = 14.8 N

the Tension at the top of circle is 14.8 N

at the bottom of circle

Tension at the bottom of circle = m * v^2/L + m * g

Tension at the bottom of circle = 0.73 * (6^2/1.2 + 9.8)

Tension at the bottom of circle = 29.1 N

10)

let the speed of the ball is v

Tension at the bottom = 2 * tension at the top

m * v^2/r + m * g = 2 * (m* v^2/r - m * g)

v^2/2.37 + 9.8 = 2 * v^2/2.37 - 2 * 9.8

solving for v

v = 8.35 m/s

the speed of the ball is 8.35 m/s

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