Physics - Circular motion question me

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A physics question involves a ball of mass 0.50 kg swung in a circle with a radius of 2.0 m and a period of 1.5 s. The calculated speed of the ball is 8.378 m/s, with an acceleration of 35.095 m/s², and a required centripetal force of 17.548 N. The mass of the central object is determined to be 1.79 kg, while the angle of the string with the vertical is calculated to be 74 degrees. Confusion arises regarding the interpretation of the string's length and angles, with some participants sharing their calculations and methods. The discussion highlights the importance of clear explanations and formulas in solving circular motion problems.
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Physics - Circular motion question..please help me..:(

A ball of mass 0.50kg is swung in a circle of radius 2.0m with a period of 1.5s.

a.) what is the speed of the ball?

b.) what is the acceleration of the Ball?

C.) What centripetal force must be exerted by the string that keeps the ball in orbit?

d.) what is the mass of the central object?

e.) What angle does the string make with the veritical?

f.) how long is the strong, L?

Thanks so much if u can help...it would be good to show me the explanation and the formulas used as well...thanks a bunch!
 
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a) 8.378m/s
b) 35.095 m/s^2
c) 17.548N
d) 1.79kg
e) 0?
f) 2m?
 
ooh! thanks a lot, i did those questions earlier..
for 8 however, i got 1.85 kg.
For e.), i got 74 degrees...for this one just did the pythagoreum thereom, since one angle is 90 degrees, and in d.) we found the other angle being 16 degrees..
but yah, thanks so much!
 
I don't know how you got 1.85kg, if you got c, just divide that by the acceleration (9.8) As for e and f, I have no clue what it wants @.@
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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