Conical pendulum: what are the tension and the angle?

AI Thread Summary
The discussion centers on a physics problem involving a conical pendulum where a 1.5 kg rock is whirled in a horizontal circle with a string length of 0.8 m and a speed of 5 m/s. Participants debate whether the given information is sufficient to solve for the tension and angle, with some expressing skepticism about the problem's clarity. The importance of maintaining algebraic expressions rather than plugging in numbers prematurely is emphasized for better verification of work. A key equation relating centripetal force and gravitational force is mentioned, suggesting that the problem may indeed be solvable with the right approach. Overall, the conversation highlights the need for clarity in problem statements and the importance of algebraic manipulation in physics.
pkc111
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Homework Statement
A rock with a mass 1.5 kg is being whirled in a horizontal circle on a string 0.8 m long. The speed of the rock is a constant 5 m/s. Find the magnitude and direction of the tension in the string.
COMMENT: There seems to be too many unknowns here.
Relevant Equations
Fc = mv2/r
W = mg
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1585533348673.png
 
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pkc111 said:
Homework Statement:: A rock with a mass 1.5 kg is being whirled in a horizontal circle on a string 0.8 m long. The speed of the rock is a constant 5 m/s. Find the magnitude and direction of the tension in the string.
COMMENT: There seems to be too many unknowns here.
Relevant Equations:: Fc = mv2/r
W = mg

View attachment 259616View attachment 259617
So what is cos2(θ) in terms of sin(θ)?

By the way, it is far better style to keep everything algebraic. Don't plug in numbers until the end. For one thing, more people will take the trouble to check your work.
 
Thank you for your reply.
Are you saying that this question is solvable with the information provided in the question?
 
Cos my gut feeling is the question is wrongly written ..as every other question in this high school physics textbook chapter needs only very straightforward maths...Is someone able to say whether the information is enough to define a specific conic pendulum case which is solvable?
 
pkc111 said:
Thank you for your reply.
Are you saying that this question is solvable with the information provided in the question?
In your last equation in post #1 there is only one unknown, so it should be solvable.
I repeat, what equation relates sin to cos (and involves no other trig function)?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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