2 problems: potential erg & tension/friction

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The discussion revolves around two physics problems related to potential energy and tension/friction. Participants verify calculations and provide corrections, noting that the initial velocity for problem 7 should be 4.76 m/s. One user acknowledges a mistake in their calculations for problem 7, realizing they mismanaged a factor of 2. For problem 5, the acceleration was confirmed to be approximately 0.57 m/s², aligning with another user's calculation of 0.56645 m/s². Overall, the thread emphasizes collaborative problem-solving and verification of physics concepts.
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Homework Statement


Question1.jpg

http://i754.photobucket.com/albums/xx183/reddiesel08/Question1.jpg
Question2.jpg

http://i754.photobucket.com/albums/xx183/reddiesel08/Question2.jpg

2. The attempt at a solution
Attempt2.jpg

http://i754.photobucket.com/albums/xx183/reddiesel08/Attempt2.jpg
Attempt.jpg

http://i754.photobucket.com/albums/xx183/reddiesel08/Attempt.jpg

Need someone to check my work and help solve these two problems, thanks in advance to anyone willing to help.
 
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5 is correct, but I did not check the numbers for this one.

7, your method is correct, but your final answer is off. My calculator gives me vi = 4.76 m/s
 
rock.freak667 said:
5 is correct, but I did not check the numbers for this one.

7, your method is correct, but your final answer is off. My calculator gives me vi = 4.76 m/s

Thank you! My mistake on question 7 was I forgot to multiply the 9.8(0.68) by 2 when I moved the 1/2 from the left side to the right side of the equation. I also came up with the answer 4.76 m/s.

On #5 I got the answer a = .57 m/s squared can someone verify this for me.
 
a = 0.56645 m/s^2, so you are correct.
 
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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