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Knightycloud
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Homework Statement
Natural length is "l" and when a "m" mass is hanged on the P edge, it dragged by another "L" length. Point "O" is "4L" far from the floor.
1. Find [itex]\lambda[/itex]
2. The mass will be hold at point "O" and released with the starting velocity √(gL). Find the velocity of the mass after it reach "L" distance.
3. Prove that f + [itex]\frac{g}{L}[/itex]x = 0. ( where "f" = acceleration)
4. From the above equation, assume that v2 = [itex]\frac{g}{L}[/itex][ c2 - x2 ] and find the value of "c". (V = velocity)
5. Show that the velocity of mass "m" is zero when it comes to the ground and show that the total time to reach the floor from the point "O" is equal to [itex]\frac{1}{3}[/itex] (3[itex]\sqrt{3}[/itex] - 3 + 2∏)[itex]\sqrt{\frac{L}{g}}[/itex]
Homework Equations
1. Tension = Weight [T = mg]
2. m[itex]\frac{dv}{dt}[/itex] = mg - T
3. T = [itex]\lambda[/itex][itex]\frac{e}{L}[/itex]
4. ω = 2∏f ( where "f" = frequency )
The Attempt at a Solution
I can do half of the problem. And these are the answers.
i . [itex]\lambda[/itex] is mg
ii. Velocity after reaching "L" length = [itex]\sqrt{3gL}[/itex]
iii. Can prove that f + [itex]\frac{g}{L}[/itex]x = 0. ( where "f" = acceleration)
iv. Can prove that velocity is zero when the mass reaches the floor.
I can't find a proper value for the constant "c" and prove the time equation.