Find Speed of Cylinder Rolling Down Loop | m=0.710 kg, h=333 cm, R=49.95 cm

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The discussion focuses on calculating the speed of a uniform solid cylinder (mass = 0.710 kg) rolling down a ramp with a height of 333 cm and a loop radius of 49.95 cm. The user initially applied the conservation of energy principle but miscalculated the height difference affecting the final speed. The correct formula derived is v = √(4/3)gh, where g is 9.8 m/s² and h is the height difference between the ramp and the loop. The user corrected the height consideration and acknowledged the mistake in their calculations.

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A uniform solid cylinder (m=0.710 kg, of small radius) is at the top of a ramp, with height height of 333 cm and which has a loop of radius, R = 49.95 cm at the bottom. Which has friction. The cylinder starts from rest and rolls down the ramp without sliding and goes around the loop. Find the speed of the cylinder at the top of the loop.

I used conservation of energy
[tex]mgh= (1/2)mv^2 + (1/2)I \omega ^2[/tex]
[tex]mgh = (1/2)mv^2 + (1/2)(1/2)(MR^2)(v/r)^2[/tex]
[tex]mgh= (1/2)mv^2 +(1/4)mv^2[/tex]
Solving for v gave me [tex]\sqrt (4/3)gh[/tex]
So plugging in 9.8 for g and 3.33 for h gave me a speed of 6.60 m/s which wasn't right.
Can someone help me?
 
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h should be the difference in height between the top of the ramp and the top of the loop.
 
I got it. Thanks
 

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