I\'m looking at classicalmechanics, by john taylor. ch4 q.8 step 2. I\'m trying

Question

I'm looking at classicalmechanics, by john taylor. ch4 q.8 step 2.
I'm trying to get from either
N-mgcos(x)= (mgR(1-cos(x))/R
OR
N-mgcos(x)= -(mgR(1-cos(x))/R
to cos(x)=1/2, (when you let N=0), but I either get cos(x)=2 OR 2/3respectively. The question states: A frictionless puck on a fixed sphere with radius R is given anudge and slides down. Through what vertical height will is dexcendbefore t leaves the surace of the sphere. Use conservation ofenergy to find puck's speed as a function of height, then usenewton's second to fing the the normal force of the sphere on thepuck. at what value of the N does the puck leave thesphere. I'm looking at classicalmechanics, by john taylor. ch4 q.8 step 2.
I'm trying to get from either
N-mgcos(x)= (mgR(1-cos(x))/R
OR
N-mgcos(x)= -(mgR(1-cos(x))/R
to cos(x)=1/2, (when you let N=0), but I either get cos(x)=2 OR 2/3respectively. The question states: A frictionless puck on a fixed sphere with radius R is given anudge and slides down. Through what vertical height will is dexcendbefore t leaves the surace of the sphere. Use conservation ofenergy to find puck's speed as a function of height, then usenewton's second to fing the the normal force of the sphere on thepuck. at what value of the N does the puck leave thesphere.

Explanation / Answer

thanks that is also what i got.  but the answer seems to saying the answer is cos(x)=1/2.  but i'm glad to see you're getting the same thing, and that my q made sense.  thanks

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