Conservation of Energy/ Centripetal Acceleration HELP

[vinny380]

A particle of mass m slides down a fixed, frictionless sphere of radius R. starting from rest at the top.
a. In terms of m, g, R. and theta, determine each of the following for the particle while it is sliding on the
sphere.
i. The kinetic energy of the particle
ii. The centripetal acceleration of the mass
iii. The tangential acceleration of the mass
b. Determine the value of theta at which the particle leaves the sphere.

I can not get the picture on here, but it is basically a picture of a sphere with a mass on the top of the sphere, and the same mass moved slightly to the right. The angle between these two masses is theta, making a V to the center of the circle.

For Part A ...
I: PE=KE
mgr=PE
mgr(r-rcos(theta))=KE
mgr(1-cos(theta))=KE <-- Does this look good?

II: Centripetal Acceleration:
A= v^squared/r
A= 2g(1-cos(theta)) <---- Look good?

III. Totally lost... help!

B. Not sure either ...sigh

 

[OlderDan]

A particle of mass m slides down a fixed, frictionless sphere of radius R. starting from rest at the top.
a. In terms of m, g, R. and theta, determine each of the following for the particle while it is sliding on the
sphere.
i. The kinetic energy of the particle
ii. The centripetal acceleration of the mass
iii. The tangential acceleration of the mass
b. Determine the value of theta at which the particle leaves the sphere.

I can not get the picture on here, but it is basically a picture of a sphere with a mass on the top of the sphere, and the same mass moved slightly to the right. The angle between these two masses is theta, making a V to the center of the circle.

For Part A ...
I: PE=KE ==> PE + KE = constant
mgr=PE ==> mgr = Initial PE
mgr(r-rcos(theta))=KE <== too maany r
mgr(1-cos(theta))=KE <-- Does this look good? Yes

II: Centripetal Acceleration:
A= v^squared/r
A= 2g(1-cos(theta)) <---- Look good? Yes

III. Totally lost... help!

B. Not sure either ...sigh

With some corrections made in the quote I and II are OK. For III I think you need to take your equation for I and express the KE in terms of velocity. Take the derivative wrt to time of both sides and see what you can do with that. For B you need to think about where the force comes from that provides the centripetal acceleration. When is there not enough force to maintain the circular motion?

 

[AVD]

Vincent Russo ! this is Mr. Lavy- you shouldn't be asking for homework help for my class! HAHAHA

 

[BoNyKiD07]

wow. mr lavy stalks. who knew =p lol

btw, I tried the first wow problem and the answer seemed a bit easy...I have to ask about it in class later.