- #1

Pat2666

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Okay, another problem from me!

http://img187.imageshack.us/img187/69/32aa2d25kf9.jpg [Broken]

A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 2.6 m down a q = 22° incline. The sphere has a mass M = 4.2 kg and a radius R = 0.28 m.

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a) Of the total kinetic energy of the sphere, what fraction is translational?

KEtran/KEtotal = *

0.71 OK

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b) What is the translational kinetic energy of the sphere when it reaches the bottom of the incline?

KEtran = J *

28.66 OK

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c) What is the translational speed of the sphere as it reaches the bottom of the ramp?

v = m/s *

3.69 OK

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|f| = N

Alrighty, so I managed to figre out all of the problem except this last bit. I thought I knew what to do after reading over the two

Since I know the Vt at the bottom of the ramp, and it being zero at the top of the ramp, I thought I could use that to solve for a (as you will see below). I then plug that into the modified equation for torque, but get the wrong answer. I don't fully understand how torque is equivilant to the force of friction, as that's what the

My Work :

http://img187.imageshack.us/img187/5945/workje4.jpg [Broken]

http://img187.imageshack.us/img187/69/32aa2d25kf9.jpg [Broken]

A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 2.6 m down a q = 22° incline. The sphere has a mass M = 4.2 kg and a radius R = 0.28 m.

--------------------------------------------------------------------------------

a) Of the total kinetic energy of the sphere, what fraction is translational?

KEtran/KEtotal = *

0.71 OK

--------------------------------------------------------------------------------

b) What is the translational kinetic energy of the sphere when it reaches the bottom of the incline?

KEtran = J *

28.66 OK

--------------------------------------------------------------------------------

c) What is the translational speed of the sphere as it reaches the bottom of the ramp?

v = m/s *

3.69 OK

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**d) What is the magnitude of the frictional force on the sphere?**|f| = N

*HELP: The frictional force provides the torque needed to give an angular acceleration. Therefore, first find the angular acceleration, then apply the rotational equivalent of Newton's 2nd Law (torque = I*a).*

HELP: Since the sphere rolls without slipping, the angular acceleration is related to the translational acceleration, which can be found from kinematic relations.HELP: Since the sphere rolls without slipping, the angular acceleration is related to the translational acceleration, which can be found from kinematic relations.

Alrighty, so I managed to figre out all of the problem except this last bit. I thought I knew what to do after reading over the two

*HELP*bits provided, but clearly I'm doing something wrong.Since I know the Vt at the bottom of the ramp, and it being zero at the top of the ramp, I thought I could use that to solve for a (as you will see below). I then plug that into the modified equation for torque, but get the wrong answer. I don't fully understand how torque is equivilant to the force of friction, as that's what the

*HELP*seems to say, but I'd also like to understand what I'm doing.My Work :

http://img187.imageshack.us/img187/5945/workje4.jpg [Broken]

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