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*From*: Pete Lohstreter <plohstreter@MAIL.HOCKADAY.ORG>*Date*: Tue, 26 Jun 2001 16:28:40 -0500

PHYS-L@lists.nau.edu writes:

A ball rolls down an inclined plane without slipping. Given the height

from which it starts, find the speed of the ball at the bottom of the

incline.

So we look at conservation of ME.

But in order to use cons. of ME, we need to be certain that there is no

work done by nonconservative forces.

The total gravitational potential energy is converted to both rotational

and translational kinetic energy. It is the friction that causes the

rotation in the mix.

OK

Forces on ball:

1. Gravity - conservative - OK

agree

2. Normal - does no work on object - perpendicular to direction of motion

- OK

Kr = 1/2 I w^2 I = rotational inertia (kg m^2) w is omega =

3. Static friction at the point of contact between ball and surface. ??

angular velocity (rad/sec)

The problem resolves to mgh = 1/2 mv^2 + 1/2 I w^2

substitute v/r for w and 2/5 mr^2 for I

to solve for velocity as a function of gravity and ramp height.

Is this what you were asking?

Pete Lohstreter Happy is he who gets to know the

reasons for things.

The Hockaday School Virgil

(70-19 BCE) Roman poet.

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plohstreter@mail.hockaday.org

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