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Re: Conservation of ME and nonconservative forces

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.

Forces on ball:
1. Gravity - conservative - OK
OK

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

3. Static friction at the point of contact between ball and surface. ??
Kr = 1/2 I w^2 I = rotational inertia (kg m^2) w is omega =
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?




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