- #1

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Is it possible to calculate the minimum inclination of the ramp that satisfies the statement above?

If needed use other variables like h for the height of the cylinder, g for gravity, etc...

- Thread starter jaumzaum
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- #1

- 369

- 19

Is it possible to calculate the minimum inclination of the ramp that satisfies the statement above?

If needed use other variables like h for the height of the cylinder, g for gravity, etc...

- #2

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I assume you mean that the slope is sufficient that theIf we had a cylinder rolling down a ramp, with scalar friction coefficient u_{s}and kinetic friction coefficient u_{c}, and we assume for example that the inclination of the ramp is enough to make the cylinder reach the acceleration needed to exceed the scalar friction of rolling.

Suppose cylinder has mass m, moment of inertia I (you didn't say whether it was hollow or solid, etc.) linear acceleration a, radius r. The normal force is N, the frictional force F. Slope has angle θ to vertical.

Forces parallel to the slope: ma = mg cos θ - F

Perpr. to slope: N = mg sin θ

Angular accn = a/r

Moments about cylinder's centre: Fr = Ia/r

At rolling limit: F = u

Fr

a = mgr

tan θ = I /((I + mr

Once it has started to slip, F reduces to u

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