Forces on a slope. Static and kinetic friction.

Version: 0.1 10-19-08
To do:
(i) Figure out arbitrary motion (initial velocity)

P = pitch of slope; m_s = coefficient of static friction; m_k = coefficient of kinetic friction; m = mass of block; g = acceleration due to gravity.

Basis vectors, rotated basis vectors and rotated coordinates:

Size of block; distance uphill:

Block with center at X=d and Y=b:

Slope & ground:

Gravitaional force and components parallel and perpendicular to incline:

Normal force and its magnitude:

F_A = applied force; F_F = friction force; F_s/k = static/kinetic friction: F_Q = net X force save friction:

Direction of kinetic friction hinky because it depends on velocity, not net applied force –
UNLESS you begin from rest (so force/acceleration tracks initial slip velocity)

Net force:

Block accelerates when net applied force exceeds maximum static friction. a=1 to disable:

Author: David A. Craig <http://web.lemoyne.edu/~craigda/>

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