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I need help in physics please anybody!!!????!!!?!?!?!?
Ok so I'm supposed to write the equilibrium expression for the coefficient of kinetic friction. How am I supposed to do that? There is a black sitting on a ramp at an angle theta and it is at equilibrium; no movement. The sum of all the forces in the horizontal direction equal 0 and all the forces in the vertical direction equal zero. I understand F of friction = m k( m is the squiggly Greek letter m) multiplied by Force normal. M k = Fk/Fn is solving for friction kinetic; but how am I suppose to derive it??? Please help me... also F=ma=> mass acceleration...
2 Answers
- 8 years agoFavorite Answer
That squiggly m is actually mu so I'll call it that. And if you say there is no movement then you're supposed to use the static friction coefficient, since kinetic friction is for when there is movement of the object on a specific surface, though if the system is in equilibrium, ma = 0, then the speed is constant going down the ramp.
Since force is equal to mass times acceleration, ma, then no movement means a is 0:
Summation of forces = 0
The only forces on the black(?) would be gravity and friction so those forces are all you need:
Force of friction - Force of gravity = 0
[(mu)kinetic x normal force(N)x cos theta] - [mass(m) x gravitational acceleration(g) x sin theta] = 0
(mu)k = (mgsin(theta)/Ncos(theta))
- gp4rtsLv 78 years ago
It is easier to sum the forces along the direction of the ramp. Downward force along the ramp is the force of gravity = m*g*sinθ; if the block is stationary, the frictional force must be equal and opposite to this; its magnitude is also m*g*sinθ
The frictional force is μ*Fn, where Fn is the normal force due to gravity against the ramp: Fn = m*g*cosθ;
then
m*g*sinθ = μ*m*g*cosθ;
μ = tanθ
However, this is the coefficient of static friction, since you have specified no movement. If the block was moving at a constant velocity down the ramp, then this would be the coefficient of kinetic friction.