A 4 kg block slides down a rough inclined plane inclined at 30° with the horizontal. Determine the coefficient of kinetic friction between the block and the surface if the block has an acceleration of 1.2 m/s2.

Question

A 4 kg block slides down a rough inclined plane inclined at 30°  with the horizontal. Determine the coefficient of kinetic friction between the block and the surface if the block has an acceleration of 1.2 m/s2.

anonymous · Answer

You can find the coefficient of friction from the equation:$$F=\mu_{k}N$$where F is the force acting parallel to the surface, mu is the coeff. of friction, and N is the normal force.


In order to find mu, you need F and N. 

N is perpendicular to the surface (which is inclined), so you will need to calculate the component of gravity that is acting in this direction. This will be equal to the normal force since the block is not accelerating into inclined plane.
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F can be found by using Newton's 2nd Law:$$F=ma$$where you've been given the mass 'm' and the acceleration 'a'.

mrnood · Answer

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It is the force mg sin 30 acting ALONG the plane that is responsible for the acceleration

the resting force is mu mg cos 30

SO the net force acting along the plane is mg sin 30 - mu mg cos 30 = ma  
(a= 1.2m/s^2)

the only unknown in that is mu so you can solve