Friction problem on inclined plane

[jhrnndz1]

Alright, I have another question that I want to make sure I did correct. The question is "an objec of mass m is at rest on a rough inclined plane with height h, length 8 m, and which makes an angle of 30degrees with the horizontal. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4m from the botton of the inclined plane as shown. The coefficient of kinetic friction on the inclined plane is 0.4 and g=10m/s^2.

What is the speed of the object ast the bottom of the inclined plane?

Alright i used the equation KEfinal -PEfinal = KEinitial -PEinitial, put in the numbers and calculated the velocity to be 12.65 m/s.

The second questin is...

What is the coefficient of kinetic friction for the horizontal surface?

I used the equation Normal force = Force of weight and got

mass*gravity*distance *coefficient of kinetic friction = mass*gravity*distance*coefficient of friction on the incline.

I canceled the mass and the gravity and put in the numbers,

(4m for distance on horizontal0*(uk)= distance of 4 m, (which i obtained from sin30=8/d)*cos30degrees*0.4(the planes coefficient of friction).

I then solved for the coefficient of fricton from the horizontal and calculated 0.35.

(Is this correct?

 

[arildno]

You do NOT have conservation of mechanical energy, since friction is present!

 

[jhrnndz1]

So, for part A, would I first find the Wnc=-ukmgd, and then set that equal to change of KE + the change of PE?

 

[Andrew Mason]

So, for part A, would I first find the Wnc=-ukmgd, and then set that equal to change of KE + the change of PE?

You have to factor in the angle. The force of friction is $\mu_kNg$ where N is the component of the block's weight perpendicular to the inclined surface. Apart from that, your approach is right.

AM