Friction problem on inclined plane

AI Thread Summary
The discussion revolves around calculating the speed of an object at the bottom of a rough inclined plane and determining the coefficient of kinetic friction on a horizontal surface. The user calculated the speed to be 12.65 m/s using the energy conservation equation, but was advised that friction must be considered, indicating that non-conservative work should be factored in. For the horizontal surface, the user derived a coefficient of kinetic friction of 0.35, but was reminded to account for the angle and the normal force in their calculations. The importance of correctly applying the work-energy principle in the presence of friction was emphasized. Overall, the calculations and methodology were mostly correct, but adjustments for friction effects were necessary.
jhrnndz1
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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?
 
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You do NOT have conservation of mechanical energy, since friction is present!
 
So, for part A, would I first find the Wnc=-ukmgd, and then set that equal to change of KE + the change of PE?
 
jhrnndz1 said:
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
 
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