Solving the Inclined Plane Puzzle

AI Thread Summary
The discussion revolves around a misunderstanding of forces acting on a mass on an inclined plane. The user initially misapplies Newton's Second Law, incorrectly combining gravitational and normal forces. The mistake is clarified when it's pointed out that the normal force is not parallel to the gravitational force. The user realizes their error and acknowledges the correction. This highlights the importance of accurately analyzing force vectors in physics problems.
rexregisanimi
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This is driving me nuts. What am I missing?

Suppose you have an inclined plane with a mass m resting on it. The free body diagram for the mass m has F_grav downward and F_normal perpendicular to the surface of the inclined plane. Thus, by Newton's Second Law, you have:

∑F=F_grav+F_norm=ma with the bolded script indicating vectors. Because F_normal=F_grav*cos(α) where α is the angle of the plane's inclination you get

F_grav+F_norm=F_grav+F_grav*cos(α)=F_grav*(1+cos(α))=ma.

But this doesn't make any sense! This indicates that, as the inclination of the plane gets lower and lower, the acceleration gets higher. It's obviously a wrong result but I can't, for the life of me, figure out where my mistake is. lol Any help would be greatly appreciated.
 
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hi rexregisanimi! :smile:
rexregisanimi said:
Because F_normal=F_grav*cos(α) …

nooo :redface: …

they're not parallel, are they? :biggrin:​
 
Ah yes. lol Thanks :)
 

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