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.
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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