Newton's 2nd Law and drawing forces

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To demonstrate that acceleration a equals g sin(alpha), the forces acting on a block on a frictionless surface are analyzed. The force along the hypotenuse, Fm, is calculated as Fm = sin(alpha) * mg. Applying Newton's 2nd Law, the net force Fnet is set equal to Fm, leading to the equation ma = sin(alpha) * mg. This simplifies to a = g * sin(alpha), confirming the relationship. The discussion effectively illustrates the application of Newton's 2nd Law in deriving the acceleration formula.
Manni
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Hey guys, how would I show that a = g sin(alpha) for the following diagram?

Fig.1.jpg
 
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You could start by drawing the forces on the block.
 
Yeah, I just figured it out.

I determined the Force acting about the hypotenuse, Fm

So, Fm = sin(alpha)*mg

Then, according to Newton's 2nd Law,

Fnet = Fm
ma = sin(alpha)*mg
a = g*sin(alpha)

N.B. The mass is assumed to be on a frictionless surface
 

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