Vivian L. answered • 02/17/14

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Hi Meg;

I am assuming that the theta of 31-degrees applies to the slope between the line perpendicular to the incline, and the force-vector g directly beneath the block. The equation is...

F=mg(cos 31-degrees)

I am assuming this because the definition of normal force is that the angle between the force of g, which is straight down from the block, and the vector perpendicular to the line formed by the surface upon which the block is sliding.

F=(47.3 kg)(9.81 m/s

^{2})(0.857)F=398. Newtons

**F=398. N**

We are using cosine rather than sin or tangent because of...

SOH CAH TOA

sin=opposite/hypotenuse

cos=adjacent/hypotenuse--(g-vector)/(vector perpendicular to angled surface)

tan=opposite/adjacent