The force required to push a 100-lb object along a 10degree inclined ramp

Question

What would be the force required to push a $100$-lb object along a ramp that is inclined $10^\circ$ with the horizontal?

I know that $\left|F^2\right|=\left|F_1^2\right|+\left|F_2^2\right|$ But I don't see a second force. What to do with the incline number?

Answer 1

Since the force is required to push the object, it means that there is a perpendicular force trying to push the object through the incline.

The formula used is $F=mg\sin\theta$

Where $m=100$lb, $\theta=10^{\circ}$

$F=100\times9.8\times\sin10^{\circ}$

Answer 2

The weight $mg$ is decomposed into two forces, $$mg \sin (10)$$ and $$mg \cos (10)$$ The $mg \cos (10)$ is perpendicular to the surface so it does not impose any effort in moving the object.

thus you need $$mg\sin(10)= 100(32.17) \sin(10)$$ force to pull the object.