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In this video here at 4:21, why do we not include sin Θ when calculating the y components of the ladder and the man on the ladder?

The equation written is just

0=-mg-mg+N

Should it not be

0=-mgsinΘ-mgsinΘ+N

Also eventually he used sin Θ for finding torque, but not with x + y components enter image description here

Harry Iguana
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1 Answers1

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Should it not be

0=-mgsinΘ-mgsinΘ+N

No, it should not. The vertical components are being calculated. Obviously, the direction of the forces on the man and ladder in the vertical direction are collinear with gravitational force. This means the normal force the ladder exerts on the ground due to both must be $N=mg+Mg$ in the vertical direction.

Also eventually he used sin Θ for finding torque, but not with x + y components

Note that this (as far as I can see) is not because of component forces. Torque is defined as the cross product between the force and the vector distance to where the force is applied. That is, $$\bf{\tau}=\bf{r\times F}=|r||F|\sin(\theta)=|F|\left(|r|\sin \theta\right)$$

or the product of the magnitude of the force and lever arm (which is the perpendicular distance from the fulcrum). To learn more about this, see this article.

joseph h
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  • So because they are same direction as gravitational force, no angle in calculations? Would the angle not affect the force of gravity though? – Harry Iguana Nov 13 '22 at 03:23
  • Oh, I see. So then for the torque equation, he uses sin Θ for weight of ladder and the man, cos Θ for the force of wall. Would cos and sin not be flipped if you make a triangle of force components? – Harry Iguana Nov 13 '22 at 04:10
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    Ohh, I see, in the example I'm doing my theta is on the bottom left of my triangle, not the top right. Makes sense, thanks! – Harry Iguana Nov 13 '22 at 04:19
  • no problems and good luck with your studies. – joseph h Nov 13 '22 at 04:30