Component of weight perpendicular to bar

AI Thread Summary
To find the component of weight perpendicular to a bar, it is essential to correctly identify the angle θ in relation to the bar and the vertical. The initial confusion arose from calculating the perpendicular component as mgcos(θ) instead of the correct mgsin(θ). The angle θ should be considered from the vertical, leading to the realization that the perpendicular component is derived using sin(π - θ). This adjustment clarifies that the correct formula for the perpendicular component is indeed mgsin(θ). Understanding the trigonometric relationships in the context of the problem is crucial for accurate calculations.
theone
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Homework Statement


http://postimg.org/image/tlvhadljz/
I am trying to find the component of weight perpendicular to the bar.

Homework Equations

The Attempt at a Solution


I tried as shown and I got mgcos(theta) but I am supposed to be getting mgsin(theta)
 
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Could you please explain the question. Even the picture seems vague.
 
theone said:

Homework Statement


http://postimg.org/image/tlvhadljz/
I am trying to find the component of weight perpendicular to the bar.

Homework Equations

The Attempt at a Solution


I tried as shown and I got mgcos(theta) but I am supposed to be getting mgsin(theta)
It's fairly basic trigonometry. The angle, θ, is obtuse, so you might be better off considering the angle π - θ which is acute. You can then more directly see that you need to use sin(π - θ) by considering opposite/hypotenuse.

Untitled.jpg
 
theone said:

Homework Statement


http://postimg.org/image/tlvhadljz/
I am trying to find the component of weight perpendicular to the bar.

Homework Equations

The Attempt at a Solution


I tried as shown and I got mgcos(theta) but I am supposed to be getting mgsin(theta)
The theta you considered is not the same with the theta that is shown in the figure on the left.
 
Oh dear they are right. theta is measured from the vertical to the ground plane (not from the ground plane itself) so the theta we considered is equal to the actual theta minus π/2. So the perpendicular component of weight is mgcos(theta-π/2)=mg(cos(theta)cos(pi/2)+sin(theta)sin(pi/2))=mgsin(theta).
 
thanks everone
 
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