Why does the resultant Fy have opposite values in my calculations?

[tomtomtom1]

TL;DR

Resolving Resultant Forces

Hello all

I was hoping someone could explain why the resultant Fy has a value of +40kN but I get a value of -40kN.

 

[SCP]

Whether Fy is positive or negative depends on your sign convention. In the free-body diagram, the component Fy is sketched directed downward, so a positive result indicates that the force component does, in fact, point downward.

A negative result would indicate that the component Fy is directed upward. From the orientation of F, we know this is not the case.

 

[AZFIREBALL]

Fsub x=cos 30 X F
Fsub y=-(sin 30 X F)

 

[tomtomtom1]

Whether Fy is positive or negative depends on your sign convention. In the free-body diagram, the component Fy is sketched directed downward, so a positive result indicates that the force component does, in fact, point downward.

A negative result would indicate that the component Fy is directed upward. From the orientation of F, we know this is not the case.

SCP

Thank you for the reply - I have to be honest, I am still struggling.

My sign convection is such that a downward pointing arrow is negative and an upward pointing arrow is positive.

In the Free Body Diagram the Fy arrow is point downwards so it would be negative.

This doesn't make sense to me?

 

[AeroGeek]

Summary: Resolving Resultant Forces

Hello all

I was hoping someone could explain why the resultant Fy has a value of +40kN but I get a value of -40kN.

View attachment 252286

Hi there,

First, see how the arrow is pointing and it's given as 80KN which is positive, and it makes an angle 30 deg with horizontal, so horizontal will become 80 Cos 30 Deg aligning to +Fx and vertical becomes 80 Sin 30 Deg. Basically aligning to the co-ordinate making it +Ve.
Try solving more problems or refer few examples you will understand the crux

 

[256bits]

SCP

Thank you for the reply - I have to be honest, I am still struggling.

My sign convection is such that a downward pointing arrow is negative and an upward pointing arrow is positive.

In the Free Body Diagram the Fy arrow is point downwards so it would be negative.

This doesn't make sense to me?

Your brief makes sense.
The figure does not show any direction for the positive direction of the x-axis, nor the y-axis, and one would normally consider your interpretation.
Perhaps the question is asking only for the magnitude of the forces Fx and Fy.
Adding the - ( minus ) sign gives a direction to the vector Fy down in compliance with your choice of positive x and y axis.

 

[tomtomtom1]

I really am baffled.

I have tried again but with a different question and still got it wrong:-

Why on Earth would Fy be -ve 21.21 WHY WHY WHY?

 

[SCP]

I really am baffled.

I have tried again but with a different question and still got it wrong:-

View attachment 252323Why on Earth would Fy be -ve 21.21 WHY WHY WHY?

I see why you're getting confused. You're thinking in terms of an external sign convention that defines the positive y-direction as up. However, the Fy vector is drawn pointing down. The vertical component of F is up. Your sign convention defines that as positive. However, the Fy vector is sketched pointing down. So the vertical component of F is opposite in direction to the sketched force Fy. In other words, using Fy to express the vertical component of F requires a negative result.

You could also re-draw your sketch with Fy pointing in your defined positive direction (i.e. - up). In this case, your positive answer would be correct.

 

[malemdk]

The particle is not in equilibrium, since all the components add in the same +ve and -ve direction , if the system to be in equilibrium one of the component has to have a negative direction that's what you get.

 

[tomtomtom1]

I think I now have it thanks you all.