Moments question help needed for part b

A uniform rod AB has length 4 m and weight 150 N. The rod rests in equilibrium in a horizontal position, smoothly supported at points C and D, where AC = 1 m and AD = 2.5 m. A particle of weight W N is attracted to the rod at a point E where AE = x metres. The rod remains in equilibrium and the magnitude of the reaction at C is now equal to the magnitude of the reaction at D.

a. Show that W = (150) / (7 - 4x)

b. Hence deduce the range of possible values of x.

I know weight must be positive so I have to do W>0 but how did they also get x bigger than or equal to 0??

$W>0$ is correct, which means that $7-4x > 0 \iff x < \dfrac{7}{4}$. But this isn't a full restriction. For instance, $x=-1$ isn't a valid option because that would place the particle off the rod completely! Hence any negative x is not allowed.

Oh okayyy but how do you know that the particle would be off the rod it's weight is unknown

I assume you've sketched a diagram. Go ahead and place the particle at x=-1 from A, then hopefullty it's obvious how it's off the rod. This part isn't to do with weight being unknown at all, it's simple observation that for particlar x values the particle isn't even on the rod.

So suppose I substitude x=-1 into W that gives me around 13.6.. as the weight. I was trying to see it that way would that work too?

It doesn't work!

Please try to understand that we have two SEPARATE conditions at play here.

(1) W > 0

(2) The particle can only be placed on one side of A.


Condition (1) alone isn't going to give us the full answer, but part of it. Sure, x=-1 satisfies x<7/4 inequality and gives as a valid weight, but we also need to make sure (2) is satisfied as well.... but x=-1 doesn't satisfy it.

Anyway, post your diagram if you are further confused.

If you don't mind me asking are you a student or a teacher?

Final year uni student

I'm assuming you're studying Physics

Straight maths

Ohh okayy at what uni?

Loughborough, it's all on my profile if you're really that interested