My Math Forum Magnitude and sense of the force applied at A to reduce the reaction at A to zero.

 Applied Math Applied Math Forum

February 7th, 2017, 03:30 PM   #1
Member

Joined: Jun 2015
From: Warwick

Posts: 37
Thanks: 1

Magnitude and sense of the force applied at A to reduce the reaction at B to zero.

A light horizontal beam $AB$, of length $9m$, supported at its ends by a force $S$ acting vertically and a force $R$ acting at an angle $\alpha$ to the line of the beam. A force of $30N$ is applied to the beam, at an angle of $30^o$, $3m$ from $B$. The beam is in equilibrium and $S=10N$, $\alpha = arctan(\frac{1}{3\sqrt3})$ and $R= 10\sqrt7N$.

Calculate the magnitude and sense of the necessary moment that would have to be applied at $A$ to reduce the reaction at $B$ to zero.

Answer given as $90Nm$ anticlockwise, but should it be clockwise, as from$A$ the moment of the force $3m$ from $B$ on top of the beam is $$6*30sin30^o =90Nm$$ anticlockwise?
Attached Files
 Horizontal beam.zip (20.4 KB, 4 views)

Last edited by Statistics132; February 7th, 2017 at 03:58 PM.

 February 11th, 2017, 12:49 PM #2 Member   Joined: Jun 2015 From: Warwick Posts: 37 Thanks: 1 No, it is anticlockwise. Assuming the conditions are the same as in the first part of the question, where $R$, $\alpha$ and $S$ had to be worked out, we now add an extra force at $A$ to create an anticlockwise moment, which is pointing directly downwards at $A$. We then take moments about $B$, and with $Rsinα = 5N$: $$M(B): -9Rsinα - 3*30sin30^o + 9F = 0$$ So $$-45 -45 = -9F$$ So $$-90 = -9F$$ Therefore $$9F = 90 Nm$$ So the necessary moment about $A$ to reduce the reaction at $B$ to zero is $90Nm$ anticlockwise. (It turns out that $F=10N$, which is the same as $S$, so $9F$ is the necessary moment, in $Nm$.) Last edited by Statistics132; February 11th, 2017 at 12:58 PM.

 Tags applied, force, forces, magnitude, moments, reaction, reduce, sense

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Statistics132 Applied Math 2 September 29th, 2015 11:02 AM girlbadatmath Chemistry 6 December 6th, 2014 09:11 PM DPXJube Physics 1 January 28th, 2012 08:32 PM sivela Physics 1 January 27th, 2011 05:51 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top