00:01
Hello, in this question we apply the principle of equilibrium of forces as well as the principle of moments.
00:10
We have an arm that is pivoted and this arm has a weight of mg where the mass is 3 .3 kilograms.
00:33
Now a force of fm inclined at an angle, an angle of 15 degrees.
00:53
Supports the arm and at a hinge or at a pivot there is another force fg force adjunct and we are to find a minimum force fm that is needed to hold the arm or support the arm so we first need to resolve the force fm to get its vertical component which is f m sign 15 as well as its horizontal component which is fm cross 15 similarly we can resolve this force to get its horizontal component let's call that fj x and its vertical component that we can call fjy.
02:07
Now the distance here from the center of mass to the distance from the force fm to the pivot is given us 12 centimeters and the distance from the pivot to the center of mass is 24 centimeters so we apply the principle of movements for forces about the the vertical component of fm is what is going to create the moment about p so the moment of fm about p is fm times 12 centimeters so fm times 12 centimeters that should be equal to the counter moment produced by the weight so this should be equal to m g times 24 centimeters we need not convert to meters because this units will cancel out and so we make our fm the subject, slotting the value for the mass, and for gravity 9 .8, and our f comes out as, our fm comes out as 250 newtons.
03:35
That is the minimum force that the mazumas, i said, so that it would have enough vertical components to create enough moment to counterbalance the moment of the arm.
03:49
And then keep the arm stretched horizontally.
03:57
For part b, we are to, sorry, proper b, we are to find the magnitude of fj.
04:05
We first find the components of fj.
04:08
We know that because there is horizontal equilibrium, fjx and fm cost 15 must balance each other.
04:18
So fjx equals fm cross 15, which is 241 newtons...