10.34. Determine the sum of the moments created by the...

10.34. Determine the sum of the moments created by the forces shown in the accompanying figure about points A, B, C and D. Problem 10.34 The figure shows a bar A B C D which is inclined at an angle of 35 degrees below the horizontal axis. The distance between A and B is 5 centimeters, the distance between B and C is 2 centimeters and the distance between C and D is 3 centimeters. A force of magnitude 50 newtons is applied perpendicular to the bar on point B, a force of magnitude 50 newtons is applied vertically on point C and a force of magnitude 100 newtons is applied vertically on point D.

Transcript

00:01 Here in this given problem this is a bar which is making an angle of 35 degree with the horizontal and few forces are being applied over it.

00:15 This is the angle 35 degree made by this bar with the horizontal.

00:23 The bar is named as a, the left most point d, the right most point, b the central point and c a point midway between b and d.

00:38 The distance from a to b that is given to be 5 centimeter, the distance between b and c that is 2 centimeter and the distance between c and d this is 3 centimeter.

01:01 A force is being applied at point b which is exactly perpendicular to the length of this rod, this force 50 newton.

01:18 Another force is vertical being applied at c this is also 50 newton.

01:25 Third force which is being applied over here at point d and that is 100 newton.

01:31 So, we need not to take the component of the length of the rod for this force of 50 newton acting at b.

01:40 In order to find moment because we know moment is given as the product of force with the perpendicular distance from the point of rotation.

01:48 So, when a is the point of rotation perpendicular distance is 5 centimeter itself, but when we will find moment created by 50 newton and 100 newton acting at c and d respectively, then we will have to take the components of the length of the rod.

02:06 So, these components will serve here as the distances.

02:13 So starting with the moment about point a, so for the moment about point a moment may also be known as torque and torque which is counter clockwise in direction that is taken as negative sorry positive and which is clockwise that is taken to be negative.

02:42 So, about a all the three forces will be creating counter clockwise moment counter clockwise torque.

02:47 So, it will be positive starting with the 50 newton acting at b the force that is 50 newton multiplied by perpendicular distance that is 5 centimeter or 5 by 100 meter.

03:02 Then plus this 50 newton and its distance that is component of this 5 plus 2 means 7 centimeter.

03:14 So, that is 7 cos 35 degree this is centimeter, so divided by 100.

03:21 Then for this 100 newton acting at d plus 100 newton the total length of the rod up to d from a that will be 10 centimeter.

03:33 So, the component horizontal component will be 10 cos 35 degree and that is centimeter, so divide this also by 100 to convert it into meter...

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