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9.3 Example 3

If we want to replace the two forces of 175 N and 380 N force with a single force applied at point P as shown the image, What should be the distance from point P to point O and the magnitude of this force? (The beam and the drum form a rigid body) Solution with FisicaLab

Select the group Static and, inside this, the module Static of solids. Erase the content of the chalkboard and select the SI system. This problem can be solved on different ways, here we will solve it as follow. First add one element Points, three elements point and the necessary elements force and resultant, as show the image below. Our initial intention is calculate the couple of the pair of 175 N forces, at point O. To the element Points, that represent the different points of the drum and that we call Drum, we have:

Name

Drum

To the element Point that represent the center O, we assume this at origin:

Name

Drum

x

0

y

0

And to the element Resultant applied here:

M

Mr

f

Fr

Now to the upper point, we have:

Name

Drum

x

0

y

45 @ mm

And to the lower point:

Name

Drum

x

0

y

-45 @ mm

And to the two applied forces:

f

175

Now click in the icon Solve to get the answer:

Mr = -15.750 N*m ;  Fr = 0.000 N ;
Status = success.

Now that we know the moment of the pair of 175 N forces, erase the content of chalkboard and add the necessary elements as show the image below: The Stationary reference system set the gravity value to default. Now to the element Beam, we call this Beam, we have:

Name

Beam

m

0

lc

0

ang

60

Here we ignore the weight of the beam. To the element of beam that represent the lower side and to the applied couple (the previous calculated value), we have:

Name

Beam

l

0

M

-15.750

Now to the element of beam where is applied the other force, and to this force, we have:

Name

Beam

l

28 @ cm

f

380

To the element of beam that represent the point P:

Name

Beam

l

d

Here the distance is an unknown data. And to the resultant applied here:

M

0

f

Fr

Here the couple is 0, because we want just a force, which is an unknown data. Now click in the icon Solve to get the answer:

d = 0.363 m ;  Fr = -380.000 N ;
Status = success.

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