7.8 Example 8

In the system shown in the image. Which is the value of the force F?

Solution with FisicaLab

Erase the content of the chalkboard and select the SI system, and add the necessary elements to make the three free body diagrams as show the image below (The white circles are just for clarify):

To the element Block, write:

m

7

To the element force applied to the block, its values is an unknown data, calling this t1, write:

f

t1

To the elements Pulley the names are irrelevant. To the downwards vertical force applied to the pulley immediately above the block, write:

f

t1

Is the same string that support the block. In that pulley, the two upwards vertical forces, are unknown data, and the same unknown data, because is the same string. Calling this t2, write to both forces:

f

t2

In the other pulley, the downwards vertical force, and the oblique force are the same string, then to the vertical force write:

f

t2

And to the oblique force, write:

f

t2

ang

25

The others two forces are the reactions that support the pulley. Calling Ry the vertical reaction, write:

f

Ry

And calling Rx the horizontal reaction, write:

f

Rx

Now click in the icon Solve to get the answer.

t2 = 34.335 N ;  Ry = 48.846 N ;  t1 = 68.670 N ;
Rx = -31.118 N ;
Status = success.

The negative sign in the Rx data is because the sense of this force, is the opposite of the force that we add to the pulley.