9.9 Example 9

A uniform ladder, of 3.5 kg and 3.8 m long, rests against a wall as show the image. If a child with a mass of 40 kg, ups to the fourth step at 3.2 m from the base, find the angle for which this position corresponds to the slip imminent if the coefficient of friction between the ladder and the floor is 0.35 (there is no friction between the ladder and the wall).

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. And add one element Stationary reference system, one element Beam, three elements of beam and the necessary elements Force and Friction, as show the image below:

The Stationary reference system set the gravity value to default. Now to the element Beam, that we call Ladder, recalling that the ladder is uniform and that the angle is unknown:

Name

Ladder

m

3.5

lc

1.9

ang

ang

To the element of beam that represent the lower side, we have:

Name

Ladder

l

0

And to the normal force and the friction:

f

N

Normal

N

u

0.35

Now to the element that represent the point where the child is supported, we have:

Name

Ladder

l

3.2

And to the force that represent the weight of this child (40 kg*9.81 m/s2 = 392.4 N):

f

392.4

Finally, to the element that represent the upper side:

Name

Ladder

l

3.8

And to the force that represent the reaction of the wall:

f

Rx

Now click in the icon Solve to get the answer:

Rx = 149.357 N ;  ang = 66.748 degrees ;  N = 426.735 N ;
Status = success.