A uniform block of 4 kg, as show the image, is placed on a slope. What is the maximum angle of inclination of the plane, so that the block does not slide or tipping (whichever comes first)? (The coefficient of friction between the block and the plane is 0.4).
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 Solid, one element of Solid, one element Angles and the necessary elements Force and Friction, as show the image below:
Our intention to introduce a frictional force is find the angle when the slip is imminent. Thus, the block element represents the point where is applied the normal and here we apply the friction force too (we can move the friction along its action line, so we can apply it in this element).
The Stationary reference system set the gravity value to default. Now on the element Solid, that we call Block, we have:
8 @ cm
18 @ cm
Here the angle is an unknown data. To the element of solid, we have:
x @ cm
The x coordinate is unknown. This must be so. Because when the sliding of block is imminent, we don’t know at where is applied the normal force. Now to the normal force:
To the element Friction:
The angle is the same as of the block. Because the friction is parallel to the plane. Now to the element Angles, we have:
Because these angles must be complementary. Once entered the data, click on the icon Solve to get the answer:
normal = 36.433 N ; ang1 = 21.801 degrees ; ang2 = 68.199 degrees ; x = 0.800 cm ; Status = success.
Then, the angle when the sliding of block is imminent is 21.801 degrees (As we expected, because
arctan 0.4 = 21.801). In the case of a negative value, this would mean that the block has already overturned.