8.7 Free body diagram (application)  (Page 3/3)

Problem : A block of mass “m” is held with the support of a spring of constant “k” on a rough incline of angle “θ”. Draw the free body diagram (FBD) of the block.

Solution : The external forces on the block are :

• Weight of the block
• Normal force due to incline
• Friction force
• Spring force

The forces are drawn from the points of respective applications. Note specially that forces are not concurrent.

As there is no rotation involved, we consider forces to be concurrent and represent them as such with a common point.

The FBD of the block as point object is shown here :

We have indicated the angle that normal force makes with the direction of perpendicular to the incline. Idea here is that we should supplement FBD with as much information as is available. We have deliberately not shown the coordinate system which may be selected, keeping in mind the inputs available.

Problem : A rod “AB” is hinged at “A” from a wall and is held with the help of a string as shown in the figure. Draw the free body diagram (FBD) of the rod.

Solution : This example is designed to highlight the characteristics of a hinge. A hinge changes the nature of contact force at the contact between two objects. The direction of contact forces are not predefined like in the normal case, but can assume any direction depending on the other forces acting on the body under consideration.

As a consequence, the contact force is represented by a unknown force “F”. In the case of coplanar force system, this unknown force can, in turn, be represented by a pair of components in “x” and “y” directions. The figure below shows the forces acting on the rod “AB”.

The FBD of the rod after removing other elements of the system is shown here :

We should note that the FBD of the rod shows the angle that the tension force makes with the vertical. Idea here is that we should supplement FBD of the rod with as much information as is available. Also, we should note that we have not reduced the rod to a point as earlier to emphasize the lateral placements of forces on the rod. As a result, the rod may involve tendencies for both translation and rotation. If only translational is involved, we can treat rod as point with its center of mass.

We have considered horizontal and vertical directions as "x" and "y" directions for denoting unknown force components " $F_x$ " and " $F_y$ ".

Problem : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw the free body diagram (FBD) of the rod.

Solution : We note that inside surface of the spherical shell is rough. It means that there will be friction between spherical shall and the rod. Thus, there are three forces operating on the rod : (i) weight of rod (ii) normal force between rod and spherical shell and (iii) friction force between rod and spherical shell. Since the rod is in contact at two end points, contact forces operate at both these end points.

The normal forces are perpendicular to the tangents drawn at “A” and “B”. As such, normal forces at these points, when extended meet at the center of the spherical shell. The friction force at the contact surface is along the tangent drawn.

Here we see that weight is shifted laterally towards “B”. Considering rod has a downward tendency at “B”, the friction is shown in the upward direction at “B” and downward direction at “A”. The FBD of the rod after removing other elements of the system is shown here.

We have deliberately not shown the coordinate system which may be selected, keeping in mind the inputs available. Also, we have not reduced the rod as point as the rod may undergo both translational and rotational motion. As such, lateral placements of forces along the rod are shown with FBD.