Question

Four separate blocks are placed side by side in a left-toright row on a table. A horizontal force, acting toward the right, is applied to the block on the far left end of the row. Draw FBDs for (a) the second block on the left and for (b) the system of four blocks.

Short answer

Question: Draw Free Body Diagrams (FBDs) for A) the second block from the left, and B) the system of the four blocks. Answer: A) For the second block from the left, the FBD consists of the following forces: F_12 (applied horizontally to the right by the first block), N_2 (normal force acting vertically upwards), W_2 (force due to gravity acting vertically downwards), and f_2 (frictional force acting horizontally to the left, if present). B) For the system of four blocks, the FBD consists of the following forces: F (applied horizontal force on the first block), N_{total} (total normal force acting vertically upwards), W_{total} (total force due to gravity acting vertically downwards), and f_{total} (total frictional force acting horizontally to the left, if present).

Step-by-step solution

Draw the FBDs for the second block from the left

First, we need to draw the FBD for the second block from the left. In this case, let's label the blocks using integers, with "1" being the far left, and "4" being the far right. So, we will draw the FBD for block 2. 1. Draw the second block as an isolated rectangle. 2. Indicate the force applied by the first block on the second block (F_12) acting horizontally towards the right. This force represents the interaction force between the first two blocks. 3. Draw the normal force (N_2) acting vertically upwards on the block. 4. Draw the force due to gravity (W_2), acting vertically downwards on the block, with equal magnitude to N_2. 5. Depending on the surface, there might also be a frictional force (f_2) acting horizontally towards the left, opposite to F_12. If there is no information on friction, assume f_2=0, which means that friction is not acting on the block.

Draw the FBD for the system of four blocks.

Now, we will draw the FBD for the whole system consisting of four blocks. 1. Draw all four blocks as a single, large, isolated rectangle representing the whole system. 2. Indicate the applied horizontal force (F) acting toward the right on the first block (far left end of the row). 3. Draw the total normal force (N_{total}) acting vertically upwards on the entire system. 4. Draw the total force due to gravity (W_{total}) acting vertically downwards on the entire system, equal in magnitude to the total normal force, N_{total}. 5. If friction is acting on any of the blocks, indicate the total frictional force (f_{total}) acting horizontally towards the left on the entire system. 6. We do not have to consider the interaction forces between the blocks, as we are considering the entire system as a single unit. Now we have drawn both FBDs as required, one for the second block from the left and another for the whole system of four blocks.