5.7 Drawing free-body diagrams  (Page 2/6)

Two blocks on an inclined plane

Strategy

Solution

We now include any force that acts on the body. Here, no applied force is present. The weight of the object acts as a force pointing vertically downward, and the presence of the cord indicates a force of tension pointing away from the object. Object A has one interface and hence experiences a normal force, directed away from the interface. The source of this force is object B, and this normal force is labeled accordingly. Since object B has a tendency to slide down, object A has a tendency to slide up with respect to the interface, so the friction $f_{\text{BA}}$ is directed downward parallel to the inclined plane.

As noted in step 4 of the problem-solving strategy, we then construct the free-body diagram in [link] (b) using the same approach. Object B experiences two normal forces and two friction forces due to the presence of two contact surfaces. The interface with the inclined plane exerts external forces of $N_{\text{B}}$ and $f_{\text{B}}$ , and the interface with object B exerts the normal force $N_{\text{AB}}$ and friction $f_{\text{AB}}$ ; $N_{\text{AB}}$ is directed away from object B, and $f_{\text{AB}}$ is opposing the tendency of the relative motion of object B with respect to object A.

Significance

Two blocks in contact

A force is applied to two blocks in contact, as shown.

Strategy

Draw a free-body diagram for each block. Be sure to consider Newton’s third law at the interface where the two blocks touch.

Solution

Significance

${\overrightarrow{A}}_{21}$ is the action force of block 2 on block 1. ${\overrightarrow{A}}_{12}$ is the reaction force of block 1 on block 2. We use these free-body diagrams in Applications of Newton’s Laws .

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Block on the table (coupled blocks)

A block rests on the table, as shown. A light rope is attached to it and runs over a pulley. The other end of the rope is attached to a second block. The two blocks are said to be coupled. Block $m_2$ exerts a force due to its weight, which causes the system (two blocks and a string) to accelerate.

Strategy

We assume that the string has no mass so that we do not have to consider it as a separate object. Draw a free-body diagram for each block.

Solution

Significance

Each block accelerates (notice the labels shown for ${\overrightarrow{a}}_1$ and ${\overrightarrow{a}}_2$ ); however, assuming the string remains taut, they accelerate at the same rate. Thus, we have ${\overrightarrow{a}}_1={\overrightarrow{a}}_2$ . If we were to continue solving the problem, we could simply call the acceleration $\overrightarrow{a}$ . Also, we use two free-body diagrams because we are usually finding tension T , which may require us to use a system of two equations in this type of problem. The tension is the same on both $m_1\text{and}{m}_2$ .

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