## 4.3 - Free Body Diagrams Revisited

The Free Body Diagram (FBD) is an excellent tool for analyzing the forces acting on an object. A well drawn, carefully analyzed FBD will yield the Net Force acting on the object and this is the key to determining how the motion of the object will change.

**Example 1**: A 20 kg crate sits at rest on a level surface. A warehouse worker then pushes the box to the right with a force of 60 N. As it slides, it encounters a frictional force of 20 N. What is the acceleration of the box?

**Analysis**– It is the NET force that causes the object to accelerate. Since we know the mass of this object, if we determine the net force, we can calculate the acceleration.

**Step 1 – Draw the Free Body Diagram. Label the forces:**

**Step 2 – Record the magnitudes of the forces.**In this case we are given the magnitudes of the push and of friction so we can record those directly. Next we can calculate the weight (Weight = mg). Finally, the crate had initially been sitting on the level surface so we know that that forces acting on it at the time (Weight and Normal force) had to be balanced. Therefore, Normal Force = Weight.

**Step 3 – Determine the Net Force**

**.**The unbalanced force acting on this crate is

**40 N to the right**(60 N Right – 20 N Left). All the rest of the forces “cancel out”. It is as if there is only one force (40 N to the right) acting on this crate.

**Step 4 – Calculate the acceleration**

**Example 2:**A 150 kg Black Bear slides down the side of a tree. Friction is definitely present. He accelerates downward at a rate of 4.5 m/s/s. What is the force of friction acting on the bear?

**Analysis**– What makes an object accelerate? The NET force acting on the object. In this case, we know the acceleration of the object so we can calculate the Net Force. Then, using the Free Body Diagram, we can find the frictional force acting on the bear.

**Step 1 – Calculate the Net Force.**

**Step 2 – Draw Free Body Diagram. Label the Forces**.

There are only

**TWO**forces acting on the bear – weight (downward) and friction (upward). The bear is

__accelerating__downward. What does that mean?

*It means that WEIGHT > FRICTION*. How much greater?

**675 N greater.**

**Step 3 – Plug in magnitudes, solve for friction force.**

The friction force is 675 N less than the weight.