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Illustration 4.2: Free-Body Diagrams

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In Illustration 4.2 an 8-kg block is pushed across the floor (position is given in centimeters and time is given in seconds). Along with the motion, several possible free-body diagrams are drawn for both the x and y components of the force. Note that only one of the possible free-body diagrams is correct for each component. Restart.

Look at the motion of the block by pressing "play." How do we analyze the motion of the block using forces? Well, the first thing we do is draw a picture that shows only the object and the direction of the forces. The picture we draw is called a free-body diagram. First we will analyze the forces in the x direction and then the forces in the y direction.

Consider the forces in the x direction (Free-Body x). What forces act? How big are they? How do we know? Click each of the four x-direction free-body diagrams. Which one do you think is correct? Usually we know all of the forces that act, but here we just know of the push that is shown in Free-Body 1x. Is that the only force acting in the x direction? Newton's second law says that a net force acting on an object means that the object must be accelerating (the object's velocity changes). Does the block's velocity change? No (You can tell either by looking at the block's motion or by calculating the velocity and showing that it does not change.); therefore there must be another force acting, that of friction that opposes the motion. This eliminates Free-Body 1x and Free-Body 3x because they show only one force. The second force not only opposes motion, but in this animation it is exactly the same size as the push. This means that Free-Body 2x is not correct either. Therefore, Free-Body 4x depicts the correct free-body diagram for the forces that act in the x direction. (The form of the frictional force will be considered in detail in Chapter 5.)

Now consider the forces in the y direction (Free-Body y). What forces act? How big are they? How do we know? Click each of the four y-direction free-body diagrams. Which one do you think is correct? Usually we know all of the forces that act, but here we just know of the force of gravity that is shown in Free-Body 1y. Is that the only force acting in the y direction? Since the block does not accelerate in the y direction, there must be another force acting. This eliminates Free-Body 1y and Free-Body 2y because they show only one force. The force that is missing is the so-called normal force (the force of the table acting on the block) that opposes gravity. The normal force not only opposes motion in the y direction but here is exactly the same size as the gravitational force, the object's weight. This means that Free-Body 3y cannot be correct either. Therefore, Free-Body 4y depicts the correct free-body diagram for the forces that act in the y direction. Note that the normal force is not always equal to the weight. If there is an acceleration in the y direction or if the block is on an incline, the normal is not equal to the weight.

Note that in order to solve the complete problem we would draw all of the forces on one free-body diagram. We have done the analysis here by breaking up the motion into components. Given what we have said above, what does the complete free-body diagram look like? The complete free-body diagram animation shows the combination of the forces in the x direction and the forces in the y direction.

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