In Chapters 3 and 4, you studied in detail how objects move, using accelerations to predict velocities and positions at various times. The study of how objects move is called kinematics. But physicists want to be able to explain why the motion occurs. Dynamics is the study of why objects move; it is concerned with forces, the central idea of this chapter.
What do we mean by a force? In everyday language we can think of a force as a push or a pull. For example, if you use your hand to push against your friend, then you exert a force. If you pull a wagon with a rope, that pull is a force. Some forces are not directly visible, but are still very real, such as the force of gravitational attraction of Earth on the Moon or a satellite or indeed on your body. Draw up a list of all the different types of forces that you can think of (Figure 5-1 may give you ideas to get started). There are many types of forces— you will encounter some in this chapter, and others throughout the rest of the book. The idea of force is one of the most important concepts in physics.
We can also define a force in the following way. A force, if not cancelled by another force acting in the opposite direction, results in acceleration in the direction of the applied force. An unopposed force will therefore change the velocity of the object. For example, a force applied to an object that was initially not moving will cause a velocity in the direction of the force. A force applied in the same direction as the original velocity of an object will increase that velocity, while a force in the opposite direction will decrease it.
In the preceding paragraph, we talked about the direction of the force, and indeed forces are vector quantities. When we describe a force, we must give both the magnitude and the direction (or use another system, such as vector components). The vector relationships you learned in Chapter 2 will be essential in this chapter.
The SI unit of force is the newton ( N ). An old British unit for force that you may encounter in everyday life is the pound ( lb ), but in this textbook we work almost exclusively with SI units. We can express the newton in terms of the fundamental SI units that you encountered in Chapter 1:
1 N = 1 kg ⋅ m s 2
You will see in Section 5-3 why the relationship has this form.
In the definition of force, we mentioned the possibility of a force being opposed by another force. What is important is the net force, the resultant when all of the forces on an object are added as vectors. Interactive Activity 5-1 will build your expertise in finding net forces for one-dimensional situations.
In this activity, you will use the PhET simulation “Forces and Motion: Basics” to find the net force when various competing forces are applied in a one-dimensional situation.
PhET Interactive Simulations - University of Colorado Boulder http://phet.colorado.edu
Use the Net Force tab (first on the left). We will explore how the net force changes as we apply different force combinations. On the top right click the selections for both Values and Sum of Forces. You add forces by dragging people to the rope, the larger people apply higher forces.
(a) Drag a small person and the largest person to the right side of the rope. What are their individual forces (in N ) and together what is the net force?
The individual force of the small person is .
The individual force of the largest person is .
The net force is to the left right .
(b) Now press the Go button and describe what happens. When finished press the Return button to get ready for the next part.
The system will accelerate to the right.
The system will remain stationary.
The system will accelerate to the left.
(c) Now drag two small persons and one largest person to the left (while leaving the people from the first part on the right). What is the total force to the left, the total force to the right, and the net force now?
The total force to the left is .
The total force to the right is .
(d) Predict and observe what now happens when you press the Go button. When finished this part press the Return button.
(e) If there was to be no acceleration how could the configuration be changed? State both ways, and try them to confirm that there is zero net force and no acceleration.
(f) Answer the following multiple-choice question to test your understanding of the concepts of this activity. There is a 850 N applied force to the right, and a 250 N applied force to the left. What third force needs to be added in order for no acceleration?
600 N force to the right.
600 N force to the left
1100 N force to the left
1100 N force to the right.
The object in Figure 5-2 is acted upon by the two forces shown, each of magnitude 470 N
The net force on the object is
470 N
940 N
zero
none of the above
In Figure 5-2 we showed the forces pushing inward on the object. In physics we usually draw the forces starting from the centre of the object and simplify the object to a point. We call this a free body diagram (FBD). We draw a simple one-dimensional FBD in Example 5-1.
You are free to select the orientation of the coordinate axes and the definitions of the positive directions for those axes, but you must be consistent throughout the question. It is good practice to state these at the beginning of a problem. It is also important to interpret the meaning of your mathematical answer, as we show in Example 5-1.
As shown in Figure 5-3, two forces act on a body. One force acts to the right with magnitude 1100 N , while the other force is to the left with a magnitude of 700 N . Find the net force acting on the object.
Figure 5-3 is already in the form of an FBD, with the vectors drawn relative to a point representing the object. We will choose the x -axis in the conventional horizontal sense, with positive being to the right. We label the force to the right as F → 1 and the one to the left as F → 2 . We can therefore write the sum of the forces in the following way using the unit vector i ^ notation from Chapter 2:
F → net = F → 1 + F → 2 = 1100 N i ^ − 700 N i ^ = 400 N i ^
Our net force is 400 N and is in the positive x -direction, which means toward the right.
The forces point in opposite directions, so we expect the net force to be the difference in the magnitudes of the two forces. Since the larger force points to the right, we expect the net force to be in that direction as well.