Having studied the laws of motion and the two important laws of force, you are ready to apply them to a variety of situations. We will describe a few examples in this chapter jus t to get you started. In each case you should note the relationship between the forces acting on an object and the acceleration that results. Then you might focus on the way the acceleration determines the subsequent motion of the object. As you gain the abili- ty to relate these ideas, you should be able to explain a wide range of phenomena. Gravitational Acceleration We have seen that an object near the earth’s surface experiences a downward force, called its weight, due to its attraction to the earth. The strength of the force is proportional to the object’s mass, so the acceleration it causes is the same as that for any other object at the same location. The force does not depend on the object’ s motion and it changes only slightly as the object moves either closer to or farther from the center of the earth. These small changes can often be neglected—as we will do—when considering the motion of falling objects. Thus, when gravity is the only important force, the object moves under the influence of an unchanging downward force and therefore has an unchanging down- ward acceleration. It is instructive to consider some ofthe different kinds of motion that can result. First, suppose an object such as a baseball is dropped from a great height. Its speed increases steadi- ly as it fal ls. After 1 second, it s speed is 35 kilome- ters/hour (about 22 miles/hour); after 2 second, it is 70 kilometers/hour; after 3 seconds, 105 kilometers/hour; and after 4 secon ds, 140 kilometers/ hour. Do you see what it means when we say that the ball has an unchang- ing acceleration ? Each second the speed increases by 35 kilometers/hour whether it is the first second, the fifth, or any other. No matter what the speed at any time, the speed will be 35 kilometers/hour greater one second later (Fig. 5.1). Next, imagine throwing the ball straight up with an initial speed of 145 kilometers/hour (about 90 miles/hour). Instead of speeding up , the bal l becomes slower as it rises. After 1 second, its speed is 110 kilome- ters/hour . At the end of another second the speed has been reduced to 75 kilometers/hour; after 3 seconds, 40 kilo- meters/hour; and after 4 seconds, 5 kilometers/hour. Do you see what it means to say that the acceleration of the ball is the same as whe n it was dropped? Each second the speed changes by 35 kilometers/hour, the same rate as before. Now the speed decreases ra ther than in creases. This is just what we would expect in a case in which the applied force, gravity, directly opposes the initial motion of the ball. The amount of accelera tion (the rate at which speed changes) is the same as before, because the strength of the gravitational force does not depend on whether the ball is going up or down (Fig. 5.2). 37 5. Applications of the Laws of Force and Motion Figure 5.1. What does not c hange as the ball falls?
