![]() When the problem states that a boy “drops” a rock it implies that the rock is starting from rest, with an initial velocity of zero. One key to solving these problems is proper interpretation. If the rock takes 2.1 seconds to hit the water, how deep is the well?Īh, the classic “boy drops a rock in a well problem.” Despite the fact that many of today”s physics students may never see a well, this classic never seems to go out of style. The only difference is that the acceleration is not usually specifically stated in these problems, because it is a constant.Ī boy drops a rock into well and times how long it takes for him to hear it strike the water below. You will find that the problems that we cover in this lesson are really just special examples of the uniform equations that we covered in Lesson 1–4. Substituting g for a is simply done to remind us that the acceleration for each of these problems is a constant, which we can count among our “given” quantities. Of course, there is really no need to memorize or even rewrite a new set of equations. Some students and teachers prefer to rewrite the formulas to include the g, as shown here, to remind them to use the value of –9.81 m/s 2 for the acceleration. This means that you can use any of the formulas for uniform acceleration for free-fall problems. It is important for you to remember that g, the acceleration due to gravity, is just a specific acceleration. The Acceleration Due to Gravity Close to the Surface of Earth Using this sign convention, that means that we will use the value of –9.81 m/s 2 for g. It is a fairly standard practice for physics students and teachers to designate “upwards” as positive and “downward” as negative. ![]() We have spent some time in this chapter discussing the idea of using signs for direction. It is very important to remember that its acceleration doesn”t change during the entire flight (g is a constant) but its velocity certainly does. After that, it will begin to come back down, and its velocity will be increasing by 9.81 m/s every second. On the way up, its velocity is decreasing at a rate of 9.81 m/s every second, until it reaches a velocity of zero. If you throw a ball upward, it will experience this acceleration during its entire flight. When we say that an object is accelerating at a rate of 9.81 m/s 2, we mean that every second that it is falling, its velocity changes by 9.81 m/s. An object that has a constant nonzero acceleration does speed up, slow down, and/or change direction. If an object has a constant velocity, it means that it doesn”t speed up, slow down, or change direction. Notice that there is a difference between constant velocity and constant acceleration. Be careful not to confuse the symbol for the acceleration due to gravity with the symbol for grams. This rate of acceleration is a constant (near the surface of Earth) called “the acceleration due to gravity,” and is given the symbol g. Gravity will cause such objects to accelerate at a constant rate of 9.81 m/s 2. ![]() When objects are made to fall close to the surface of Earth, where the only unbalanced force acting on them is gravity, we say that they are “falling freely” or experiencing free fall. We won”t discuss why the objects accelerate yet, but we will discuss how they accelerate. The force of gravity causes objects to accelerate, but we said that we wouldn”t discuss forces in this chapter. Why do objects accelerate as they fall? You will learn more about this in our next chapter, as we study Newton”s second law of motion. This is clear evidence that objects accelerate (speed up) as they fall.Ĭan you imagine what the world would be like if objects didn”t accelerate as they fell? If objects maintained a constant velocity as they fell, then jumping off a 50-story building would be the same as jumping down from the curb! Dropping a glass from an inch above the floor would be the same as dropping one off a cliff! But, of course, falling objects do accelerate. Why is it that when you throw a baseball a few feet into the air you can catch it with your bare hand and not feel a sting, but when a baseball falls from a much higher point, like when someone hits a pop fly, the ball hits your hand hard enough to hurt? The answer, of course, is that the ball is falling faster when it has fallen a greater distance. Have you ever dropped an object, such as a glass, and been relieved when it didn”t break? Did you ever drop water balloons out of a high window? Did you ever make a connection between how high a baseball flies, and how much it stings your hand when you catch it? Think about some of the experiences that you have had with falling objects.
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