Physics
Free Falling Object
A free falling object is an object that is falling under the sole influence of gravity, with no other forces acting upon it. In this state, the object experiences a constant acceleration due to gravity, typically denoted as 9.81 m/s^2 near the surface of the Earth. The motion of a free falling object can be described using equations of motion derived from Newton's laws of motion.
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eBook - PDFWorkshop Physics Activity Guide Module 1
Mechanics I
- Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
In the absence of air resistance, any two objects dropped at the same time will fall in exactly the same way and will hit the ground at the same time. Of course, because air resistance is almost always at play in the real world, our everyday experience suggests that a heav- ier object will land slightly before a lighter object. But careful experiments done in controlled situations demonstrate very clearly, and perhaps surprisingly, that objects with different masses accelerate at exactly the same rate. 5 Let’s see if we can understand this observation using Newton’s second law. To do so, we need to introduce an important concept known as a free-body diagram. The Free-Body Diagram: An Introduction In its basic form, a free-body diagram is constructed by drawing a simple rep- resentation of an object, perhaps a circle to represent a ball or a rectangle to represent a block of wood, and then drawing an arrow to represent each force acting on the object. The arrows are drawn according to the following rules: • The tail of each arrow is placed at the point where the force is acting. • Each arrow points in the direction the force acts and is labeled by its magnitude. • The length of each arrow is proportional to the magnitude of the force. There are a few important details worth mentioning. First, the point at which a force acts is not always obvious, and some forces act at more than one location. For example, there is a tiny gravitational attraction between every point in Earth and every point in an object. However, the result of all these micro-forces is extremely well approximated by a single force acting at the center-of-mass of 5 A truly spectacular example of free-fall with no air resistance is demonstrated in an episode of the BBC series The Human Universe, where a bowling ball and some feathers are dropped from a height of over 100 feet in a near perfect vacuum.
Available until 9 Apr |Learn more- Carlos A. Smith, Scott W. Campbell(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
19 2 Objects in a Gravitational Field This chapter is essentially an extension of Chapter 1 in that it shows how basic physics helps in developing mathematical models, and how basic calculus helps in obtaining the analytical solutions of models. The chapter also shows a method to keep track of the equa-tions and unknowns while developing models; we strongly recommend the reader to use it. An object in a gravitational field (gravity acting on objects) is the topic of the chapter. As we mentioned in Chapter 1, any modeling starts by using a basic physical law, followed by equations describing physical elements and experimental facts of phenomena related to the physics of the system . In the case of objects in a gravitational field, the physical law that helps is Newton’s second law: F m a = where the arrows above the force F and the acceleration a indicate that these quantities are vectors (meaning that direction and magnitude must be specified). Because in this chapter we will only be considering forces acting on the object to be perpendicular to the ground, in the y direction, such as gravity, we write the law again as F m a y y = ∑ (2.1) The summation sign is used in F y when there is more than one force acting on the object. In modeling the systems in this chapter, we have to choose a direction, up or down, as pos-itive. In all cases, unless otherwise specified, the positive direction is the “up direction.” 2.1 An Example An object of 20 kg is held in the air 30 m above the ground and released; Figure 2.1 shows the setup. Develop the models that describe the velocity and position of the object as a function of time once it is released. As an object falls, the two most common forces acting on it are gravity and air resistance.
eBook - PDF- David R. Sokoloff, Ronald K. Thornton, Priscilla W. Laws(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
A prime example of an invisible force is the gravitational force—the attraction of the Earth for objects. When an object falls close to the surface of the Earth, there is no obvious force being applied to it. Whatever is causing the object to move is invisible. Most peo- ple rather casually refer to the cause of falling motions as the action of “gravity.” What is gravity? Can we describe gravity as just another force? Can we describe its effects mathematically? Can Newton’s laws be interpreted in such a way that they can be used for the mathematical prediction of motions that are influenced by gravity? In this lab you will first study vertical motion and the gravitational force. Then you will look at the motion of an object along an inclined ramp. You will also explore the relationship between mass and weight, and the meaning of mass. Later you will examine the mechanism for normal force—a common type of force that often opposes the gravitational force to keep an object from moving. INVESTIGATION 1: MOTION AND GRAVITY Let’s begin the study of the phenomenon of gravity by examining the motion of an object such as a ball when it is allowed to fall vertically near the surface of the Earth. This study is not easy, because the motion happens very quickly! You can first predict what kind of motion the ball undergoes by tossing a ball in the lab- oratory several times and seeing what you think is going on. A falling motion is too fast to observe carefully by eye. You will need the aid of the motion detector and computer to examine the motion quantitatively. For- tunately, the motion detector can do measurements just fast enough to graph this motion. To carry out your measurements you will need • computer-based laboratory system • RealTime Physics Mechanics experiment configuration files • motion detector • tape or other mechanism to attach motion detector to the ceiling • basketball or other uniformly round large ball
No longer available |Learn morePhysics for Scientists and Engineers
Foundations and Connections, Extended Version with Modern Physics
- Debora Katz(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 130 CHAPTER 5 Newton’s Laws of Motion 5-7 Some Specific Forces As you study physics, you will encounter many forces. You should expect to learn three things about each one: its source, its magnitude, and its direction. This section presents a partial list that will make our study of Newton’s laws less abstract. Gravity Near the Earth’s Surface Gravity, or the gravitational force (the two terms are synonymous), is the field force that keeps us on the surface of the Earth and keeps the planets in orbit around the Sun. In general, any two objects that have mass exert an attractive gravitational force on each other. The closer the objects are together, the stronger their gravitational attraction. The general gravitational force between any two bodies is described in Chapter 7. For now, let’s focus on the gravitational force exerted by the Earth on objects located near its surface. From Chapter 2, when an object is in free fall, the only force acting on it is grav- ity. Experiments show that in the absence of air resistance, all objects in free fall near the surface of the Earth have the same downward acceleration g. Because the Earth’s gravitational force F u g is the only force acting on such an object, Newton’s second law for this situation is simply F u tot 5 F u g 5 ma u (5.4) If we choose an upward-pointing y axis, we can represent the acceleration as a u 5 2g e ˆ (5.5) Substitute Equation 5.5 into Equation 5.4 to find the gravitational force acting on an object of mass m near the Earth’s surface: F u g 5 2mg e ˆ (5.6) The gravitational force is always attractive; that is, all objects are always pulled to- ward the center of the Earth. Because of its role in Equation 5.6, g is also known as the local acceleration due to gravity. There is an intimate connection between gravity and what we call weight.
eBook - PDFThe Mechanical Universe
Mechanics and Heat, Advanced Edition
- Steven C. Frautschi, Richard P. Olenick, Tom M. Apostol, David L. Goodstein(Authors)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
THE LAW OF FALLING BODIES Example 2 The flower pot in Example 1 falls past a window partway down with a speed of 24 ft/s. How far above this window did the flower pot originate? The relation obtained above by eliminating r from Eqs. ( 2.14 ) and ( 2.15 ), v -/2gs, can be used here as well in the form £ m (24 ft/s) m 2g 2 x 32 ft/s 2 Note that in these examples we put in numbers only at the last step, after first solving for 5 algebraically. This is usually the best way to proceed, both because the algebraic answer is so informative (e.g., in the present case it gives s for any v and-g) and because when numerical values are inserted at an early stage, carrying them through subsequent steps is a cumbersome and error-prone process. 2.9 A FINAL WORD One of the jobs of physics is to find simple, economical underlying principles that explain the complicated world we live in. We have done that here. If we drop an object, it falls. As it falls, its motion is opposed, with varying degrees of success, by the air through which it moves. If we can imagine disposing of the air and describing the effect of gravity alone, we discover a dramatic and surprising fact: all bodies fall at the same rate. We could be satisfied with that fact. After all, discovering it was quite an impressive accomplishment. But of course, we are not satisfied. We want to know, why is it true? What is the nature of gravity that leads to such strange behavior? That question has tumed out to be one of the most profound in the history of physics. It has persisted even into our own century. It was the starting point from which Albert Einstein built his celebrated general theory of relativity. But we are getting ahead of our story. Once we knew there was one law for all falling bodies, the job was then to express that law with precision. We have done that too. We learned that all bodies fall with the same constant acceleration.
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