Acceleration Due to Gravity
Acceleration due to gravity is the rate at which an object accelerates towards the Earth due to gravity. Near the surface of the Earth, this acceleration is approximately 9.81 meters per second squared. It is a constant value for a given location and is a fundamental concept in physics, influencing the motion of objects in free fall.
8 Key excerpts on "Acceleration Due to Gravity"
eBook - ePub- AlanJoel Witten(Author)
- 2017(Publication Date)
- Routledge(Publisher)
...2.7). Here the relevant values are Figure 2.7. Illustration of the parameters used to compute the Earth's gravitational acceleration. the universal gravitational constant G = 6.67 X 10 -8 dynes-centimeters squared per gram squared (the dyne is a unit of force), the mass of the Earth M = 5.97 X 10 27 grams, and the radius of the Earth R = 6.37 X 10 8 centimeters. Using these values in Equation 2.4 yields the well-known value for g of 980 cm per second squared. There is a special name given to gravitational force that distinguishes it from all other forces and this name is 'weight.' Although weight, being a force, is a vector, it is more commonly treated as scalar characterized by its magnitude, with its directional taken as downward (more properly radially inward towards the center of the Earth). It is well known that an object will weigh less on the moon than on the Earth. This is because the moon has far less mass than Earth so that by Equation 2.4 the gravitational acceleration,£, produced by the moon is less than that produced by the Earth and, by Equation 2.3, the resulting force, or weight, is proportionally less. The final element of this section is a more rigorous definition of force and acceleration. Acceleration is a change in velocity over some period of time and velocity is a vector characterized by a magnitude (speed) and a direction. Thus, an acceleration can be produced by a change in speed or a change in direction. From Newton's Law, a force is a vector equal to the product of the mass of an object times its acceleration. Since mass is a scalar, the direction of acceleration is the same as the direction of the force from which it was produced. Accelerations can be 'sensed' by the forces they produce. For example, depressing the accelerator of an automobile causes a change in speed and this type of acceleration is a change in magnitude...
eBook - ePub- Alan Hendrickson(Author)
- 2012(Publication Date)
- Routledge(Publisher)
...To do this involves using integration (this is not a technique you need to know, it is included only as a glimpse into the mathematics beyond the equations of constant acceleration): Δ x = ∫ 0 Δ t t o t a l v d t Any combination of just acceleration and deceleration, illustrated at the left below, must reach 1.9 m/sec to cover the 9.5 meters in 10 seconds. All combinations that involve one period of constant acceleration, constant velocity, and deceleration, as is illustrated at the right, will have a maximum velocity somewhere between 0.95 and 1.9 m/sec (equal accelerations and decelerations are shown on this graph, but this is not a requirement). Since the triangular motion profile’s maximum velocity is always exactly twice the velocity found if the move occurred all at one speed, calculating either alone essentially gives you both answers. The Acceleration Due to Gravity Gravity causes unsupported objects to fall, and the rate at which they accelerate can be measured. For a given spot on Earth, the Acceleration Due to Gravity is constant. At different places though, there are slight variations in this acceleration depending mainly on latitude and elevation. The spinning Earth has a slight tendency to throw objects off its surface, and this effect is greatest at the equator and nil at the poles. Elevation alters acceleration because the gravitational attraction between objects depends on the distance between their centers of mass. At high altitude, the centers are further apart, and both the attraction and acceleration are less. For most uses, and undoubtedly all theatre uses, the Acceleration Due to Gravity can be assumed to be 32.2 ft/sec 2 (9.81 m/sec 2). Even this is often reduced to simply 32 ft/sec 2 (9.8 m/sec 2) with a loss of accuracy of less than 1%...
eBook - ePub- John Bird(Author)
- 2019(Publication Date)
- Routledge(Publisher)
...Chapter 18 Acceleration Why it is important to understand: Acceleration Acceleration may be defined as a ‘change in velocity’. This change can be in the magnitude (speed) of the velocity or the direction of the velocity. In daily life we use acceleration as a term for the speeding up of objects and decelerating for the slowing down of objects. If there is a change in the velocity, whether it is slowing down or speeding up, or changing its direction, we say that the object is accelerating. If an object is moving at constant speed in a circular motion – such as a satellite orbiting the earth – it is said to be accelerating because change in direction of motion means its velocity is changing even if speed may be constant. This is called centripetal (directed towards the centre) acceleration. On the other hand, if the direction of motion of the object is not changing but its speed is, this is called tangential acceleration. If the direction of acceleration is in the same direction as that of velocity then the object is said to be speeding up or accelerating. If the acceleration and velocity are in opposite directions then the object is said to be slowing down or decelerating. An example of constant acceleration is the effect of the gravity of earth on an object in free fall. Measurement of the acceleration of a vehicle enables an evaluation of the overall vehicle performance and response. Detection of rapid negative acceleration of a vehicle is used to detect vehicle collision and deploy airbags. The measurement of acceleration is also used to measure seismic activity, inclination and machine vibration...
eBook - ePub- J Jones, J Burdess, J Fawcett(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
...The acceleration vector will always be in the same direction as the resultant force vector. Laws 1 and 2 apply only to motion relative to frames of reference which are either stationary or translating with constant velocity. Such frames are called inertial frames of reference and the acceleration measured in such a frame is always the absolute acceleration of the particle. However, the errors introduced by neglecting the accelerations due to rotation of the Earth are insignificant in most engineering applications, and the accelerations measured relative to the Earth may be considered as absolute. From the Second Law we also see that when the acceleration of a particle is zero the sum of the forces acting upon it is zero. The particle is then said to be in equilibrium under the action of the applied forces and F = 0. If the particle also has zero velocity it is in static equilibrium. 2.2 Units If we choose a set of units such that one unit of mass multiplied by one unit of acceleration gives one unit of force, k will have a value of one. Under these conditions we may express the Second Law as A system of units in which the product of any two unit quantities is the unit of the resultant quantity is called a coherent system of units. The SI system (Système International d’Unites), which will be used throughout this text, is a coherent system of metric units. It is now becoming established in many countries as the only legal system of units. We have already come across two basic units in our study of kinematics, the metre, which is the basic unit of length, and the second, the basic unit of time. All the other units in kinematics, i.e. those of velocity and acceleration, are expressed in terms of these two basic units. In dynamics we need to introduce the basic unit of mass, the kilogram. These three units, the kilogram (kg), the metre (m), and the second (s) are the only basic units required in the study of dynamics...
eBook - ePubBasic Engineering Mechanics Explained, Volume 1
Principles and Static Forces
- Gregory Pastoll, Gregory Pastoll(Authors)
- 2019(Publication Date)
- Gregory Pastoll(Publisher)
...To understand this, we need to understand the connection between weight and gravity. Weight, Newton’s Law of Gravitation, and gravitational acceleration Isaac Newton, following the work of Robert Hooke, confirmed that a gravitational force exists between any two objects in the universe. Simply due to the fact that the objects have mass, they attract each other. This means that if two rocks are drifting in space, near one another, they will each exert a pull on the other, the result of which is that they will gradually accelerate towards one another. The more mass the two objects possess, the greater is this force. The further apart they are, the smaller is this force. Newton’s Law of Gravitation tell us that the magnitude of the gravitational force, F, depends on these variables, in the following relationship: F = (Gm 1 m 2)/r 2 Where G is the universal gravitation constant, m 1 and m 2 are the masses of the two objects, and r is the distance between their centres of gravity. This law applies to all bodies, not only to the gravitational force between a given object and the Earth. Every object that possesses mass attracts every other object with a force of attraction given by the above equation. It might be hard to believe that two pencils lying on your desk exert a gravitational pull on one another, but they do. The magnitude of this pull is insignificant, because both of their masses are vastly smaller than the mass of the earth. The magnitude of the gravitational force of attraction between two small objects was first determined in a famous experiment by the British scientist Henry Cavendish in 1797. A torsion wire suspended from an overhead beam supported a horizontal rod, on the ends of which were mounted two small lead spheres. When the rod had settled into an equilibrium position, two larger spheres were brought from a distance, to a position on the circle of movement close to the small ones, and equidistant from them...
eBook - ePub- Bertrand Russell(Author)
- 2009(Publication Date)
- Routledge(Publisher)
...What this means is as follows: When you apply a given force 1 to a heavy body, you do not give it as much acceleration as you would to a light body. What is called the ‘inertial’ mass of a body is measured by the amount of force required to produce a given acceleration. At a given point of the earth’s surface, the ‘mass’ is proportional to the ‘weight’. What is measured by scales is rather the mass than the weight: the weight is defined as the force with which the earth attracts the body. Now this force is greater at the poles than at the equator, because at the equator the rotation of the earth produces a ‘centrifugal force’ which partially counteracts gravitation. The force of the earth’s attraction is also greater on the surface of the earth than it is at a great height or at the bottom of a very deep mine. None of these variations are shown by scales, because they affect the weights used just as much as the body weighed: but they are shown if we use a spring balance. The mass does not vary in the course of these changes of weight. The ‘gravitational’ mass is differently defined. It is capable of two meanings. We may mean (1) the way a body responds in a situation where gravitation has a known intensity, for example, on the surface of the earth, or on the surface of the sun; or (2), the intensity of the gravitational force produced by the body, as, for example, the sun produces stronger gravitational forces than the earth does. The old theory says that the force of gravitation between two bodies is proportional to the product of their masses. Now let us consider the attraction of different bodies to one and the same body, say the sun. Then different bodies are attracted by forces which are proportional to their masses, and which, therefore, produce exactly the same acceleration in all of them...
eBook - ePub- Laura Fermi, Gilberto Bernardini(Authors)
- 2013(Publication Date)
- Dover Publications(Publisher)
...In their experiment they tried to approximate as much as possible the simple conditions of an ideal phenomenon, but they know that they can do this only to a certain point. They know, for instance, that it will be practically impossible to observe the departure of the true path of a projectile from a parabola provided the heights from which projectiles are thrown are very small in respect to the radius of the earth. Under these conditions the effect of the curvature of the earth and the variations of the acceleration of gravity with the distance from the center are negligible, and the direction of this acceleration is constant. Hence, in “local motion” the acceleration of gravity is everywhere constant in magnitude and direction. In a similar way Salviati says that they know the resistance of air will not appreciably alter the velocity of a thrown body provided this velocity is not too great (that is, very small in comparison with the constant velocity that the body would acquire after a long fall through the air). Galileo’s great contemporary, Descartes, writing about Two New Sciences a few years after its publication, maintained that he had nothing to learn from Galileo and that Galileo’s theory was wrong, leading to results that went against those of observation...
eBook - ePub- Gino C. Segrè, John D. Stack(Authors)
- 2022(Publication Date)
- University of Chicago Press(Publisher)
...The addition of V cent to V g does account for centrifugal effects, but it leaves out the Coriolis force. The latter comes into play only when the body being considered is moving relative to the Earth, e.g., a part of the atmosphere which is in motion as in a storm, discussed further in Sec. (6). For a body of mass μ hanging at rest from a string connected to an earthbound support, there is no Coriolis force and the tension in the string is given by This provides a simple way to measure g. Equipotentials and Gravitational Acceleration What is commonly called Clairaut’s theorem, is an equation for the gravitational acceleration on the Earth’s surface as a function of latitude or equivalently, the polar angle θ. As will be seen below, it is easy to derive from our expression for V tot as given in Eq. (2.14) and holds at the same level of accuracy. Using Eq. (2.15) to obtain g leads to an expression of the form Both g r and g θ depend on r and θ. To proceed, one needs to find the surface of the Earth. Specifically, for a given latitude or polar angle, what is the value of r that corresponds to being at the surface of the Earth? The answer to this question depends on the notion of equipotential, an equipotential being a surface on which V tot is constant. An important property of an equipotential is that the gravitational force on a mass is always perpendicular to the equipotential surface on which the mass is located. A fluid cannot support a force tangent to its surface, so the surface of a fluid which is in mechanical equilibrium will coincide with a gravitational equipotential. As a simple example of this, consider a handheld container of water. If the container is tilted, the surface of the water remains horizontal at a constant elevation h, and therefore at a constant value of the local gravitational potential, gh. Applying this same reasoning to the Earth as a whole, it is clear that the surface of the ocean must be an equipotential...
