Physics
Gravitational Acceleration
Gravitational acceleration refers to the acceleration experienced by an object due to the force of gravity. It is a constant value near the surface of the Earth, approximately 9.81 meters per second squared. This acceleration causes objects to fall towards the Earth at a consistent rate, regardless of their mass.
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10 Key excerpts on "Gravitational Acceleration"
- Thais Russomano, Gustavo Dalmarco, Felipe Prehn Falcao(Authors)
- 2022(Publication Date)
- Springer(Publisher)
Gravitation is also responsible for keeping the Earth and the other planets in their orbits around the sun, the Moon in its orbit around the Earth, the formation of tides, and various other natural phenomena that are commonly observed (Figure 1.1). Gravity, however, is the gravitation related to Earth. It is then the gravitational force that occurs between the Earth and other bodies, the force acting to pull objects toward the Earth. It is expressed as 1G (capital “G,” as opposed to the acceleration g). Bodies with less mass than the Earth will have values lower than 1G (the Moon has 1/6G), and bodies with mass bigger than the Earth will have values higher than 1G (planet Jupiter has 3.5G). C H A P T E R 1 General Concepts in Physics— Definition of Physical Terms 2 EFFECTS OF HYPER- AND MICROGRAVITY ON BIOMEDICAL EXPERIMENTS Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to and is expressed by the symbol m. Acceleration (expressed by the symbol a) is defined as the rate of change of velocity. It is thus a vector quantity with dimension length/time² (SI units m/s²), and the instantaneous accelera- tion of an objection is given by Equation 1.1. By being a vector, it must be described with both a direction and a magnitude. It can have positive and negative values — called acceleration (increasing speed) and deceleration (decreasing speed), respectively, as well as change in direction. a dv dt (1.1) where a is acceleration, v is velocity, t is time, and d is Leibniz’s notation for differentiation. Gravitation is one of the four fundamental interactions in nature, the other three being the electromagnetic force, the weak nuclear force, and the strong nuclear force. Compared to the other three fundamental interactions in nature, gravitation is the weakest one. It, however, acts over great distances and is always present. Gravitation is interpreted differently by classic mechanics, relativity, and quantum physics.
eBook - PDFWorkshop Physics Activity Guide Module 1
Mechanics I
- Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
First, recall that the sign is related to the direction of the acceleration, which depends on the coordinate system we choose. The motion sensor defines the pos- itive direction as pointing up in this experiment. Therefore, a negative acceler- ation tells us that the acceleration vector points down. Second, the measured acceleration may not be exactly what you expected. The reason for this dis- agreement is likely due to air resistance on the ball’s motion; it can be surpris- ingly challenging to record free-fall data that is not affected by air resistance to some degree. 2 Third, the phrase “acceleration due to gravity” can lead to mis- conceptions about how the gravitational force acts on objects. A better phrase might be “free-fall acceleration,” but even this has its problems. What we really need to understand is the gravitational force and how this force relates to the acceleration. Wests/Getty images 6.4 THE GRAVITATIONAL FORCE In the previous activity, we saw that a ball experiences an acceleration without the aid of a visible, applied force. However, if we believe Newton’s second law to be true—and we do!—then the fact that the object accelerates implies that there must be a force acting on the object. We call this the gravitational force. More specifically, because this force seems to emanate from Earth, we call it the gravitational force of Earth acting on the ball. Our task in this section is to investigate this gravitational force. For now, we will only consider the gravi- tational force near the surface of Earth. 2 Any object, including a basketball, will be affected by air resistance to some degree, but air resistance can be minimized by choosing a smaller, heavier object. Probably the best one can do in a classroom setting is to use a bowling ball. Of course, one must be extremely careful when tossing a bowling ball, as it can do serious damage if it lands on a motion sensor or someone’s foot!
- Daniel Fleisch, Julia Kregenow(Authors)
- 2013(Publication Date)
- Cambridge University Press(Publisher)
54 Gravity Using F g as the force in Newton’s Second Law gives a = F g m 1 = G m 1 m 2 R 2 m 1 = G m 1 m 2 R 2 m 1 = G m 2 R 2 . (2.4) So the acceleration of m 1 due to the force of gravity depends only on the mass of the other object ( m 2 ) and its distance – not on the amount of mass of the object itself ( m 1 ). That’s why, in the absence of other forces such as air resistance, all objects fall to Earth with the same acceleration regardless of their mass. How can this possibly be true? Shouldn’t an object with bigger mass fall faster, since the gravitational force between that object and Earth is greater? Well, it’s true that objects with greater mass experience a greater gravita-tional force from the Earth, but remember Newton’s Second Law: objects with greater mass resist acceleration more than objects with less mass (that is, more-massive objects have greater inertia). So, although the gravitational force is directly proportional to mass, acceleration is inversely proportional to mass, and combining these dependencies means that the acceleration of an object due to gravity does not depend on the object’s mass. To find the acceleration of an object near the surface of the Earth, just plug the values for the Earth’s mass and radius into Eq. 2.4 : a = G m Earth R 2 Earth = 6 . 67 × 10 − 11 N m 2 kg 2 6 × 10 24 kg ( 6 . 38 × 10 6 m ) 2 = 9 . 8 m s 2 . If you don’t see how the units work out in this equation, remember that newtons are equivalent to kg m/s 2 , as discussed in Section 1.1.6 . So, near the surface of the Earth, all objects experience the same acceler-ation due to gravity. In some texts, this Gravitational Acceleration is called g , which you should be careful not to confuse with G , the universal gravitational constant. Here are some exercises to check your understanding of Newton’s Laws of Motion; you’ll find additional problems at the end of this chapter.
eBook - PDF- David R. Sokoloff, Ronald K. Thornton, Priscilla W. Laws(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
LAB 6: GRAVITATIONAL FORCES 127 LAB 6: GRAVITATIONAL FORCES Name Date Partners And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction of gravity . . . —Isaac Newton OBJECTIVES • To explore the nature of motion along a vertical line near the Earth’s surface. • To extend the explanatory power of Newton’s laws by inventing an invisible force (the gravitational force) that correctly accounts for the falling motion of objects observed near the Earth’s surface. • To examine the magnitude of the acceleration of a falling object under the in- fluence of the gravitational force near the Earth’s surface. • To examine the motion of an object along an inclined ramp under the influ- ence of the gravitational force. • To define weight and discover its relationship to mass. • To discover the origin of normal forces. OVERVIEW You began your study of Newtonian dynamics in Lab 3 by developing the concept of force. Initially, when asked to define forces, most people think of a force as an obvious push or pull, such as a punch to the jaw or the tug of a rubber band. By studying the acceleration that results from a force when little friction is present, we came up with a second definition of force as that which causes acceleration. These two alternative definitions of force do not always appear to be the same. Push- ing on a wall doesn’t seem to cause the wall to move. An object dropped close to the surface of the Earth accelerates and yet there is no visible push or pull on it. 128 REALTIME PHYSICS: MECHANICS The genius of Newton was to recognize that he could define net force or com- bined force as that which causes acceleration, and that if the obvious applied forces did not account for the degree of acceleration then there must be other “invisi- ble” forces present. A prime example of an invisible force is the gravitational force—the attraction of the Earth for objects.
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.
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
First, let’s assume that Earth is a uniform sphere of mass M, and then let’s consider the magnitude of the gravitational force from Earth on a particle of mass m, located outside Earth a distance r from Earth’s centre. We rewrite Newton’s equation F = G m 1 m 2 r 2 as F = G Mm r 2 . (13.7) If the particle is released, it will fall towards the centre of Earth because of the gravitational force F, with an acceleration called the Gravitational Acceleration a g . Newton’s second law tells us that magnitudes F and a g are related by F = ma g . (13.8) From these last two equations, we can write the Gravitational Acceleration as a g = GM r 2 . (13.9) Table 13.1 shows values of a g computed for various altitudes above Earth’s surface. TABLE 13.1 Variation of a g with altitude Altitude (km) a g (m/s 2 ) Example 0 9.83 Mean Earth surface 8.8 9.80 Mt Everest peak 41.4 9.70 Highest parachute jump 400 8.70 International Space Station 35 700 0.225 Communication satellite Notice that a g is significant even at 400 km for the International Space Station. Crew members there may seem to float weightlessly, but they and the ISS are actually in free fall while also moving along the orbital path. Thus a g only appears to be zero. Since module 5.1, we have assumed that Earth is an inertial frame by neglecting its rotation. This simplification has allowed us to assume that the free‐fall acceleration g of a particle is the same as the particle’s Gravitational Acceleration (which we now call a g ). Furthermore, we assumed that g has the constant value 9.8 m/s 2 any place on Earth’s surface. However, any g value measured at a given location will differ from the a g value calculated with a g = GM/r 2 for that location for three reasons. Pdf_Folio:246 246 Fundamentals of physics 1. Earth’s mass is not distributed uniformly. 2. Earth is not a perfect sphere.
eBook - PDF- Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
a M /a a r 2 a /r 2 M (6400 km) 2 /(380,000 km) 2 2.8 10 4 . 300 Chapter 14 / Gravitation Figure 14-1. Both the Moon and the apple are accelerated toward the center of the Earth. The difference in their motions arises because the Moon has enough tangential speed v to main- tain a circular orbit. Moon Apple r M r a Earth v a M (= g ) a a confused with g, the free-fall acceleration on Earth, which is not universal and has different dimensions. The gravitational constant is a very small number, which explains why we do not ordinarily notice the gravita- tional force between objects around us. For example, the force between two 1-kg particles separated by a distance of 0.1 m would be of order 10 8 N, about equivalent to the weight of a speck of dust! Nevertheless, using sensitive ap- paratus physicists can measure these small attractive forces between common objects. Normally, however, it is only when the mass of at least one of the interacting bodies is large (planet-sized) that the effects of the gravitational force become significant. Equation 14-1 is in the form of an inverse-square force law, because the force depends on the inverse square of the distance. Electromagnetic forces also have the form of in- verse-square laws. None of the three fundamental quantities (force, mass, and distance) that appears in Eq. 14-1 is defined by that equation. In particular, force and mass were defined in Chapter 3. The gravitational force is just one type of force that represents the interaction of a particle with other parti- cles in its environment. As we discuss in the next section, once G is determined by experiment for one pair of bodies, that value can then be used to find the force between any other pair of bodies. The Vector Force Figure 14-2 a represents the gravitational force exerted by two particles on each other, which form an action – reaction pair according to Newton’s third law.
eBook - PDF- Philip Dyke, Roger Whitworth(Authors)
- 2017(Publication Date)
- Red Globe Press(Publisher)
Figure 5.1 shows a particle in motion under gravity. For now, we neglect air resistance, so that the only force acting is gravity itself. Gravity is assumed to be constant, hence this is a special case of motion under constant acceleration, which was dealt with in Chapter 1. Let us derive the equation of motion for the simple system shown in Figure 5.1. Note that we have chosen the x -axis to point in the opposite direction to the force due to gravity; therefore: mg m acceleration 5 : 1 99 x m O Figure 5.1 A falling particle (apple?) We recall that acceleration can be expressed in a number of different forms, so we need to select one that is convenient for our particular problem. You should use d v = d t if you are interested in obtaining velocity as a function of time, and v d v = d x if you are interested in obtaining velocity as a function of distance. Finally you should use d 2 x = d t 2 and integrate twice if you want displacement (distance above ground) as a function of time. Our equation of motion, after cancelling the mass m from both sides, is thus one of the following: d v d t g v d v d x g d 2 x d t 2 g 5 : 2 In order to become adept at choosing which of these equations to apply, we need to solve particular problems. Here are some examples that will help to focus these ideas. Example 5.1 An apple of mass 0.3 kg falls from a tree. Find (a) its velocity after 2 s, ignoring air resistance and assuming it has not hit the ground, and (b) the distance it travels. Solution (a) We wish to find v as a function of time, hence we use the first of the equations (5.2): 100 Guide to Mechanics d v d t g Integrating this with respect to time gives: v gt A where A is an arbitrary constant. We determine the value of A by using the condition that at time t 0, v 0. Hence, A 0. Taking g 9 : 81 m s 2 , we obtain: v gt 9 : 81 t 5 : 3 Hence for a particular time, v is completely determined.
eBook - PDF- L Z Fang, R Ruffini;;;(Authors)
- 1983(Publication Date)
- WSPC(Publisher)
The property of gravitation which enables gravity to be elimin-ated locally is commonly known as the principle of equivalence. This principle is the most fundamental characteristic of gravity. Why must we emphasize local limits time and again? This is be-cause real gravitational fields are only constant locally: gravitation-al acceleration g points to the earth's centre so that its direction varies from point to point around the earth, and its magnitude also varies, with height above the earth's surface. For a rigid lab falling freely, only its centre of mass is in free-fall, and all other parts of the lab, strictly speaking, are not in free-fall. Now, if there are two particles in the laboratory (see Fig. 1.4), their accelerations W m » * Fig. 1.4 Gravity can be eliminated only for a local system falling freely 16 point towards the earth's centre and are not parallel to each other. They have a relative acceleration, which causes them to approach one another. Suppose the two particles are initially at rest relative to each other. It is easy to show that the relative speed with which the particles approach one another is given by u = 4 ^26 M e h or u = -f-v£gh , Re * e where h is the distance fallen, d their separation, R e and M e are the radius and mass of the earth respectively, and gravitational 2 acceleration g = GM©/R e . The speed u is yery small. For example, -3 by taking d = 10 m, h = 10 km, then u * 10 m/s. The tides are brought about by the same relative acceleration mentioned above, so that the related force is called a tidal force. Since the tidal force cannot be eliminated by transforming the coordi-nates, it is possible, in principle, to detect the existence of gravita-tional fields. As u is proportional to d, the smaller the dimen-sions of a laboratory the more difficult it would be to carry out these observations. Strictly speaking, to state that all phenomena of gravity can be eliminated would be correct only for a point-like system in free-fall.
eBook - PDFApplied Mechanics
Made Simple
- George E. Drabble(Author)
- 2013(Publication Date)
- Made Simple(Publisher)
So, for any single given body falling freely to earth, we may be assumed to know the force acting upon it (its weight) and also its resultant acceleration (g). Denoting the weight by W, we may now substitute Wfor i 7 , and g for a in equation (1) thus: F = Ca Hence W = Cg ^ W and C = — g We now have a value for the constant number C for a body, providing we know its weight. Substituting this value back into our equation (1), we get the Equation of Motion for a body: It is of course a known fact that W 9 the weight of the body, varies from point to point in space, and (theoretically at least) can be zero. How, then, can the quantity Wig be a constant of proportionality for a body? The answer is that as W varies from place to place, g varies in exactly the same proportion. If our body is transported to the Moon, its weight will then be approximately one-fifth its weight on Earth. But the value of g M , the Moon's Gravitational Acceleration, will also be approximately one-fifth the value of g on Earth. In other words, bodies will fall to the Moon's surface at a rate of acceleration 46 Applied Mechanics Made Simple approximately one-fifth of the rate they fall on Earth, or approximately at 2 metres per second per second. This number which we have called C, and which we can now evaluate for any particular body (assuming we can weigh it), represents a measure of the resistance of the body to a force. The bigger the C, the smaller the acceleration for a given force. It is a number expressing quantitatively the inertia of the body. Unlike the weight of the body, which varies from place to place, inertia is constant. At least it is constant for a given system of measurement. If we choose to change our measurement of acceleration from metres per second per second to feet per second per second, the number C will of course be different.
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