物理学专业英语B09

1、Physics Professional English,物理学专业英语,Physics Professional English,B8 Circular motion,NEW WORDS Page.34,NEW WORDS Page.35,Gravitational force,B9 Gravitation,All massesattract each other with a gravitational force. If point massesm1 and m2, are a distance r apart, and F is the force on each, then acco

2、rding to Newtons law of gravitation:,With a suitable constant, the above proportion can be turned into an equation:,B9 Gravitation,G is called the gravitational constant. It is found by experiment using large laboratory masses and an extremely sensitive force-measuring system. In 51units, the value

3、of G is 6.67 X 10-11 N m2 kg-2.,The equation on the left is also valid for spherical masses of uniform density, with centres r apart, as above. Note: Newtons law of gravitation is an example of an inverse square law. If the distance r doubles, the force F drops to one quarter, and so on. Gravitation

4、al forces are always forces of attraction. Gravitational forces are extremely weak, unless at least one of the objects is of planetary mass or more.,B9 Gravitation,Gravitational field If a mass feels a gravitational force, then it is in a gravitational field. The gravitational field strength. g is d

5、efined like this:,B9 Gravitation,For example, if a mass of 2 kg feels a gravitational force of 10 N, then g is 5 N kg-1.,Note: Gravitational field strength is a vector. g is a variable and can have different values. The symbol g above does not imply the particular value of 9.81 N kg-1 near the Earth

6、s surface. The force acting on a mass in a gravitational field can be found by rearranging the equation above: F = mg.,B9 Gravitation,Note: The gravitational field around a spherical mass is shown above. It is called a radial field because of its shape. Inside the mass the equation on the left does

7、not apply. g falls to zero at the centre. Equipotential lines are explained on the next page.,B9 Gravitation,The Earths gravitational field strength,B9 Gravitation,At the surface If M is the Earths mass, R is its radius, and go is the gravitational field strength at its surface, then:,(1),B9 Gravita

8、tion,Note: go is 9.81 N kg-1 It is more commonly known as g (without the 0) Here however, the 0 has been added to distinguish it from other possible values of g. Using measured values of go R, and G in the above equation, the Earths mass M can be calculated. With R known, the Earths average density

9、can also be found. Above the surface In this case, g = GM l r2. From this and equation (1), the following result is obtained: So as the distance from the Earth increases, g decreases.,B9 Gravitation,Gravitational potential,Work must be done to move a mass against a gravitational field. Above, mass M

10、 causes a gravitational field. Mass m has been moved through this field, from an infinite distance (where the gravitational force is zero), to point P.,B9 Gravitation,The gravitational potential V (at point P) is defined as V = W / m where W is the work done in moving a mass m from infinity () to po

11、int P. Note: Like energy, gravitational potential is a scalar. At infinity, the gravitational potential is zero. Elsewhere, the gravitational potential is negative. This is because gravity is a force of attraction. Work is done by the mass as it is pulled from 00 to P, so negative work is done on it

12、. For example, if 1000 J of work are done by a 2 kg mass when it moves from 00 to P, then -1000 J of work are done on it. So V = -1000 / 2 = -500 J kg-1.,B9 Gravitation,Linking potential and field strength,Above, work W is done on a small mass m in moving it from P to P in a uniform gravitational fi

13、eld g. So, from (2): W = mv This equation gives the work done on the mass.,B9 Gravitation,So work done by mass = -mv But work done by mass = force x distance moved = mg r So mg r = -m V Therefore g = - V/ r In calculus notation, there is a more general version of this equation which also applies to

14、non-uniform fields: Note: In the above equations, the minus sign indicates that g is in the direction of decreasing potential.,B9 Gravitation,Gravitational potential in a radial field A radial field is shown on page 34. Provided r is not less than the radius of the sphere: g = GM / r2,Combining thes

15、e, and using calculus, gives V = - GM / r,B9 Gravitation,Note: V 1/r. So if the distance r doubles, the gravitational potential V halves, and so on. (Inside the mass, this does not apply.) In the diagram on the opposite page, each equipotential line is a line joining points of equal potential. In th

16、e case of the Earth, the gravitational potential Vo at the surface is -GMIR, where R is the radius.,B9 Gravitation,Escape speed This is the speed, vesc at which an object must leave a planets surface to completely escape its gravitational field (i.e. be thrown to infinity). For this, the object must be given enough KE t