1、.9: Motion in Fields9.2 Gravitational field, potential and energy.GravityRecap:Newtons universal law of gravitation:Gravitational field strength:the force per unit mass experienced by a small test mass (m) placed in the field.F = GMm r2g = GM r2.GPE in a uniform fieldWhen we do vertical work on a bo

2、ok, lifting it onto a shelf, we increase its gravitational potential energy (Ep). If the field is uniform (e.g. Only for very short distances above the surface of the Earth) we can say. GPE gained (Ep) = Work done = F x d = Weight x Change in height so. Ep = mghE.g. In many projectile motion questio

3、ns we assume the gravitational field strength (g) is constant.GPE in non-uniform fieldsHowever, as Newtons universal theory of gravity says, the force between two masses is not constant if their separation changes significantly. Also, the true zero of GPE is arbitrarily taken not as Earths surface b

4、ut at infinity. If work must be done to “l(fā)ift” a small mass from near Earth to zero at infinity then at all points GPE must be negative. (This is not the same as change in GPE which can be + or -)InfinityEp = 0Lots of positive work must be done on the small mass!Ep = negative.The GPE of any mass wil

5、l always be due to another mass (after all, what is attracting it from infinity?)Strictly speaking, the GPE is thus a property of the two masses.E.g. Calculate the potential energy of a 5kg mass at a point 200km above the surface of Earth. ( G = 6.67 10-11 N m2 kg-2 , mE= 6.0 1024 kg, rE= 6.4 106 m

6、)The gravitational potential energy of a mass at any point is defined as the work done in moving the mass from infinity to that point.Ep = - GMm r.The gravitational potential energy of a mass at any point is defined as the work done in moving the mass from infinity to that point.Q. What do the indic

7、ated properties of these two graphs represent?ab.Gravitational PotentialWhereas gravitational force on an object on Earth depends upon the mass of the object itself, gravitational field strength is a measure of the force per unit mass of an object at a point in Earths field.Similarly, whereas the GP

8、E of say a satellite, depends upon both the mass of Earth and the satellite itself, gravitational potential is a measure of the energy per unit mass at a point in Earths field.Thus for a field due to a (point or spherical) mass M:So .E.g. Calculate the potential of a 5kg mass at a point 200km above

9、the surface of Earth. What would be the potential of a 10kg mass at the same point? ( G = 6.67 10-11 N m2 kg-2 , mE= 6.0 1024 kg, rE= 6.4 106 m ) V = - GM rV = Gravitational potential (Jkg-1)The gravitational potential at a point in a field is defined as the work done per unit mass in bringing a poi

10、nt mass from infinity to the point in the field. V = Ep = - GMm mr m.Gravitational Potential in a uniform field.For a uniform fieldEp = mgh So V = Ep = mgh m mV = gh.How far apart are the equipotentials in this diagram?.Vr.Equipotential SurfacesEquipotential surfaces or lines join points of equal po

11、tential together. Thus if a mass is moved around on an equipotential surface no work is done.Thus the force due to the field, and therefore the direction of the field lines, must be perpendicular to the equipotential surfaces at all times.Potential GradientThe separation of the equipotential surface

12、s tells you about the field:- Uniform fields have equal separation- Fields with decreasing field strength have increasing separation.If the equipotentials are close together, a lot of work must be done over a relatively short distance to move a mass from one point to another against the field i.e. t

13、he field is very strong. This gives rise to the concept of potential gradient.The potential gradient is given by the formula. Potential gradient = V rIt is related to gravitational field strength. g = - V r.Escape speedIf a ball is thrown upwards, Earths gravitational field does work against it, slo

14、wing it down. To fully escape from Earths field, the ball must be given enough kinetic energy to enable it to reach infinity. Loss of KE = Gain in GPE mv2 = GMm (Note this also = Vm) rSo. but soThe escape speed is the minimum launch speed needed for a body to escape from the gravitational field of a larger body (i.e. to move to infinity).Note we could also say. mv2 = GMm = Vm rSo.v = (2V).Note we could also say. mv2 = GMm = Vm rso.v = (2V)Assumptions- Planet is a perfect sphere- No other forces other than gravitational attr