DHS 07 Gravitational Field (Tutorial)

Dunman High School (Senior High Physics) 9749 Physics (2024) Topic 7: Gravitational Field 7 – Tutorial Questions -1 Tutorial: Gravitational Field Summary 1 Gravitational field strength g at a point is the gravitational force per unit mass exerted on a ______________ mass placed at that point. i.e. g = ______ Force acting on an object of mass m placed there, F = mg 2 Newton’s law of gravitation states that the gravitational force between two point masses is directly proportional to the product of the masses and ______________ proportional to the ____________ of their separation. i.e. F = ____________ 3 Gravitational field strength g due to a point mass M at a distance r from it is given by g = −___________ where G = 6.67 × 10−11 N m2 kg−2 (negative sign indicates that the field strength is directed towards M) Force acting on an object of mass m placed there, F = −____________ 4 Gravitational potential φ at a point is the work done per unit mass in bringing a __________________ mass from _____________ to that point. i.e. φ = 5 Gravitational potential φ due to a point mass M at a distance r from it is given by φ = −____________ 6 Gravitational potential energy U of an object of mass m placed at a point is given by U = mφ 7 Gravitational potential energy U of an object of mass m placed at a point distance r from M is given by U = −____________ 8 Satellite of mass m round the Earth (mass ME) with orbit radius r : W m

Dunman High School (Senior High Physics) 9749 Physics (2024) Topic 7: Gravitational Field 7 – Tutorial Questions -2 Gravitational force acting on the satellite by the Earth, F = This gravitational force provides the centripetal force: = mrω2 = mr  T2 = r3 (Kepler’s 3rd law) 9 Energies of satellite of mass m in orbit of radius r round the Earth (mass ME): From =  KE, K = = PE, U =  TE, E = K + U = + = i.e. E = 10 Geostationary orbit, for satellite to appear stationary when viewed from a fixed point on the rotating Earth, (a) has period T = Earth’s period of rotation = ____________ (b) is in the plane of ______________ (c) moves from ________ to ________, same sense as self-rotation of the Earth 11 Relation between gravitational force F and potential energy U F = − Divide both sides by m, g = − ______ 2 EGM m r 2 EGM m r 2 2 T π  24 EGM π   2mv r 2 EGM m r 2 2 mv 2 EGM m r EGM m r− 2 EGM m r EGM m r − 2 EGM m r− 2 U dU dr

Dunman High School (Senior High Physics) 9749 Physics (2024) Topic 7: Gravitational Field 7 – Tutorial Questions -3 Self-Attempt Questions S1 The force of attraction between two masses 3 kg and 2 kg is F when the distance between them is r. Express the new force of attraction, in terms of F, if the distance between the two masses is doubled. (F/4) [2] S2 The radius of the Eart