HCI 07B Gravitation Solutions (Self-Review Questions)

Tutorial 7B Self-Review Suggested Solutions S1 D φ = - GM/r φY = ½ φX = ½ (-800) = -400 kJ kg-1 Work done by external force = change in gravitational potential energy = m (φY – φX) = 3 [-400 – (-800)] = +1200 kJ (the positive sign indicates that the mass gains GPE) S2 Increase in GPE = final GPE – initial GPE = -[G(Mm)/(6,370,000 + 92,000)] – [-G(Mm)/(6,370,000)] = 7.22 × 108 J The trickier questions often give the “height of the mass above surface of the Earth” When applying the formula for gravitational force or potential energy, you should always consider the distance between the two masses i.e. (Earth radius + height). S3 Remember that since gravitational force is attractive in nature, and potential at infinity is taken to be zero, the gravitational potential at a point is always negative. You should develop the “feel” that when an object is brought nearer to source mass, the GPE will be more negative, when the object is brought away from the source mass, the GPE will increase towards zero. Can you sketch the GPE- distance graph?

S4 Alternatively, you could take: Decrease in GPE = Iecrease in KE from infinity to surface. Always remember that we set gravitational potential = 0 at infinity. Make sure you are familiar with the definition of gravitational potential, gravitational potential energy and be able to explain why the gravitational potential is always negative. S5 Note that the energy analysis is specifically on satellites in orbits, which is different from projecting a mass away from the Earth (see S3). Can you also sketch the KE-radius, GPE-radius and Total energy-radius graphs? (refer to lecture example on page 28)