lec15rqh Gravity Problems: directions

2. ans: 9.6 x1024 kg; F=20=GmM/r2, so M=20r2/(mG).

3. ans: 40 m/s2; too easy! a=F/m.

4. ans: 1/4; accel =GM/r2.

5. ans: 5,600 m/s; v2/r =g/4 so v =sqrt(r*g/4).
Don't forget that r above is 2R E.

6. ans: 0.05 radians/s; not really a gravity problem. we want the centripetal acceleration r*(ang.vel)2 to =g, so ang.vel =sqrt(g/r).

7. ans: 3.7 m/s2; since accel =GM/R2, accel =0.107/0.532 times Earth's.

8. ans: 42,000 km; centripetal acceleration r*(ang.vel)2 must =g*(R/r)2, where R =radius of E and r =distance of satellite. solve for r3 = g*(R/ang.vel)2. ang.vel of E =2pi/(24*3600) rad/s.