Chapter 13: Do listed problems.  
Simulations
Quiz 13
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2, 8, 13, 14, 17, 18, 25, 28, 33, 34, 40
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NOTE: In some cases the masteringphysics.com problem has been randomized with different numbers than the book problem. The hints below are done according to book problem. If odd -numbered,  you can check your answer in  back of book before submitting to masteringphysics.com. 
highlight  #1: Note on #28:
FxNET =  - GmM/(0.10)2 - [Gm'M/(0.202 + 0.102)]cosØ.
FyNET = [Gm'M/(0.202 + 0.102)]sinØ,
highlight #2: Note on #25: m + M = 150 kg
2. 
(a) F = GmM/r2 .  Where m and M are the 0.100 kg and 10 kg ball,  respectively.  r = 0.10 m
(b) Compute F' = mg   and compare with part (a). It should be very much larger. 
You can divide  answer to part (a) by answer to part (b) . In other words, compute: ( GmM/r2 ) / (mg  ) .
8. g = GM/R2 where M and R are the mass and radius of planet or moon  in question. 
(a) M and R are the mass and radius of the Moon (Earth's moon) 
(b) M and R are the mass and radius of Jupiter.  Jupiter's g is larger than the moon.  Not surprising since Jupiter  is  two and a half times as massive as ALL of the other planets in our Solar System combined. For more information go here : http://en.wikipedia.org/wiki/Jupiter
13. See example 13.2 for the Planet Earth. The formula for other planets is  identical; just plug in planet mass and radius. 
14. This is a case when the launch speed is larger than  escape speed of example 13.2. Use conservation  of energy:  
½mv12 -  GmME/RE   =  ½mv2+ 0 since the potential energy at infinity is zero. Given the first speed, solve for the second. 
17. Using equation 13.25, find radius of  orbit with  5-earth-year period T. Please understand the derivation of equation 13.25. M = sun mass. Then find speed v  = (circumference of circle)/T.  See sec. 13.6.  Note: one earth year = 
(365)(24)(3600) seconds.
18. Look up  Earth's orbital radius and period and use equation 13.25 to find sun mass M. Note: one year = 
(365)(24)(3600) seconds.
25.  
m + M = 150 kg and 
8x10-6 N = GmM/r2 , where r = 0.20 m
Solve these two equations for m and M. Here is the set up:
First off solve for m*M = ( 8x10-6 N)*r2/G = real number.
Then substitute m*M = (150 kg - M)*M = real number computed on the above line. 
Carefully solve this *quadratic* equation for M. Then find m.  
28.  No good book examples  help explain this problem.  This problem is important for Physics 4B. That is where I step in. 
(a) This is the easiest because the two forces  acting on the mass are perpendicular. Each represents a component of the net force. Plug the components   into  Pythagorean Theorem to find the magnitude. 

Let M = 20 kg. The x-component of the force on M   is Fx = GmM/(0.10)2 , where m = 5.0 kg.   The y-component is Fy = Gm'M/(0.20)2,  where m' = 10 kg. The magnitude obeys  F2 = Fx2 + Fy2.  The vector points in the first  quadrant .  CW (clockwise) angle with y-axis is Ø = tan-1(| Fx|/| |Fy|) or you could find the angle with the x axis: Ø = tan-1(| Fy|/| |Fx|) 
(b) Yo, this is more complicated. 

Let m = 5.0 kg. 

From  M = 20.0  kg,  x-component  is Fx = - GmM/(0.10)2 .  

From m ' = 10.0 kg , the x-component of net force is Fx = - [Gmm'/(0.202 + 0.102)]cosØ, where Ø= tan-1(20/10).
From m ' = 10.0 kg , the y-component of net force is  [Gmm'/(0.202 + 0.102)]sinØ, where Ø= tan-1(20/10).

FxNET =  - GmM/(0.10)2 - [Gm'M/(0.202 + 0.102)]cosØ.
FyNET = [Gm'M/(0.202 + 0.102)]sinØ,
The magnitude F obeys equation F2 = FxNET2 + FyNET2.  The vector points in the second  quadrant . The CCW angle with  y-axis is Ø = tan-1(| Fx|/| |Fy|) or you could find the angle with the negative x axis: Ø = tan-1(| Fy|/| |Fx|) 
33.
(a) ½mv12 -  GmME/r =  ½mv2-  GmME/r2 .
The initial speed indexed by 1  is zero,  r2 = RE  and   r1 = RE + 500 km (convert to meters.)
Find the second  speed.
(b) ½mv12 + mgy =  ½mv2+ mgy2 , where the initial speed indexed by 1  is zero,  y2 =  0   and   y1 = 500 km (convert to meters.)
Find second  speed and compare with part (b).
34. ½mv12 -  GmME/r =  ½mv2-  GmME/r2 .
The initial speed indexed by 1 is 10,000 km/hr ( convert to m/s),  r1 = RE  . If the second speed is zero, find  r2 . Substract the Earth radius to get the height above the ground. 
40.  ½mv12 -  GmME/(r' + Rmoon) -  GmMmoon/Rmoon=  0, where r' = distance between moon and earth centers.   Solve for v1  .
highlight  #1: Note on #28:
FxNET =  - GmM/(0.10)2 - [Gm'M/(0.202 + 0.102)]cosØ.
FyNET = [Gm'M/(0.202 + 0.102)]sinØ,
highlight  #2: Note on #25: m + M = 150 kg