10. Use the form of the equation for universal gravitation to determine the units for . 11. Looking up any values necessary, use the equation for universal gravitation to calculate the size of the following gravitational forces: a. The force of the sun on Jupiter b. The force of the sun on an 80 kg human, who is standing on the surface of the Earth c. The force of the Earth on an 80 kg human, who is standing on the surface of the Earth d. The force of the same 80 kg human on the Earth The gravitational force has a direction as well as a magnitude—it is a vector. Here is the expression for the force of the sun on the planet Jupiter: H a n d o u t 1 • p . 4 Using GlowScript to Solve Problems L e s s o n 6 (PHYSICS, PROGRAMMING)
J o u r n e y s i n F i l m : H i d d e n F i g u r e s 12. The ^ or “hat” over the last r SJ means that it is a “unit vector.” A unit vector is a vector that has a magnitude of 1. Unit vectors are useful in situations where direction is important, but magnitude is not. Identify which of the following are unit vectors: a. b. c. d. 13. A unit vector can be created by dividing a vector by its magnitude. When this process is carried out, the arrow over the vector is replaced by the hat. For example, . The symbol is pronounced “vee hat.” Calculate the unit vector versions of each of the following vectors: a. m b. kg•m/s 14. What are the units of a unit vector? 15. The vector is the vector pointing from the sun to Jupiter. Make a sketch of the sun and Jupiter, and show the following vectors: , , , and . Which way does point? Why is there a negative sign in the equation? 16. Create a new GlowScript program called “Sun-Jupiter,” copy this code into the program, and run it. Verify that you see a yellow sphere representing the sun and a red sphere representing Jupiter. GlowScript 2.4 VPython scalefactor = 100 G = 6.67E-11 # universal gravitational constant, SI units mS = 1.99E30 # mass of Sun, kg mJ = 1.90E27 # mass of Jupiter, kg RJ = 6.99E7 # radius of Jupiter, m H a n d o u t 1 • p . 5 Using GlowScript to Solve Problems L e s s o n 6 (PHYSICS, PROGRAMMING)
J o u r n e y s i n F i l m : H i d d e n F i g u r e s RS = 6.96E8 # radius of Sun, m dSJ = 7.78E11 # mean distance of Jupiter from Sun, m T = 11.86* 365.25*24*60*60 # orbital period of Jupiter speed = 2*pi*dSJ/T Sun = sphere(pos=vec(0,0,0), radius=RS*scalefactor, color=color.yellow) Jupiter = sphere(pos=vec(dSJ,0,0), radius=RJ*scalefactor, color=color.red, make_trail=True) a. Change the value of scalefactor to 50, and run the program again. Then change it to 10, and run the program. What value of scalefactor displays a representation to scale of the sun and Jupiter? What does the program display when you use this value? b. The orbital period of Jupiter is 11.86 years. This is the time is take Jupiter to orbit the sun once. Explain the other factors in the calculation of T in the program.
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