# In-Class Activities

Dr Lim Zhi Han

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Published 2022-07-28

# 2.4 In-Class Activities

# 2.4.1 Activity 1: How to win an Ig Nobel Prize

Observe the decay of beer foam and think of science.

# 2.4.2 Activity 2: Love plot

For some chosen values of R_{0},k_{1} and k_{2}, plot R(t) and J(t) on the same graph on Desmos .

\begin{align*}
R & =R_{0}\cos(\sqrt{k_{1}k_{2}}t)\\
J & =-\sqrt{\frac{k_{2}}{k_{1}}}R_{0}\sin(\sqrt{k_{1}k_{2}}t)
\end{align*}

Open a new Desmos window and plot R vs J.

Can you form a conserved quantity using R and J? (A quantity that do not change with time t.)

# 2.4.3 Activity 3: Numerical solution for love

Solve the case of love numerically with

Euler Method
Euler-Cromer Method

Compare the numerical solutions with the analytical solution.

Also use the conserved quantity to compare the two numerical methods.

# 2.4.4 Activity 4: VPython code for the Earth-Sun system

Take a close look at the code below. In you group, discuss and make sense of the code below.

GlowScript 2.7 VPython
#constants
R=15e9
Re=150e9
Ms=2e30
Me=6e24
G=6.67e-11

#creating the Sun
sun=sphere(pos=vector(0,0,0), radius=R, color=color.yellow)
sun.m=Ms
#sun.p=vector(0,0,0)*sun.m

#creating Earth
earth=sphere(pos=vector(Re,0,0), radius=0.4*R, color=color.green)
earth.m=Me
earth.p=vector(0,30e3,0)*earth.m

#Some physics
#here I set the momentum of sun so that the total momentum is zero
sun.p=-(earth.p)

#aesthetics
attach_trail(sun)
attach_trail(earth)
t=0
dt=50

#now the "serious coding"
while t<15000000000:
    rate(10**5)
    
    #vector from sun to earth
    rse=earth.pos-sun.pos

    #calculate grav force on sun due to earth
    #Newton’s law of gravitation
    #Fse is the force the Sun exerts on the Earth
    Fse=-G*sun.m*earth.m*norm(rse)/mag(rse)**2
    
    #Fes is the force the Earth exerts on the Sun. By Newton’s third law,
    Fes=-Fse

    #update momentum (with total vector force)
    #Newton’s second law
    earth.p=earth.p+(Fse)*dt
    sun.p=sun.p+(Fes)*dt
    
    #update position
    #relation between momentum and position vectors
    sun.pos=sun.pos+sun.p*dt/sun.m
    earth.pos=earth.pos+earth.p*dt/earth.m
    t=t+dt

Run the code in Trinket .

In your program, change parameters one at a time and observe the difference in results. For example change the initial Earth momentum to

earth.p=vector(0,38e3,0)*earth.m

Play around and record any notable ''discoveries''.

Get an account in Trinket . Sign in, create a new trinket program (select Glowscript) and copy and paste the the Sun-Earth code. Now the program is yours!