PHYS 35100 - FALL 2024

Homework Set 2

Due Sep 25 via Blackboard submission, before 12:00 pm.

Instructions: Prepare responses to the following questions. Each one is worth the same amount. [A] means that a problem is meant to be done analytically, i.e. with paper and a pencil. [C] means that the problem is meant to be done with computationally, i.e. with software* Homework sets will be submitted electronically. Please submit one pdf document that contains all the work you want me to see. For the [A] ones, please scan your original, handwritten work and include in the pdf. For [C] problems, save your code/notebook as a pdf (not a screenshot) and include that pdf in the submission. Also link to the Colab notebook online and make sure it is viewable/commentable by me (jhedberg@ccny.cuny.edu). Please title your submission PHYS35100-HW2-LASTNAME-FIRSTNAME.pdf.

  1. Teenagers [A+C]

    A group of teenagers decides to drop stuff of a 80 foot tall tower (because they were inspired by Galileo). They choose 15 pound USBC regulation bowling ball and a normal professional basketball. After choosing the right air resistance model for this, look up other important factors and:

    1. Figure out the terminal velocity in each case.
    2. Figure out how long they each take to hit the ground.
    3. Write a python script that will generate the answer for these given any object's mass and diameter. (Note: the intention here is to just write some code that will generate the answer using the analytical solutions we did in class, not create a numerical methods differential equation solver - we'll save that for later)

  2. Both kinds [A]

    An object is moving at uniform velocity, $v_0$ in the horizontal direction. All of a sudden, it starts experience both a linear and quadratic drag force: $f = -bv - cv^2$

    1. Analyze the ensuing motion by solving Newton's second law for this force and arriving at a function for $v(t)$.
    2. Show how after a long time, the quadratic drag term stops having an effect.

  3. Need to know [A]

    We'd like to figure out the angular frequency and oscillation amplitude of a simple oscillating body. (Simple mean of course that it it's motion is described by Hooke's Law.) Show that if you know the speed of the mass at two precise locations, $x_1$ and $x_2$, then you can express:

    1. the angular frequency $\omega$
    2. the amplitude of motion $A$

    with only these 4 values.

  4. Damped [A + some calculator type work]

    You measure the frequency of an undamped oscillator and obtain a value of 1000.0 Hz. Then, the oscillator is damped and the frequency is measured again and is now 989.0 Hz.

    1. What are the periods of these two oscillations?

    2. Figure out the damping factor $\beta$.

    3. How many oscillations will it take for the amplitude of oscillation to decrease to half the original amplitude?



* This means that I'd like you to extend the techniques we use, and not use other software, libraries, etc. That means for plotting, use matplotlib, not plotly for example.