Homework 2, General Physics, Fall '10

Due Friday Sept. 17

1. Show your data from class for the relationship between H and L. Do a curve-fit to find a mathematical equation that accurately summarizes your data.

2. Let's agree on the following "class consensus" formula for the relationship between period and length arising from last week's lab: L = k*T2 with k = 24 +/- 1 cm/sec2. (EDIT: Based on the version from Wednesday's class: k = 24.3 +/- 0.1 cm/sec2.) Using this formula, do the algebraic exercise explained in the Freefall Lab Description to arrive at a mathematical formula relating H (the height from which a ball is dropped) and t (the time it takes to hit the ground from that height). Make sure to report uncertainties and units on any constants that appear in your equation.

3. Now reflect on your H vs. t equation. What does it mean? For example, if H were proportional to t, this would mean that the time it takes to fall from a certain height is just proportional to the height itself -- which would indicate that objects in freefall fall with constant speed. What, along these lines, does your actual equation imply?

4. Find a friend (not necessarily somebody from the class) and do the following experiment: go back to the library balcony (where we dropped stuff on Monday) and use a stopwatch to time the freefall of (say) an apple from the railing down to the ground. (The friend should stand guard below to make sure you don't conk somebody on the head with an apple! Also, please don't leave any messy apple shrapnel on the walkway.) Now plug this value for t into your H vs. t equation to compute the height of the library balcony railing above the ground. Is your result reasonable?