physics bullshit midterm that sucks so much ass

Sample

small subset of a population

parameter

numerical summary/measure of population

Statistic

a measure describing the sample data

μ

population mean

σ

Population standard deviation

x̄

sample mean and infers u

s

S is sample standard deviation and infers a

central limit theorem

the mean of all sample means is equal to population mean. same goes for standard deviation but square sample deviation. large sample size the mean looks like a bell curve. The standard deviation of the sample means, σx̄ , is given by: (σ/√n)

assigning uncertainty (δx̄) to a sample mean

δx̄ = (s/√n)
The uncertainty of the sample is written as x̄ ± (s/√n)
example: 1.77 ± 0.02

T-test

used to determine if two sample data sets are significant

if T is greater or equal to 3

the two sample data sets are distinguishable

if t' is less than or equal to 3

The two sample data sets are indistinguishable

period of a pendulum

The time required for one complete oscillation

strategies to build a simplified model

Identify variables that might affect the system
Make simplifying assumptions to reduce the complexity of the model ex. no air resistance
make sure the parameters used in the physical model are consistent with the "dimensions" of the system we are trying to describe.

T = 2𝜋√(l/g) simplified

paper

Period of a Pendulum Assumptions

only forces are gravity and tension, the initial angle is small, the pendulum sting is massless, and the bob behaves as a point mass. the period of a pendulum does not depend on the mass of the bob or angle of amplitude.

coefficient of restitution (e)

ratio of speed after collision to the spreed before collision. 1 means no energy lost while 0 means all energy lost

Vout

√h2 and is height of second bounce

Vin

√h1 height of first bounce

Vin in terms of h1

vin=√(2g(h1))

Vout in terms of h2

vout = √(2g(h2))

derived from 3rd kinematic equation because there's no t value