Homework Assignment #8 Solutions - Physics 325, Fall 2010
1) Show that the shortest distance between two points on a plane is a straight line.
Solution: Following the work we did in class, lets dene our two points to be in the x-y
plane as A = (xa , ya )
Physics 325 Homework 9 Solutions Fall 2010
1) A hoop of mass m and radius R rolls without slipping down an inclined plane of mass
M, that makes an angle with the horizontal. Find the Lagrange equations and the
integrals of the motion if the plane can slid
Physics 325, Fall 2010
Homework Assignment #12
Solutions
1. Taylor 9-18 (15 Points) A particle with mass m is conned to move, without friction,
in a vertical plane, with axes x horizontal and y vertical up. The plane is forced to rotate
with constant angu
Physics 325
Spring 2011
Homework 7A
Name: _
Due: Apr 6, 2011 by 9am (lecture or 325 box)
1. (10 points) A soap bubble placed between two centered hoops will take the shape with the
minimum area. Use the calculus of variations to find the curve y( x) that
Physics 325, Fall 2010
Homework Assignment #1
Due Thursday 2 September at 11:15 am
1) (5 points) Obtain the three lowest non-zero terms in the Taylor expansion
of
f (x) =
1+x
around x = 1
2) (15 points) A projectile is red with initial speed v0 at an elev
Physics 325 Homework #3
due in 325 homework box by Fri, 1 pm
Homework rules are at the top of Homework #1, e.g. NO WORK = NO POINTS : answers or solution steps
given without explanation get zero points. However you may use without proof any relation from
Physics 325 Homework #4
due in 325 homework box by Fri, 1 pm
Important: the midterm is coming, we want to post solutions, so NO LATE ASSIGNMENTS will be accepted.
SUMMARY : Collective Treatment of Multi-particle Systems
You may use anything her
Physics 325 Homework #6
due in 325 homework box by Fri, 1 pm
Lecture 6A is posted as a series of 4 videos on http:/mediaspace.illinois.edu in the channel PHYS325 - Fall
2016 - N.C.R. Makins. In the Blackboards folder are links to the channel and to each
Homework 7 Solution
Physics 325 Homework #7 Solution
Problem 0 : Elastic Collision
Problem 0 : Elastic Collision
Problem 1 : RPG
(a)
H7sol Page 1
(b) In the CM frame of the grenade, the grenade is at rest so it has zero kinetic energy, but the final
Physics 325 Homework #1
due in 325 homework box1 by Friday, 1 pm
All solutions must clearly show the steps and/or reasoning you used to arrive at your result. You will lose points
for poorly written solutions or incorrect reasoning. Answers given without
Phys 325 Discussion 1 Some Math Review
a.k.a. Post-vacation Reboot
Q1. Accelerating Bee
Checkpoints 1
A bee moves along a helical path given by the equation r (t) = xb sin t + y b cos t + z ct 2 .
Calculate the magnitude the bee's acceleration in terms
Phys 325 Discussion 2 Drag Force Intuition
The resistance exerted by uids on moving objects is well described by a linear drag force thats proportional
to the objects speed plus a quadratic drag force thats proportional to the objects speed-squared:
fair
Phys 325 Discussion 14 Life Goes on in Accelerating Frames
! !
Summary: Since all the pseudo-forces are proportional to mass, we rst dene f F / m = force per unit mass.
This quantity is actually familiar to you already, from gravity: the gravitational acc
Phys 325 Discussion 13 Life in Accelerating Frames
This week we will study mechanics in non-inertial reference frames. A good way to think of a reference frame
is as a coordinate system, i.e. an origin plus a set of x, y, z axes. A non-inertial frame is
Phys 325 Discussion 8 Energy : To Use or Not To Use?
In last weeks lectures, we discussed the conservation of (T+U) the version of energy conservation that is
useful to us for doing calculations. (T+U)-conservation provides a very useful tool for calculat
Phys 325 Discussion 12 Effective Potential and more Lagrangian Practice
Before Lagrangian mechanics, we had two methods for doing equilibrium analysis of a system:
Method A: Analyze the rst and second derivatives of the potential energy U(q).
Meth
Phys 325 Discussion 10 Drilling Euler-Lagrange with Geodesics
Summary of Variational Calculus: If you want to extremize a quantity S that is integrated over some path
cfw_qi (t) of your system between xed endpoints, and S is described by the integral
S =
Phys 325 Discussion 11 Welcome to Lagrangian Mechanics
Procedure for Lagrangian Mechanics: In last weeks lectures, we presented the elements of Lagrangian
mechanics and worked some examples. This week we will prove that the approach is valid, but the proo
Phys 325 Discussion 9 Equilibrium & Energy
Equilibrium Analysis : Is U enough?
In class, we discussed two methods for nding a system's equilibrium points and determining their stability.
For a system with one independent coordinate "q" the methods are:
Phys 325 Discussion 7 Small Oscillations & Equilibrium
Here is a phrase that pops up all over the place: Small Oscillations. It is closely connected to the notions of
equilibrium and stable-vs-unstable equilibrium. Lets investigate!
If a system is oscill
Phys 325 Discussion 6 Rollers, Strings, and Pulleys
Many rigid body problems include rolling objects, massless connectors, and/or strings & pulleys. Working
with these objects requires some thought. Specically, each of these three object classes brings wi
Phys 325 Discussion 15 Complex Numbers and Driven Oscillators
Problem 1 : Linear Differential Equations Superposition
Checkpoints1
Linear differential equations (LDEs) are a very friendly class of differential equations that always merit
special sections