Week 45
(7/21/03)
Sliding along a plane
A block is placed on a plane inclined at angle . The coefficient of friction between
the block and the plane is = tan . The block is given a kick so that it initially
moves with speed V horizontally along the plane

Uniform and Accelerated Motion
Dorina Kosztin
Meera Chandrasekhar
Department of Physics and Astronomy
University of Missouri, Columbia
Support: National Science Foundation
Math-Science Partnership Institute Grant
NSF DUE 0928924
www.physicsfirstmo.org
Wha

Uniformly Accelerated Motion
College Physics Lab
PH 141
Uniformly Accelerated Motion
Purpose: To investigate the motion of a particular system; to determine whether or not the
acceleration is uniform, and, if it is, to determine the value of the accelerat

Week 41
(6/23/03)
Speedy travel
A straight tube is drilled between two points (not necessarily diametrically opposite)
on the earth. An object is dropped into the tube. How much time does it take to
reach the other end? Ignore friction, and assume (errone

Week 40
(6/16/03)
Staying ahead
In a two-way election, candidate A receives a votes and candidate B receives b
votes, with a > b. If the ballots are removed one at a time from the ballot box, and
a running total of the score is kept, what is the probabili

Invited talk presented at the conference, World View on Physics Education in 2005:
Focusing on Change, Delhi, August 21-26, 2005. To be published in the proceedings.
PROBLEM SOLVING
AND THE USE OF MATH IN PHYSICS COURSES
EDWARD F. REDISH
Department of Phy

Week 43 (7/7/03)
Infinite Atwoods machine
Consider the infinite Atwoods machine shown below. A string passes over each
pulley, with one end attached to a mass and the other end attached to another
pulley. All the masses are equal to m, and all the pulleys

Solution
Week 77 (3/1/04)
Relativistic momentum paradox
The reasoning is not correct. The horizontal speed of the masses remains the same.
The system does not slow down in the x-direction. We can see that this must be the
case, by looking at the setup in

Solution
Week 82 (4/5/04)
Standing in a line
First solution: Let TN be the expected number of people who are able to make
the given statement. If we consider everyone except the last person in line, then
this group of N 1 people has by definition TN 1 peo

Week 42
(6/30/03)
How much change?
You are out shopping one day with $N , and you find an item whose price has a
random value between $0 and $N . You buy as many of these items as you can with
your $N . What is the expected value of the money you have lef

Week 19
(1/20/03)
Block and bouncing ball
A block with large mass M slides with speed V0 on a frictionless table towards a
wall. It collides elastically with a ball with small mass m, which is initially at rest
at a distance L from the wall. The ball slid

Week 18
(1/13/03)
Distribution of primes
Let P (N ) be the probability that a randomly chosen integer, N , is prime. Show
that
1
P (N ) =
.
ln N
Note: Assume that N is very large, and ignore terms in your answer that are of
subleading order in N . Also, m

Week 13
(12/9/02)
Unchanged velocity
A ball rolls without slipping on a table. It rolls onto a piece of paper. You slide
the paper around in an arbitrary (horizontal) manner. (Its ne if there are abrupt,
jerky motions, so that the ball slips with respect

Week 12
(12/2/02)
Decreasing numbers
Pick a random number (evenly distributed) between 0 and 1. Continue picking
random numbers as long as they keep decreasing; stop picking when you obtain a
number that is greater than the previous one you picked. What i

Week 11
(11/25/02)
Break or not break?
Two spaceships oat in space and are at rest relative to each other. They are
connected by a string. The string is strong, but it cannot withstand an arbitrary
amount of stretching. At a given instant, the spaceships

Week 10
(11/18/02)
Product of lengths
Inscribe a regular N -gon in a circle of radius 1. Draw the N 1 segments
connecting a given vertex to the N 1 other vertices. Show that the product of the
lengths of these N 1 segments equals N . The gure below shows

Week 9
(11/11/02)
Fractal moment Take an equilateral triangle of side , and remove the "middle" triangle (1/4 of the area). Then remove the "middle" triangle from each of the remaining three triangles (as shown), and so on, forever. Let the final object h

Week 7
(10/28/02)
Mountain climber A mountain climber wishes to climb up a frictionless conical mountain. He wants to do this by throwing a lasso (a rope with a loop) over the top and climbing up along the rope. Assume that the mountain climber is of negl

Week 6
(10/21/02)
Flipping a coin
(a) Consider the following game. You ip a coin until you get a tails. The number
of dollars you win equals the number of coins you end up ipping. (So if you
immediately get a tails, you win one dollar; if you get one head

Week 5
(10/14/02)
The raindrop
Assume that a cloud consists of tiny water droplets suspended (uniformly distributed, and at rest) in air, and consider a raindrop falling through them. What
is the acceleration of the raindrop? (Assume that when the raindro

Week 4
(10/7/02)
Passing the spaghetti
At a dinner party, there are N people seated around a table. A plate of spaghetti
starts at the head of the table. The person sitting there takes some spaghetti and
then passes the (very large) plate at random to his

Week 3
(9/30/02)
Balancing a pencil
Consider a pencil that stands upright on its tip and then falls over. Lets idealize
the pencil as a mass m sitting at the end of a massless rod of length .1
(a) Assume that the pencil makes an initial (small) angle 0 wi

Week 2
(9/23/02)
Green-eyed dragons
You visit a remote desert island inhabited by one hundred very friendly dragons,
all of whom have green eyes. They havent seen a human for many centuries and
are very excited about your visit. They show you around their

Week 1
(9/16/02)
Basketball and tennis ball
(a) A tennis ball with (small) mass m2 sits on top of a basketball with (large)
mass m1 . The bottom of the basketball is a height h above the ground, and
the bottom of the tennis ball is a height h + d above th

Solution
Week 5
(10/14/02)
The raindrop
Let be the mass density of the raindrop, and let be the average mass density
in space of the water droplets. Let r(t), M (t), and v(t) be the radius, mass, and
speed of the raindrop, respectively.
We need three equa

Solution
Week 4
(10/7/02)
Passing the spaghetti
(a) For the case of n = 3, it is obvious that the two people not at the head of the
table have equal 1/2 chances of being the last served (BTLS).
For the case of n = 4, label the diners as A,B,C,D (with A be

Solution
Week 3
(9/30/02)
Balancing a pencil
(a) The component of gravity in the tangential direction is mg sin mg. There
fore, the tangential F = ma equation is mg = m , which may be written as
= (g/ ). The general solution to this equation is
(t) = Aet

Solution
Week 2
(9/23/02)
Green-eyed dragons
Lets start with a smaller number of dragons, N , instead of one hundred, to get
a feel for the problem.
If N = 1, and you tell this dragon that at least one of the dragons has green
eyes, then you are simply te