Physics 41
Mechanics
Problem Set 10
Moment of Inertia; Rotational Energy
Static and Dynamic Equilibrium
Written parts (1-3) are due by 6 p.m. Fri., March 15, in your TAs mailbox in Hewlett.
No late problem sets will be accepted. Solutions will be posted
Problem Set 9 Challenge Problem
Lucas Peeters, [email protected]
March 2, 2013
1
Relativistic energy
The second-order Taylor expansion around x = 0 for any well-behaved function f (x) is
1
f (x) f (0) + f (x)x + f (x)x2
2
(1)
which we we will use with
PH 41 W13- Problem set 10 Solution Draft
Emperor Jiecheng Zhang, Andrei Kamalov (with some edits by Pat Burchat)
March 15, 2013
1
Door on Hinges
(a) Extended free body diagram
(b) For the rest of this problem, we will follow the convention dened in
our fr
Pat Burchat, March 2013
Physics 41 Problem Set 9 Challenge Problem
This challenge problem is optional and will not be graded. If you are interested in
learning more about Einsteins Special Theory of Relativity, consider taking PHYSICS
70, Introduction to
Physics 41 Winter 2013 Homework 9
Alexander Hristov, Yajie Yuan
March 3, 2013
Problem 1
Part (a)
As directed, I begin with
Ug =
The key step is to rewrite the denominator as RE (1 +
Ug =
GMe m
.
RE + h
h
RE ),
GMe m
1
GMe m
=
h
RE 1 + R
RE
while the num
PHYSICS 41- Problem Set 8 Solutions
March 1, 2013
1
Problem 1
(a) Before the impact of the meteor, the relevant forms of energy are the gravitational potential
energy of the meteor Ug , and the kinetic energy of the meteor KM .
Before impact, the gravitat
Physics 41
Mechanics
Problem Set 9
Power; Conservative Forces
Torque; Center of Mass; Static Equilibrium Revisited
Before tackling problem 3 below and the last assigned MasteringPhysics problem (Person on a
Ladder), review Problem Solving Strategy 12.2 on
Physics 41
Mechanics
Problem Set 7
Kinetic and Gravitational Potential Energy; Collisions
Written parts (13) are due by 6 p.m. Fri., Feb. 22, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 4) is due online by 6 p.m. Fri., Feb. 22.
Solu
Physics 41
Mechanics
Problem Set 8
Elastic Potential Energy; Work
Written parts (1-3) are due by 6 p.m. Friday, March 1, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 4) is due online by 6 p.m. Saturday, March 2.
Read Secs. 10.4-10.6
Problem Set 7 Solutions
Simon Foreman, Lucas Peeters
February 22, 2013
1
Kinetic Energy in an Elastic Collision
In this question, we would like to show explicitly that the total kinetic energy is conserved in a onedimensional elastic collision of two part
PHYSICS 41- Problem Set 6 Solutions
Matthew Dodelson, Andrew McLeod
February 17, 2013
1
Problem 1
km
(a) The pilots speed is v = 300 hour = 83 m , so the centripetal acceleration during this pilots arc
s
is given by
~r =
a
v2
m
r = 35 2 r 3.5g r
r
s
which
Physics 41
Mechanics
Problem Set 6
Nonuniform Circular Motion; Impulse and Momentum
Written parts (13) are due by 6 p.m. Fri., Feb. 15, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 5) is due online by 6 p.m. Fri., Feb. 15.
Read Secs.
Physics 41 Problem Set 5 - Challenge Problems
Jae Hwan Kang
January 31, 2013
1
Ch.8 Problem 59
In the absence of air resistance, a projectile that lands at the elevation from which it was launched
achieves maximum range when launched at a 45 angle. Suppos
Problem Set 5 Solutions
Physics 41
Problem 1.
Consider the following force diagram:
We know that the only acceleration in this problem is centripetal acceleration, and hence must have mag2
nitude mv and point inwards (in the r direction). We also know tha
Physics 41
Mechanics
Problem Set 5
Uniform Circular Motion; Centripetal Acceleration
Written parts (12) are due by 6 p.m. Fri., Feb. 8, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 3) is due online by 6 p.m. Fri., Feb. 8.
Midterm I w
Physics 41
Mechanics
Problem Set 4
Newtons 3rd Law; Kinematics in 2D; Relative Motion
Written parts (13) are due by 6 p.m. Fri., Feb. 1, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 4) is due online by 6 p.m. Fri., Feb. 1.
Solutions
PHYSICS 41- Problem Set 4 Solutions (Final)
Jake How, Lampros Lamprou
February 3, 2013
1
Problem 1
We call the vertical axis z and we choose the positive direction to point upwards.
The forces are shown in the free body diagram.
(a) Newtons 2nd law:
mass
Pat Burchat, January 2013
Physics 41 Problem Set 2 Challenge Problem
Fundamental Constants of Nature and Plancks Units
The challenge problem is optional and will not be graded.
1
Three Fundamental Constants of Nature
Special Theory of Relativity
The funda
PHY41 Problem Set 3 - Challenge Problems
Andrei Kamalov
January 21, 2013
problem 6.66
part a
Terminal speed implies that an object in free-fall has attained a speed that
cannot be exceeded due to drag. This is to say, the object in question (a dust
partic
Physics 41
Mechanics
Problem Set 3
Newtons 1st and 2nd Laws; Static and Dynamic Equilibrium
Written parts (14) are due by 6 p.m. Fri., Jan. 25, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 5) is due online by 6 p.m. Fri., Jan. 25.
Re
Physics 41 Problem Set 3 Solutions
1
Object Under Forces
Figure 1: Free body diagram for 1a.
b) Initially at time t = 0, the object is at rest. Therefore its initial velocity is zero. v(0) = 0
The object is at the origin at time t = 0, so the initial posi
Week 2
Challenge Problem
Exercise: Find a combination of c, h, and G that has dimensions of length
(call this length lP ), of time (tP ), and of mass (mP ).
2
L
L3
Solution: We began with the constants [c] = T , [h] = M L , [G] = M T2 .
T
For a general co
Problem Set 2 Solutions
Alborz Bejnood, Byungwoo Kang
Stanford University
January 20, 2013
1
Moon Astronaut
Part (a) The velocity of the rock at time t is dependent on both the initial upward velocity v(t = 0) and the
Moons gravity, as the rock initially
Physics 41
Mechanics
Problem Set 2
Kinematics in One Dimension
Written parts (14) are due by 6 p.m. Fri., Jan. 18, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 5) is due online by 6 p.m. Fri., Jan. 18.
Review Ch. 2 and 3 in Knight.
Physics 41
Mechanics
Problem Set 1
Dimensions; Kinematics in One Dimension
Written parts (1, 2, 3) are due by 6 p.m. Fri., Jan. 11, in your TAs mailbox in Hewlett.
The MasteringPhysics portion (item 4) is due online by 6 p.m. Sun., Jan. 13.
Read Preface
Discussion Section 9: Potentials and Conservative Forces
Consider the following graph of potential energy U (x) versus position x for a one dimensional system in which all forces are conservative; i.e., Emech = K + U is conserved. In
order to build physic