MIT OpenCourseWare
http:/ocw.mit.edu
8.012 Physics I: Classical Mechanics
Fall 2008
For information about citing these materials or our Terms of Use, visit: http:/ocw.mit.edu/terms.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.012
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01T
Fall Term 2004
Practice Exam 2 Solutions
Problem 1: static equilibrium
You are able to hold out your arm in an outstretched horizontal position thanks to the
action of the deltoid m
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01 TEAL
Fall Term 2004
Exam 2: Equation Summary
One Dimensional Kinematics:
r
r
r
r
v = dr / dt , a = dv / dt
t =t
vx (t ) vx ,0 =
ax (t )dt
t =t
x(t ) x0 =
t = 0
v (t )dt
x
t = 0
Co
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01T
Fall Term 2004
Practice Exam 1 Solutions
Concept Questions: Briefly answer the following questions.
1. When a car accelerates forward, which force is responsible for this accelerati
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01 TEAL
Fall Term 2004
Exam 1: Equation Summary
One Dimensional Kinematics:
r
r
r
r
v = dr / dt , a = dv / dt
t =t
vx (t ) vx ,0 =
ax (t )dt
t =t
x(t ) x0 =
t = 0
v (t )dt
x
t = 0
Co
Massachusetts Institute of Technology
Department of Physics
8.01T
Fall 2004
Study Guide Final Exam Solutions
Part A: Kinetic Theory, First Law of Thermodynamics, Heat Engines
Problem 1 Energy Transformation, Specific Heat and Temperature
Suppose a person
Massachusetts Institute of Technology
Department of Physics
8.01T
Fall 2004
Study Guide Final Exam
The final exam will consist of a two sections.
Section 1: multiple choice concept questions. There may be a few concept questions on
time and special relati
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01T
Fall Term 2004
Exam 3: Solutions
Problem 1a: (5 points)
A physical pendulum consists of a ruler of mass m oscillating about a fixed point. The
ruler is pulled to one side and allowe
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01 TEAL
Fall Term 2004
Exam 3: Equation Summary
Momentum:
r
r
r r total
rr
dptotal
p = mv , Fave t = p , Fext =
dt
t =t f
r
r
r
Impulse: I F(t )dt = p
t =0
rr
r
rr
r
Torque: S = rS ,P F
MIT OpenCourseWare
http:/ocw.mit.edu
8.012 Physics I: Classical Mechanics
Fall 2008
For information about citing these materials or our Terms of Use, visit: http:/ocw.mit.edu/terms.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.012
MIT OpenCourseWare
http:/ocw.mit.edu
8.012 Physics I: Classical Mechanics
Fall 2008
For information about citing these materials or our Terms of Use, visit: http:/ocw.mit.edu/terms.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.012
Massachusetts Institute of Technology
Department of Physics
Physics 8.01L
SAMPLE EXAM 2
SOLUTIONS
November 1, 2005
Problem 1
i) a) Object A Same force, smaller mass, so A has a bigger acceleration and moves the same distance in a
shorter time.
ii) c) Both
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01T
Fall Term 2004
Exam 2 Solutions
1
1.
2
Part 2: Analytic Questions: Show all your work.
Problem 2: (20 points) A child is trying to shoot a marble of mass m in order to hit the
cente
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01 TEAL
Fall Term 2004
Exam 2: Equation Summary
One Dimensional Kinematics:
r
r
r
r
v = dr / dt , a = dv / dt
t =t
vx (t ) vx ,0 =
ax (t )dt
t =t
x(t ) x0 =
t = 0
v (t )dt
x
t = 0
Co
Problem 1: Dynamics (15 pts)
Two blocks of mass m1 and m2 are put on a frictionless level surface as shown in the gure below.
The static coecient of friction between the two blocks is . A force F acts on the top block m1 .
m1
no friction
F
m2
(a) When the
MIT OpenCourseWare
http:/ocw.mit.edu
8.012 Physics I: Classical Mechanics
Fall 2008
For information about citing these materials or our Terms of Use, visit: http:/ocw.mit.edu/terms.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.012
Massachusetts Institute of Technology
Department of Physics
Physics 8.01L
SAMPLE EXAM 1
SOLUTIONS
September 26, 2005
Problem 1
a)
x=
12
1
At = A(2)2 = 2A
2
2
Vx = At = 2A
b)
8 seconds to run 100 2Am at speed 2A.
8(2A) = 100 2A 18A = 100 A =
100
18
x = 2A
Problem 1
A sprinter running a 100 meter race starts at rest, accelerates at constant acceleration with
magnitude A for 2 seconds, and then runs at constant speed until the end.
a) Find the position (relative to the start position) and speed of the runner
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01T
Fall Term 2004
Exam 1 Solutions
Problem 1: (10 points) Concept Questions: Briefly answer the following
questions.
a) (5 points) Two people are running forward at the same speed. One
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 TEAL Fall Term 2004
Exam 1: Equation Summary
One Dimensional Kinematics: t =t r r r r v = dr / dt , a = dv / dt vx (t ) vx ,0 = ax (t )dt
t = 0 t =t
x(t ) x0 =
t = 0
v (t )dt
x
Co
Massachusetts Institute of Technology
Department of Physics
Physics 8.01L
SAMPLE EXAM 3
SOLUTIONS
December 4, 2005
Problem 1
m
a)Flef t = (GMm = 4GMm , Fright = G(2M )2 =
D/2)2
D2
(D/2)
FT OT = Fright Flef t = 8GMm 4GMm
D2
D2
FT OT = 4GMm , to the right.
8 .0 1 L
Fall 2005
Exam 3 Sample Problems
Note that some of these problems were from an exam allowing calculators. Your exam will
not allow calculators.
Problem 1
a) Two large spherical stars with masses of M and 2M
m
M
2M
are positioned a distance D apar
Massachusetts Institute of Technology
Department of Physics
Physics 8.01L
SAMPLE FINAL EXAM
SOLUTIONS
Problem 1
a) V =
N kT
P
, VN EW =
Nk T
3
P
10
=
10 N kT
3P
,
V goes up
b) (i) F = mg = 8(10) = 80N
(ii)FBuoy = (1000)(.002)(10) = 20N,
F = 80 20 = 60N
FINAL EXAM SAMPLE PROBLEMS
The Final Exam will be given on Monday, January 30 from 9 am - Noon
There will be no makeup exam.
You will be provided with a copy of the formula sheet during the exam. You may wish to
memorize other formulas but a good understa