MAE 102
FINAL EXAM
FALL 2009
1. The disc of mass m and radius r is connected to the wall by the spring of stiness k = mg/r, and the disc rolls without slipping on the horizontal oor. The block of mass m slides on the oor, and there is no friction between
MECHANICAL & AEROSPACE ENGINEERING DEPARTMENT UNIVERSITY OF CALIFORNIA, LOS ANGELES MAE 102 Mechanics of Particles and Rigid Bodies Winter, 2008 INSTRUCTOR CHATTERJEE, A. K.
MIDTERM EXAMINATION February 22, 2008
INSTRUCTIONS: SHOW ALL CALCULATIONS
MAE 102: Dynamics of Particles and Rigid Bodies
Midterm
DETAILS AND INSTRUCTIONS:
This 100 pt. exam is closed book and closed notes, with the exception of a single, double-sided
8.5x11 handwritten cheat sheet. Except for a scientific or graphing calculato
MAE 102
FINAL EXAM
SPRING 2013
1. The disc has mass m, radius r and moment of inertia IG = mr2 /2. The spring constant is
k = mg/r. The disc is released from rest when the spring is unstretched, and the disc rolls
without slipping. Let x be the position o
University of California, Los Angeles
Mechanical and Aerospace Engineering Department
MAE 102: Mechanics of Particles and Rigid Bodies
Text: Engineering Mechanics, Dynamics, 7th Edition., by Meriam, J. L. and Kraige, L. G., Wiley
Publication, March, 2012
Problem 1 (3+3+2+5+7)
A moving particle is at P at time t on the path as shown in Fig. 1a.
1. Define the velocity of the particle at time t
2. Define the acceleration of the particle at time t
3. What is the component of the velocity along the normal
to t
Solution to Problem1 continued
5. For the connected system shown in Fig. 1b, use the definitions
of velocity and acceleration to determine the acceleration of B
in terms of the velocity and acceleration of A at the instant
shown.
Solution
MAE-102: Solutio
MECHANICAL & AEROSPACE ENGINEERING DEPARTMENT
UNIVERSITY OF CALIFORNIA, LOS ANGELES
MAE 102
Mechanics of Particles and Rigid Bodies
Summer, 2006
INSTRUCTOR
CHATTERJEE, A. K.
MIDTERM EXAMINATION
July 26, 2006
INSTRUCTIONS:
SHOW ALL CALCULATIONS ON THESE PA
Problem 2 (4+4+7+5)
1. At the instant shown, a particle of mass m is subjected to three given
forces F1, F2 and F3 as shown. What is the direction and
F1
F2
P,t
magnitude of its acceleration?
2. The small pendulum of mass m is suspended from a trolley whi
3. Conservation of energy equation is derived from the work-energy equation under the
assumption that all forces applied to a given particle are conservative, i.e., there is a potential
energy associated with each force so that work done is path-independe
Problem 3 (3+3+2+7)
1. What is the definition of a conservative force?
2. What is the fundamental difference between the work-energy equation and conservation-ofenergy equation?
3. Which one of the above two equations is applicable to all problems and why
MECHANICAL & AEROSPACE ENGINEERING DEPARTMENT
UNIVERSITY OF CALIFORNIA, LOS ANGELES
MAE 102
Mechanics of Particles and Rigid Bodies
Winter, 2007
INSTRUCTOR
CHATTERJEE, A. K.
MIDTERM EXAMINATION
February 14, 2007
INSTRUCTIONS: SHOW ALL CALCULATIONS ON THES
Problem 3 (10+5)
The magnitudes and directions of the velocities ot two
identical frictionless balls before impact are as shown. If
e = 0.90 , find the magnitudes and directions of the balls
after impact. Also find the percentage loss in the total
kinetic
Problem 1 (7+3)
A bead P of mass m is given an initial speed v 0 at A along the
smooth, horizontal guide. The radius of curvature at B is ,
Using R = ma , determine the magnitude and direction of force
%
%
exerted by the guide on the bead at B. Express y
MAE-102: Final Examination: Winter 2007
Chapter 5
Rotation of the lever OA is controlled by the
motion of the contacting circular disk of radius
r = 3 m, whose center is given a horizontal
velocity v . At the instant shown,
m
, and the angular velocity
s
Problem 2 (5+5+5+5)
At the instant shown, link AB has a counterclockwise angular
velocity AB . Using the method of connected rigid body
kinematics, determine
1. the angular velocities of rods CD and OA
2. the velocity of the point D
3. velocity of the mid
Formula Page
1. For a rigid body motion, the velocity of a point P at a distance r from the ICR C is r
where is the angular velocity of the rigid body, and the velocity is normal to the line
CP.
2. Above formula is also valid for the velocity of P relativ
Problem 3 (10+5)
The magnitudes and directions of the velocities ot two
identical frictionless balls before impact are as shown. If
e = 0.80 , find the magnitudes and directions of the balls
after impact. Also find the percentage loss in the total
kinetic
Problem 4 (10+10)
The 3-kg slider is released from rest at A, and
moves in the vertical plane along the smooth,
circular guide as shown. The attached spring has
an unstretched length of 0.4 m and a stiffness of
200 N/m. Determine
1. the velocity of the sl
Problem 1
(3+3+4+5+5)
(a) Define Instantaneous center of Rotation (ICR) of a rigid body.
(b) For the following two cases, show how to find the ICR graphically.
vB
vB
vA
B
A
A
B
vA
c. At a certain instant, the vertex B of the righttriangular plate has a ve
Formula Page
1. Tangential and normal components of acceleration are
dv
dv
v2
=v
, an =
at =
dt
ds
2. Work-energy equation between two states of motion at any two times, is
T2 = T1 + U12 where T1,T2 are the kinetic energies at state-1 and state-2 respecti
Problem 4 (10+5)
A sphere A of mass 25 kg collides with a sphere of mass 5 kg
as shown. The coefficient of restitution is 0.30 and friction is
neglected.
1. Determine the post impact velocities of the spheres, and
2. the angles A and B made by the rebound
Problem 3 (5+10)
1. Using the equation of motion R = ma , show that the time rate of change of angular
%
%
momentum HO of a particle about a fixed point O, is equal to the sum of the moments of
the external forces about O.
2. A particle moves along an ell
Problem 2
(10)
Small metal blocks are discharged with a velocity of
0.4 m / s onto a ramp by the upper conveyor belt shown.
Blocks are observed to slip on the lower conveyor belt with a
relative velocity of 0.1 m / s to the right. If = 16o ,
calculate the
Problem 5 (7+6+6+6)
The extremities of a 4-ft rod, weighing 50 lb, may move
freely with no friction along the two straight tracks as
shown. If the rod is released from rest with no linear or
angular velocity at the position shown, determine
1. the angular
Problem 4 (5+7+8)
A disk of radius r is mounted on an axle of length 2r . The axle is
attached to a vertical shaft AD which rotates at the constant rate
1 , and the disk rotates about the axle AB at the constant rate 2 .
If the angle remains constant, usi
MAE 102
MIDTERM EXAM 1
Fall 2013
1. Block A is given the constant vertical acceleration a0 . Block B has mass m, and block B can
slide without friction on block A. The acceleration of block B is horizontal; i.e., aB = ax i.
(The unit vector i points to th
MAE-102 Final Exam 2002
MAE-102 Final Exam 2002
MECHANICAL & AEROSPACE ENGINEERING DEPARTMENT
UNIVERSITY OF CALIFORNIA, LOS ANGELES
MAE 102
Mechanics of Particles and Rigid Bodies
Summer, 2005
INSTRUCTOR
CHATTERJEE, A. K.
Final EXAMINATION
August 17, 2005
A Sinai coiiar of mass: m is given an initiai veioc-
ity 0f magnitude. cfw_:3 0n the horimntai sirauiar track
fabricatmi mn a Skmder rod. If the mfficim; (3f Ri-
netic cfw_listian is cfw_Lb determina the distance travgleal
befarsa le caar comes cfw_.4 re
Discussion 8
MAE 102, Spring 2017
Peter Ferguson
Questions from Lectures?
?
?
?
?
Feedback
30
25
Discussions Worthwhile
20
TA Communicates Effectively
Material Covered Helpful
Office Hours Helpful
15
Approachable/Accessible
TA Well Prepared
TA Cares
10
Ov
Discussion 9
MAE 102, Spring 2017
Peter Ferguson
Questions from Lectures?
?
?
?
?
Problem 1: 6/91
IG
1
m(b 2 h 2 )
12
Problem 1: 6/91
Given: mass, dimensions, constraints
Need: angular acceleration , and tension force TA
Use: F=m*a, M=I*, relative accele