University of Toronto
Applied Science and Engineering
MIE100 — Dynamics
Final Exam
April 26, 2013: 2:00pm — 4:30pm
Examiners: A. Sinclair, L. Sinclair, P. Sullivan, L. You
Permitted Aids: One 8%” by 11” aid sheet (any colour) and a non-
programmable calcu
2 (a)
The current length of the spring equals to
l1
L
3
( )2 L
2
4
2
l2
L L
2 4
2
(
2
2.8 2 3
) u 2.8
2
4
2
2.52m
5
L 1.565m
4
The unstreched length of the spring equals to
l10
l 20
l0
2
L 1.97 m
2
(1)
The spring forces will be
F1
k l1 l10
F2
k l 2
University of Toronto
Faculty of Applied Science and Engineering
MIE100 Dynamics
Final Examination
April 18, 2011, 2:00pm to 4:30pm
Instructors: J. Postma, C. Simmons, A. Sinclair and L. Sinclair
Aids Permitted: One non-programmable calculator
One 8 1/ by
122.
When a train is traveling along a straight track at 2 m/s, it
begins to accelerate at a = 160 v-42 m>s2, where v is in m/s.
Determine its velocity v and the position 3 s after the
acceleration.
s
SOLUTION
a =
dv
dt
dt =
dv
a
v
3
dt =
0
L
3 =
dv
-4
2
132.
The crane lifts a bin of mass M with an initial acceleration a.
Determine the force in each of the supporting cables due to
this motion.
Given:
M
b
a
3
m
2
3
c
700 kg
4
s
kN
3
10 N
Solution:
2T
c
2
Mg
2
b c
Ma
b2 c2
2c
T
M ( a g)
T
5.60 kN
Ans.
143.
The crate, which has a mass of 100 kg, is subjected to the
action of the two forces. If it is originally at rest, determine
the distance it slides in order to attain a speed of 6 m>s. The
coefficient of kinetic friction between the crate and the
surf
154.
The baseball has a horizontal speed v1 when it is struck by the bat B. If it then travels away
at an angle T from the horizontal and reaches a maximum height h, measured from the
height of the bat, determine the magnitude of the net impulse of the ba
Problem # 1
Solution:
Problem # 2
Solution:
1
Problem # 3
Solution:
2
Problem # 4
Solution:
3
4
5
Problem # 5
6
Solution:
Problem # 6
Solution:
7
Problem # 7
Solution:
8
Problem # 8
Solution:
9
Problem # 9
Solution:
10
Problem # 10
Solution:
11
Problem #
Problem # 1
Solution:
1
Problem # 2
Solution:
2
Problem # 3
Solution:
3
Problem # 4
4
Solution:
5
Problem # 5
Solution:
6
Problem # 6
Solution:
Problem # 7
7
Solution:
8
Problem # 8
Solution:
9
10
Problem # 9
Solution:
11
12
Problem # 10
Solution:
13
14
P
MIEIOOS Dynamics Midterm Examination
6:10 . 7:55 PM, Thursday March 6, 2008
This is a 1 hour 45 rnin exam. It is type C test; only one aid sheet and an approved caiculator
(Casio 260, Sharp 520, T130) are allowed. Answer ail three questions.
_ Questio
mie 100
rectilinear motion: a particle moving along a straight line
position is measured from a xed origin
average velocity: the quotient of the displacement and the time interval
in m/s
instantaneous velocity: allows the time interval to become inni
Midterm Test
MIE 100- Winter 2009
Thursday 6:154:45 pm, March 5 2009
Aids allowed: non-programmabie calculator and aid sheet
lBox A is at rest on a conveyor beit that is initiaily at rest. As the belt is started in the upward
direction, slipping occurs be
MIE100S Dynamics Spring 2012
Midterm Test February 28, 2012
6:15pm 7:45pm
COVER PAGE
General Instructions:
Answer all questions in the exam booklets provided.
Write your full ROSI name, student # and TUTORIAL # on your exam booklet(s).
Number of Pages:
4
University of Toronto
_ Faculty of Applied Science and Engineering
MIE100 Dynamics
Final Examination
April 18, 2011, 2:00pm to 4:30pm
Instructors: J. Postma, C. Simmons, A. Sinclair and L. Sinclair
Aids Permitted: One non-programmable calculator
One 8 1/2
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
Department of Mechanical and Industrial Engineering
FINAL EXAMINATION
April 23, 2010 9:30am
Exam Duration: 2.5 hours
First Year
MIElOOHl S DYNAMICS
Calculator Type 2 (non programmable calcul
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
Department of Mechanical and Industrial Engineering
FINAL EXAMINATION
April 23, 2010 9:30am
Exam Duration: 2.5 hours
First Year
MIE100H1S DYNAMICS
Calculator Type 2 (non programmable calcula
University of Toronto
Faculty of Applied Science and Engineering
Department of Mechanical and Industrial Engineering
FINAL EXAMINATION
May 01, 2009 2:00pm
Exam Duration: 2.5 hours
First Year Mechanical and Industrial Engineering
MIEIOO w Dynamics
Calculat
University of Toronto
Faculty of Applied Science and Engineering
M|E100 Dynamics
Final Examination
April 23, 2012, 9:30 am. - noon
Instructors: C. Simmons, A. Sinclair, L. Sinclair and P. Sullivan
Aids Permitted: One non-programmable calculator
One 8 1/2"
Problem # 1
Solution:
Problem # 2
Solution:
Problem # 3
Solution:
Problem # 4
Solution:
Problem # 5
Solution:
Problem # 6
Solution:
Problem # 7
Solution:
1716.
Determine the mass moment of inertia of the thin plate
about an axis perpendicular to the page and passing
through point O. The material has a mass per unit area of
20 kg>m2.
200 mm
O
200 mm
SOLUTION
Composite Parts: The plate can be subdivided into
.
The bar has a mass M and is suspended from
two springs such that when it is in equilibrium,
the springs make an angle T with the horizontal
as shown. Determine the natural period of
vibration if the bar is pulled down a short
distance and released. Each
185.
The spool has a mass of 60 kg and a radius of gyration
kG = 0.3 m. If it is released from rest, determine how far its
center descends down the smooth plane before it attains an
angular velocity of v = 6 rad>s. Neglect friction and the
mass of the cor
1665.
At the instant shown, the truck is traveling to the right at speed v. If the spool does not slip at B,
determine its angular velocity so that its mass center G appears to an observer on the ground to
remain stationary.
Given:
m
s
v
8
r
1.5 m
Solutio
199.
The wheel having a mass of 100 kg and a radius of gyration
about the z axis of kz = 300 mm, rests on the smooth
horizontal plane. If the belt is subjected to a force of
P = 200 N, determine the angular velocity of the wheel and
the speed of its cente
171.
z
Determine the moment of inertia Iy for the slender rod. The
rods density r and cross-sectional area A are constant.
Express the result in terms of the rods total mass m.
l
SOLUTION
A
x
Iy =
LM
x 2 dm
l
=
=
L0
x 2 (r A dx)
1
r A l3
3
m = rAl
Thus,
I
19 4.
The slender rod of mass M rests on a smooth floor. If it is kicked so as to receive a
horizontal impulse I at point A as shown, determine its angular velocity and the speed of its
mass center.
Given:
M
4 kg
l1
2m
l2
1.75 m
I
8Ns
T
60 deg
Solution:
G