182.
The wheel is made from a 5-kg thin ring and two 2-kg
slender rods. If the torsional spring attached to the wheels
center has a stiffness k = 2 N # m>rad, and the wheel is
rotated until the torque M = 25 N # m is developed,
determine the maximum angul

Problem # 1
Solution:
Problem # 2
Solution:
Problem # 3
Solution:
Problem # 4
Solution:
Problem # 5
Solution:
Problem # 6
Solution:
Problem # 7
Solution:

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

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 #

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

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

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.

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

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

LAST Name: First Name: Student #:
MIEIUOS: Dynamics winter 2013: Quiz A
quiz duration — 25 minutes
At time I = 0, a particle is moving counterclockwise in a circle of radius 6 meters around the origin, and slowing down at a
rate of 0.35 m/sz. At time t 2

MIElOOS Dynamics: Winter 2015
Final Exam — April 29, 2015
9:30 am. — noon
General Instructions:
0 Answer all questions in the exam booklets provided.
0 Print your Last Name and First Name neatly on each booklet, as they appear on R081.
0 Print your studen

MIElOOS Dynamics: Winter 2014
Final Exam —- April 25, 2014
9:30 am. — noon
General Instructions:
0 Answer all questions in the exam booklets provided.
a Print your full ROSI name and student # on each booklet.
o All rough work must be nearly shown to earn

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12131.
At a given instant the train engine at E has a speed of
20 m>s and an acceleration of 14 m>s2 acting in the
direction shown. Determine the rate of increase in the
trains speed and the radius of curvature r of the path.
v
75
a
r
SOLUTION
at = 14 cos

161.
The angular velocity of the disk is defined by
v = 15t2 + 22 rad>s, where t is in seconds. Determine the
magnitudes of the velocity and acceleration of point A on
the disk when t = 0.5 s.
A
0.8 m
SOLUTION
v = (5 t2 + 2) rad>s
a =
dv
= 10 t
dt
t = 0.5

225.
When a 3-kg block is suspended from a spring, the spring is
stretched a distance of 60 mm. Determine the natural
frequency and the period of vibration for a 0.2-kg block
attached to the same spring.
SOLUTION
k =
3(9.81)
F
=
= 490.5 N>m
x
0.060
k
490.

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

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

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

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

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

.
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

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

17110. The spool has a mass of 100 kg and a radius of
gyration of
200 mm about its center of mass . If a
vertical force of
200 N is applied to the cable,
determine the
acceleration of
and the angular
acceleration of the spool. The coefficients of static a