2016/04/28
Work and Kinetic Energy
MEC2023F
MEC2023F
It was noted in the previous lecture that the work-energy
equation for rigid bodies has three cases:
Rigid bodies: Power,
Efficiency &
Potential Energy
Lecture 36
(a) For rigid body translation:
= 12 2
MEC2023F
Surname
Tutorial Test 6
Name
Student Number
The velocity vector diagram of the slotted mechanism
for the instant shown is given (to scale). Bar AB has an
angular acceleration of 10 rad/s2 (CW). Draw the
acceleration vector diagram in the space pr
2016/04/08
General Equations of Motion
MEC2023F
Plane Kinetics of
Rigid Bodies
Translation
For planar motion of rigid bodies, Newtons second law of
motion can be written as
= =
where and is the resultant unbalanced force acting on the
particle, and is
2016/04/28
Work and Kinetic Energy
MEC2023F
For particles, the work-energy equation was derived:
MEC2023F
1 + 12 = 2
where:
Rigid bodies: Work
and Kinetic Energy
12 represents the total work done by all forces acting on the
particle as it moves from state
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
1. A car drives down a spiral ramp that has a constant
radius and constant rate of descent as shown. If the
car drives at a constant speed of = 1.5 m/s,
determine the magnitu
Dynamics
th
(Meriam and Kraige, 7 Ed. ,2013)
Chapter 1. Introduction
Engineering Mechanics
Statics:
Statics
Dynamics
Strength of Materials
Vibration
(F
+ Fr ) = 0 ,distribution of reaction force Fr from the applied
force Fa
Dynamics:
a
(F
a
+ Fr ) = mx
MEC2023F
Surname
Tutorial Test 5
Name
Student Number
For the mechanism shown, = 60, and bar OQ has
a constant clockwise angular velocity of 4.0 rad/s
and counter-clockwise angular acceleration of 2.0
rad/s2 .
a. Draw the relative velocity vector diagram o
Solution
A link with a slot is pinned at O and its rotation is
given by = 4 2 [rad]. The link drives a peg P for a
short distance along the spiral guide = (4) m.
a. Determine the magnitudes of the velocity and
acceleration of the peg at the instant the pe
MEC2023F
Surname
Tutorial Test 4
Name
Student Number
Bar AB rotates in the counter-clockwise direction at 9.2 rad/s.
Determine, using instantaneous centres, the angular velocity of
bar BD and the velocity (unit vector notation) of point D.
IC
The geometry
MEC2023F
Surname
Tutorial Test 3
Name
Student Number
At a given instant in an airplane race, airplane A is flying
horizontally in a straight line, and its speed is being decreased
at the rate of 10 m/s2 Airplane B is flying at the same altitude
as airplan
MEC2023F
Surname
Tutorial Test 01
Name
Student Number
The rocket sled starts from rest and accelerates at
a = 30t m/s2 until its velocity is 400 m/s. It then hits a
water brake and its acceleration is a = 0.3v m/s2 until its
velocity decreases to 100 m/s.
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
2016
MEC2023F Dynamics I
Tutorial 7
1. The 2 kg wooden block A is at rest on a flat surface when the 8 kg mass
B is released. After mass B has descended 2.5 m, its speed is found to be
= 4.5 m/
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
2016
Tutorial 9
1. The wheel and its hub have a mass of 30 kg
with a radius of gyration about the centre of 450
mm. A cord wrapped securely around its hub is
attached to the
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
2016
MEC2023F Dynamics I
Tutorial 8
1. The van shown has a weight of 22500 N and
a centre of gravity at . It carries a fixed 4000
N load which has a centre of gravity at . If
the van is travelli
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
1.
The 200-mm-radius disk rolls without sliding on the
surface shown. The distance BG is 160 mm and at the
instant shown the disk has an angular velocity of 8 rad/s
counter-c
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
2016
Tutorial 6
Instructions:
All of the problems below require that you draw (to scale) velocity and acceleration vector diagrams.
Using the geometry of the velocity vector
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
1.
The flywheel turns clockwise with a constant speed
of 600 revmin. The connecting link
slides
through the pivoted collar at C. Calculate, using
absolute motion analysis, th
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
1. A car drives down a spiral ramp that has a constant
radius and constant rate of descent as shown. If the
car drives at a constant speed of = 1.5 m/s,
determine the magnitu
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
1. A skier skis down a slope and then launches off
a ramp at position A where the ramp makes an
angle of = 25 with the horizontal. If he
lands on the ground at B, determine
a
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
1. The vt graph for a particle moving through a field
from one plate to another has the shape shown in the
figure, where t = 0.2 s and vmax = 10 m/s. When
t = t/2 the particl