School of Mechanical and Electrical Engineering, Faculty of Health, Engineering... MEC2401 Dynamics I, S2, 2014, Assignment 2

School of Mechanical and Electrical Engineering, Faculty of Health, Engineering... MEC2401 Dynamics I, S2, 2014, Assignment 2

MEC2401 Dynamics I
S2, 2014
School of Mechanical and Electrical Engineering, Faculty of Health, Engineering and Sciences,
MEC2401 Dynamics I, S2, 2014, Assignment 2
Answer all questions (200/1000) Due Date 27th October 2014
Assignment must be submitted electronically and student should follow the instructions given in the
instructions for assignment preparation which is posted on the course study desk
Take gravitational acceleration g = 9.81 m/s2
Q1. (Marks 30/200)
The free rolling ramp shown in Figure Q1, a has mass of 90 kg . A crate whose mass is 60 kg slides from rest at A
6m down to the ramp to B.
I. Determine the ramps speed when the crate reaches B (Assume that the ramp surface and the floor are
smooth)
0
(10 Marks)
II. Determine the distance the ramp travels when the crate reaches B
0
(Assume that the ramp surface
and the floor are smooth) (10 Marks)
III. Describe the motion of rolling ramp, If the sliding friction coefficient of the ramp surface and the crate is
0.58 and the inclination angle
0
(10 Marks)
A
6m
B
Floor
Figure Q1
1
MEC2401 Dynamics I
S2, 2014
Q2. (Marks 50/200)
At the instant shown in the Figure Q2, link AB has an angular velocity AB = 6 rad/s. angular acceleration
AB
= 2 rad/s2. Each link is considered as a uniform slender bar each with a mass of 1.5 kg/m,
I. Determine the angular velocity and angular acceleration of link BC and CD (20 Marks)
II. Determine the kinetic energy of each link (AB, BC and CD) (15 Marks)
m
III. Determine the horizontal and vertical components of acceleration at point C (15 Marks)
A
45
0
m
90
90
AB
= 6 rad/s
AB
=2 rad/s2
35 0
C
B
m
0m
70 0
75
500 mm
D
Figure Q2
2
MEC2401 Dynamics I
S2, 2014
Q3. (Marks 40/200)
Figure Q3 shows a 10Mg front-end-loader used to move Ore in the loader bucket. The centres of mass (CM) for
the front-end-loader and the Ore load at G and GL respectively.
I.
Determine the reactions exerted by the ground on the pairs of wheels at A and B, if the front-end-loader
is moving forward at a constant acceleration of 1.6 m/s2 from the rest. The Ore Load is 2.5Mg and the CM
(GL) is at height h = 3.5 m and x = 2.0 m (from the centre of front wheel A). (20 Marks)
II.
The front-end-loader with a 1 Mg Ore Load CM (GL) at h = 2.85 m and x= 2.6 m is moving forward at a
constant velocity of 40 km/hr. Can the front-end-loader completely come to a rest safely without tipping
over, if the operator suddenly applied brakes? Assume that all wheels are locked when the brakes are
applied and the coefficient of static friction between the wheels and the ground is 0.55. (20 Marks)
170
Figure Q3
3
MEC2401 Dynamics I
S2, 2014
Q4. (Marks 40/200)
Figure Q4 shows a uniform disk attached to a shaft at A (in vertical plane). Disk has a mass (M) 15 kg
and G is the centre of mass. A constant torque of T = 50 N m is exerted on the disk by the shaft at A and
I
0
I.
.
Derive an expression for the resulting angular acceleration
acceleration at the instant
II.
0
of the disk and calculate the angular
. (15 Marks)
Calculate the rotational speed (rpm) of the disk around A, kinetic energy of the disk and the work
done by the torque T after
III.
time t = 0 s
0
. (15 Marks)
Calculate the radial force acting on the shaft by the disk and its direction with respect to Y axis,
when at
0
. Illustrate it on a free-body-diagram (Marks 10)
(List all your assumptions)
Y
Ø1m
M= 15 kg
X
G
T = 50 Nm
A
Elevation
4
MEC2401 Dynamics I
S2, 2014
Figure Q4
Q5. (Marks 40/200)
Figure Q5 shows a collision of a high speed locomotive engine and an oil tanker at an unprotected railway
crossing. The locomotive A has mass MA and was travelling in constant velocity of 120 km/hr and the Tanker B has
mass MB and was travelling in constant velocity of 80 km/hr. MA = 5 Mg and MB = 1.8 Mg
I. Calculate velocities of the locomotive and the tanker after the collision if the locomotive and the tanker
become entangled and move off together after the collision. (10 Marks)
II. Calculate velocities of the locomotive and the tanker after the collision in terms of e (0<e <1) which the
coefficient of restitution between the locomotive and the tanker. (20 Marks)
III. Calculate the possible energy loss for Case (i) and Case (II) for two values of e; 0.2, and 0.8. Comment on
the severity of collision depending on your calculated values. (10 Marks)
List all the assumptions clearly for each case.
200
V (train) = 120 km/hr
Train A
Tanker B
V (Tanker) 80 km/hr
Figure Q5
5