Download Applied Mechanics I - Nepal Engineering College

Nepal Engineering College
Changunarayan, Bhaktapur
Assessment
Level: Bachelor
Year: 2015
Program: Civil, Computer, Electrical, Electronics
Full marks: 100
Course: Applied Mechanics I
Time: 3 hrs
Candidates are required to give their answers in their own words as far as practicable
Figure in the margin indicates full marks
1a A steel tank is to be positioned in an excavation. Determine the magnitude and direction of the
smallest force P for which the resultant R of the tow forces applied at A is vertical. Also find the
corresponding magnitude of R. [Figure 1]
[7]
Figure 1
1b
1a
Figure 2
A square foundation mat supports the four columns with the weight as shown. Determine the
magnitude and point of application of the resultant of the four loads. [Figure 2]
OR
Determine the required length of cord AC so that the 8 kg lamp can be suspended in the position
shown. The undeformed length of spring AB is 0.4 m, and the spring has a stiffness of kAB = 300
N/m. [Figure 3]
[8]
[7]
Figure 3
1b
1a
Figure 4
Determine the resultant produced by forces FB and FC about point O. [Figure 4]
OR
If the 1.5 m long cord AB can withstand a maximum force of 3500 N, determine the force in cord
BC and the distance y so that the 200 kg crate can be supported. [Figure 5]
[8]
[7]
Figure 5
1b
2a
Figure 6
The 800 N cylinder is supported by three chains as shown. Determine the force in each chain for [8]
equilibrium. Take d = 1 m and r = 1 m. [Figure 6]
Knowing that the coefficient of friction between the 25 kg block and the incline is µ s = 0.25 [7]
determine, (a) smallest value of P required to start the block moving up the incline (b) the
corresponding value of β. [Figure 7]
OR
P
β
30°
2a
2a
2b
Figure 9
Figure 7
Figure 8
The uniform 10 kg ladder rests against the smooth wall at B, and the end A rests on the rough [7]
horizontal plane for which the coefficient of static friction is 0.3. Determine the angle of inclination
θ of the ladder and the normal reaction at B if the ladder is on the verge of slipping. [Figure 8]
OR
If the coefficient of static friction at contact points A and B is µs = 0.3, determine the maximum
[7]
force P that can be applied without causing the 100-kg spool to move. [Figure 9]
Determine the force in member DF, FG, GH of the truss as shown in figure 10
OR
Determine the force in member BD, BE, CE of the truss as shown in figure 10
OR
Determine the force in member HJ, JH, IK of the truss as shown in figure 10
10 kN 10 kN 10 kN 10 kN 10 kN
F
D
H
J
3
B
[8]
A
E
C
2
4
G
4
I
4
L
K
4
2
All dimensions are in m
Figure 10
3a
Locate the centroid of the shaded area as shown in the figure 11
[7]
3b
3
Figure 11
Calculate the moment of inertia of a triangle about its base by the first principle.
OR
Calculate the centroid and moment of inertial about coordinate axes of the shaded area as shown.
[Figure 12]
[8]
[15]
Figure 12
3
OR
Calculate the moment of inertia of the shaded area about its centroidal axes. [Figure 13]
[15]
y
4
10
10
x
4
4
4
All dimensions are
in cm
Figure 13
Draw the shear force and bending moment diagram for the beam as shown in the figure 14.
20 kN/m
20 kN/m
25 kN
2m
4
10
1m
1m
[15]
2m
Figure 14
OR
Draw the shear force and bending moment diagram for the beam as shown in the figure 15.
[15]
10 kN
3 kN/ m
3 kN/ m
C
A
B
5m
4
5m
Figure 15
Draw the shear force and bending moment diagram for the beam as shown in the figure 16.
[15]
2 kN/m
2m
5a
2m
Figure 16
The motion of the particle is defined by the relation a= 9t+5, where ‘a’ is expressed in m/s2and t in
s. At t = 0, v = 2m/s and x = 5m.
i. Write equations of motion
ii.
Determine the position, velocity and acceleration at t=4s
[7]
OR
5a
5a
5b
The chipping machine is designed to eject wood chips at vo = 25 ft/s as shown in the figure 17. If
the tube is oriented at 30° from the horizontal, determine how high, h, the chips strike the pile if at
this instant they land on the pile 20 ft from the tube.
Figure 17
OR
Car A and B are traveling respectively at the constant speeds (vA)o = 36 km/h and (vB)o = 27 km/h
on an ice-covered road. To avoid overtaking car B, the driver of car A applies his brakes so that his
car decelerates at a constant rate of 0.042 m/s2. Determine the distance d between the cars at which
the driver of car A must apply his brakes to just avoid colliding with car B. [Figure 18]
Figure 18
A mixing drum of 125mm outside radius rests on two casters each of 25mm radius. The drum
executed 15 revolutions during the time interval t, while its angular velocity is being increased
uniformly from 20 to 50 rpm. Knowing that no slipping occurs between the drum and casters
determine, (i) Angular acceleration of the casters, (ii)Time interval t [Figure 19]
[7]
[7]
[8]
Figure 19
5b
OR
The belt shown moves over two pulleys without slipping. At the instance shown the pulleys are
rotating clockwise and the seed of point B on the belt is 4 m/s, increasing at the rate of 32 m/s 2.
Determine, at this instant, (a) angular velocity and angular acceleration of each pulley, (b) the
acceleration of point P on pulley C. [Figure 20]
[8]
B
160 mm
A
5b
6
6
100 mm
C
Figure 20
OR
Disk B is at rest when it brought into contact with disk A which is rotating freely at 450 r/min
clockwise. After 6 s of slippage, during which each disk has a constant angular acceleration, disk A
reaches a final angular velocity of 140 r/min clockwise. Determine the angular acceleration of each
disk during the period of slippage. [Figure 21]
Figure 21
The cylinder has a mass of 80 kg. A horizontal force P = 750 N is applied to a cable wrapped
around its outer surface. If the cylinder is originally at rest, determine its angular velocity after the
center of the cylinder O has moved s = 2 m. The cylinder rolls without slipping. Neglect the mass
of the cable. [Figure 22]
[8]
[15]
Figure 22
OR
The two blocks (ma=100 kg, mb=150 kg) shown are originally at rest. Assuming that the
coefficients of friction between the blocks and the inclines are μs =0.25 and μk =0.20, determine
a) acceleration of block A
b) tension in the cord [Figure 23]
Figure 23
C
A
B
6
[Figure 24]
Neglecting the mass of pulleys and effect of friction in the pulleys, calculate the acceleration of [15]
each pulley and tension in the rope. Take mA = 25 kg, mB = 15 kg and mc = 10 kg. [Figure 24]
7
Write short note on any two
[10]
a.
b.
c.
d.
e.
f.
g.
Rectangular components of a force
Centre of gravity
Linear momentum and angular momentum
Normal and tangential component of acceleration
Static determinacy stability of beam
Principle of transmissibility of force
Translational and rotational force