Get premium membership and access revision papers, questions with answers as well as video lessons.

Got a question or eager to learn? Discover limitless learning on WhatsApp now - Start Now!

Mechanics Ii Question Paper

Mechanics Ii

Course:Bachelor Of Science (Control & Instrumentation)

Institution: Jomo Kenyatta University Of Agriculture And Technology question papers

Exam Year:2013

UNIVERSITY EXAMINATIONS 2012/2013.
SECOND YEAR EXAMINATION FOR THE DEGREE OF
BACHELOR OF SCIENCE
B.SC CONTROL AND INSTRUMENTATION
SPH 2200: MECHANICS II
DATE:APRIL 2013 TIME:2 HOURS
INSTRUCTIONS: ANSWER QUESTION ONE AND OTHER TWO QUESTIONS.QUESTION ONE CARRIES 30 MARKS WHILE THE OTHERS EACH CARRIES 20 MARKS.
QUESTION ONE.
(a)The vectors A and B are given by:
A=2i +3j +7k
B=-i + 6j -5k
Calculate:-
(i)A×B (ii)A•B (iii) Angle between A and B. (9 marks)
(b)Prove that for any vector function A, the divergence of its curl is zero as in the equation below,
Show that[??•(??×A)]=0 (4 marks)
(c)(i)State the principle of conservation of angular momentum.(1 mark)
(ii)If a particle of mass (m) at a point, whose position vector is (r) moves in a force field F, show that the torque produced is the rate of change in angular momentum.(4 marks)
(d)The depth (h) of a valley in metres is given by;
h(x,y) =3 x2 + 2y2 -50x + xy +20y +300
where y is the distance in meters north and x is the distance in meters east of a tower
Determine:
(i)Co-ordinates of the lowest point on the valley from the tower.
(ii)The depth of the valley . (7 marks)
(e) A body has an initial angular velocity of 3 rad/sec and a constant angular acceleration of 2 rad/sec2. Calculate the
(i)Angular displacement after 3 seconds.
(ii)Angular velocity at t= 3 seconds (5 marks)
QUESTION TWO.
(a)(i)Define a conservative force field.( 1 mark)
(ii)A conservative force may be expressed as:
?(?-F )=- ?(?-? ?(?-V ))
Show that for such a force, ??×F = 0 (4 marks)
(iii)Show that a force field defined by;
F=(6xyz + z2)i + 3 x2yz j + (3 x2y + 2xz)k is a conservative force field. (3 marks)
(iv) Determine the associated potential (V) to the above force field in (a) (iii) (4 marks)
(b) A particle of mass 3 units moves in a force field depending on time t given by;
F=12t2i +(6t – 3)j -3tk .If its position vactor at time t=0 seconds is given by; ro= 2i + j -2 k and its initial velocity at this instant given by; Vo=4i +5 j + 3k
Detemine
Its velocity and position at any time(t).(4 marks)
Torque and angular momentum about the origin for the particle at time(t)
QUESTION THREE.
(i)state TWO conditions for any system of forces acting on an object to be at equilibrium.(2 marks)
(ii)Test whether the following system of forces are in equilibrium.
F1=i –j, acting at a point r1=i + k
F2= i- k, acting at a point r2=2i
F3= 2j + k, acting at a point r3=i-2j
F4=-2i-j , acting at a point r4 =3i + j + k (5 marks)
(b)(i) State the fundamental theorem for gradients.(1 mark)
(ii)For the function; T=x2 + 4 xy + 2 yz3 and the points a=(0, 0, 0), b= (1, 1, 1), check the fundamental theorem for gradients.(5 marks)
(c)(i)Write the mathematical statement for the divergence theorem, explaining the geometrical significance of it. (2 marks)
(ii)Verify divergence theorem for the function;
V=(x2-z2)i+ 2xy j + (y2 + z)k for a unit cube situated at the origin, bounded by the six planes x=y=z=0, x=y=z=1 (5 marks)
QUESTION FOUR.
(a)Define the following terms;
(i)Angular velocity .
(ii)Torque.
(iii)Radius of gyration. (3 marks)
(b)(i) State the parallel axes theorem.(1 mark)
(ii)Show that the moment of inertia of a uniform rod of mass (m) and length(l) about an axis passing through its mid-length perpendicular to the rod is given by;
I= (Ml^2)/12
If the axis of rotation passes through to a point situated at ? th of the length of the rod, determine its moment of inertia using the parallel axis theorem.(2 marks)
(c)(i) Show that the moment of inertia of a solid disc of mass M and radius R about an axis through its centre and perpendicular to its plane is given by, (3 marks)
I=(MR^2)/2
(ii) A circular disc of radius 0.1m and mass 1 kg is rotating at a rate of 10 revolutions per second about its axis. Find the work that must be done to increase the rate of its revolution to 20 revolutions per second.(3 marks)
(iii)A uniform disc of mass 10 kg and radius 10 cm is mounted on a horizontal cylindrical axle of radius 2 cm and negligible mass. If a tangential force of 20N acts on the axle for 10 seconds from rest. Calculate:
Angular velocity acquired after 10 seconds.(2 marks)
Kinetic energy of the disc after 10 seconds. ( 1 mark)
Time taken to bring the disc to rest if a force of 2N is applied tangentially to the rim of the disc opposing its motion.(2 marks)

Mechanics Ii Question Paper

More Question Papers

Popular Exams