Download Fiz 235 Mechanics 2002

Name:
14.1.2003
Dr.Yılmaz KAPTAN
No:
Fiz 235 Mechanics 2002-2003 Fall Semester
Make Up Examination
Answer only 5 questions
1) A 20 kg body is moving in the direction of the positive x-axis with a speed of 200 m/s when
due to an internal explosion, it breaks into three parts. One part, whose mass is 10 kg,
moves away from the point of explosion with a speed of 100 m/s along the positive y axis. A
second fragment with a mass 4 kg moves along negative x-axis with a speed of 500 m/s.
a) What is the velocity of third (6 kg) particle?
A'
b) How much energy is released in the explosion?
2) For a uniform thin rod (mass M, length L)
- L/2
a) Find the moment of inertia (IAA’)
b) Find the radius of gyration,
about AA’ axis.
A
+L/2
3) A projectile is fired from the origin with initial velocity
v0=vxo i+vyo j+vzo k.
The air resistance (Fair) is proportional to the velocity of the particle
and the wind velocity vw=w j. [ Fair = -b(v - vw) , b=constant ]
Solve the equation of motion for x, y and z as function of time t.
4)
a) Evaluate and xfor the vector A=(x2y) i –(2y2z) j +(xy2z2) k at point (1,-2,-1).
b) Show that the force F=(6abz3y-20bx3y2)i + (6abxz3-10bx4y)j + (18abxz2y)k
is conservative and find the potential energy.
c) Find the work done in moving an object in this field from (0,1,1) to (2,1,2).
5) Set up the Lagrangian function and obtain the equation of motion for a one dimentional
harmonic oscillator by using Lagrange’s Equation and solve this equation.
6) A pendulum bob of mass m is suspended by a string of length L
from a point of support. The point of support moves along the x-axis
according to the equation u=a.coswt.
Assume that the pendulum swings only in a vertical plane and
let angle is the generalized coordinate.
a) Set up the Lagrange Function,
b) Find the Lagrange's equation of motion.
7) A body is dropped from rest at a height z above the surface of the
earth in the Northern Hemisphere. Find the direction and show that the
net displacement of the point of impact due to the coriolis force is
w/3.[(2z)3/g)]1/2.sin
Where,  is the angle between v and w , g is the effective gravitational
acceleration.
U=a.coswt
Name:
14.1.2003
Dr.Yılmaz KAPTAN
No:
Fiz 235 Mechanics 2002-2003 Fall Semester
Make Up Examination