PHYS 3032 (Spring 2015) Tutorial 5 Classwork
9, 11 March 2015
Problem 1
Consider a particle of reduced mass orbiting in a central force with where kn > 0.
Explain what the condition kn > 0 tells us ab
PHYS 3032 (Spring 2015) Tutorial 7 Classwork
1. The Coriolis force can produce a torque on a spinning object. To illustrate this, consider a
horizontal hoop of mass m and radius r spinning with angula
PHYS 3032 (Spring 2015)
Homework 7 [20 points each]
Due time: 10:30 am on April 13, 2015
1. Find the differential equations of motion for an elastic pendulum: a particle of mass m
attached to an elast
Chapter 9
Motion of Rigid Bodies in 3D
Angular Momentum for an Arbitrary Angular Velocity
v i mi ri ( ri )
The angular momentum L mi ri =
for an arbitrary axis passing through a fixed point
An arbit
PHYS 3032 (Spring 2015)
Homework 8 (Total 100 points)
Due time: 10:30am on 20 April 2015
1. (20 points) A particle slides on a smooth inclined plane whose inclination is increasing at
a constant rate
PHYS 3032 (Spring 2015)
Homework Solution 6
Problem 1:
(a)
Circular motion of radius
(b)
(c)
where
Let
Try a solution of the form
So
Also at the coordinate systems coincide so
so,
Thus,
Problem 2:
Let
PHYS 3032 (Spring 2015)
Homework 9 [20 points each]
Due time: 11:50 m on April 27, 2015
1. Use the method of Lagrange multipliers to find the tensions in the two strings of the double
Atwood machine o
Comments on HW10
Question 1, surprisingly many students got integration wrong. Also, check your
units.
Question 2, well done.
Question 3, well done.
Question 4, some students did not, or could not cor
PHYS 3032 (Spring 2015)
Homework 10 (20 points each)
Due time: 10:30am on May 4, 2015
1. A paraboloid is bounded by z = (x2 + y2)/b and the plane z = b.
(a) Find the coordinates of its centre of mass.
Comments on HW8
Question 1, not required.
Question 2, students could find the differential equation, but some could not show
that particle remains between two horizontal circles.
Question 3, it seems
PHYS 3032 (Spring 2015)
Homework 6 (20 points each)
Due time: 10:30am on March 30, 2015
1.
2. A cockroach crawls with constant speed in a circular path of radius b on a phonograph
turntable rotating w
Homework 5 Solution
Problem 1
We are given the satellites heights at perigee and at apogee. The corresponding distances from
the earths center are and . We know from (8.50) that and ,from which it fol
PHYS 3032 (Spring 2015)
Homework 3
Due time: 10:30am on 2 March, 2015
Problem 1 (a, d only) (15 points)
Problem 2 (a, d only) (15 points)
Problem 3 (20 points)
Problem 4 (25 points)
Problem 5 (25 poin
Homework 4 Solution
Problem 6.3, 6.4 and 6.7:
6.3
The gravitational force on the particle is due only to the mass of the earth that is inside
the particles instantaneous displacement from the center o
PHYS 3032 (Spring 2015)
Homework 5 (total 100 points)
Due time: 10:30am on 23 March, 2015
1.
(15 points) The height of a satellite at perigee is 300 km above the earths surface and it is
3000 km at ap
PHYS 3032 (Spring 2015)
Homework Solution 7
Problem 1:
,
Problem 2:
(a) For x the distance of the hanging block below the edge of the table:
and
,
(b)and
,
Problem 3:
Let x be the slant height of the
PHYS 3032 (Spring 2015)
Homework Solution 9
Problem 1:
Note: 4 objects move their coordinates are labelled: The coordinate of the movable, massless
pulley is labelled.
Two equations of constraint:
Thu
Chapter 7
Dynamics of Systems of N Particles
The Center of Mass
The motion of the Centre of
Mass is a simple parabola.
(just like a point particle)
The motion of the entire
object is complicated =
(mo
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PHYS 3032 (Spring 2015) Quiz 3, 27 April 2015
Duration: 20 minutes (10 points)
A block of mass M is rigidly connected to a massless circular track of radius a on a frictionless
horizonta
PHYS 3032 (Spring 2015) Quiz 1, 2 March 2015
Suggested Solutions
Problem 1 (20 Points)
Setting and plot to get a sense of how V changes with x over the domain , we have the
following diagram:
We can o
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PHYS 3032 (Spring 2015) Quiz 2, 16 March 2015
Duration: 20 minutes (10 points)
Particles of mud are thrown from the rim of a rolling wheel. If the forward speed of the
wheel is , and the
PHYS 3032 (Spring 2015) Quiz 2, 16 March 2015
Suggested solutions
The maximum height for a projectile motion is where is the initial upward speed.
The initial position of the mud is . Hence the maximu
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PHYS 3032 (Spring 2015) Quiz 1, 2 March 2015
Duration: 20 minutes (10 points)
(a) A particle of mass m moves under a conservative force with potential energy
where c and a are positive c
PHYS 3032 (Spring 2015) Quiz 3, 27 April 2015
Suggested Solutions
(a) As the motion of the system is confined to a vertical plane, use a fixed coordinate
frame x, y and choose the x coordinate of the
Comments on Quiz 2
Most students could write the expression for height h in terms of time and angle,
.and knew how to find time at which particles will reach greatest height
Students should remember t
Comments on Quiz1
For part (a), many students do not know how to show the equilibrium point is
stable/unstable. Some algebraic mistakes are found when differentiating the
potential, this part should b
HW8 Suggested solutions
Problem 1. Let x be the slant height of the particle
,
The solution to the homogeneous equation
, is
Assuming a particular solution to have the form ,
At time , and
From Appen
PHYS 3032 (Spring 2015)
Homework Solution 11
9.1 (a)
and
From the perpendicular axis theorem:
(b)
,
,
From equation 9.1.10
(c)
From equation 9.1.29
(d) From equation 9.1.32:
9.3 (a)
From equation 9.