PHYS 251 Problem Set 1
due date: Friday, September 11, 2015
1. The acceleration of gravity can be measured by projecting a body upward and measuring the
time that it takes to pass two given points in both directions. Show that if the time the body takes
t
PHYS 251 Problem Set 11
due date: Friday, November 27, 2015
1. A 2 kg mass on a frictionless table is attached to one end of a massless spring.
The other end of the spring is held by a frictionless pivot. The spring produces a
force of magnitude 3r Newton
PHYS 251 Problem Set 6
due date: Friday, October 16, 2015
1. A block of mass M slides along a horizontal table with speed v0 . At x = 0 it hits a spring with
spring constant k and also begins to experience a friction force. The coefficient of friction is
PHYS 251 Problem Set 9
due date: Friday, November 13, 2015
1. A uniform stick of mass M and length l is suspended horizontally with end B
on the edge of a table, and the other end, A is held by hand. Point A is suddenly
released. At the instant after rele
PHYS 251 Problem Set 12
due date: Friday, December 4, 2015
1. A thin hoop of mass M and radius R rolls without slipping about the z axis. It
is supported by an axle of length R through its centre, as shown. The hoop circles
around the Z axis with angular
PHYS 251 Problem Set 4
due date: Friday, October 2, 2015
1. The logarithmic decrement is defined to be the natural logarithm of the ratio of successive
maximum displacements (in the same direction) of a free damped oscillator.
(a) Show that = /Q.
(b) Find
PHYS 251 Problem Set 7
due date: Friday, October 30, 2015
1. A small ball of mass m is placed on top of a superball of mass M and the
two balls are dropped to the floor from a height h. How high does the small ball
rise after the collision? Assume that co
PHYS 251 Problem Set 5
due date: Friday, October 9, 2015
1. Material is blown into cart A from cart B at a rate b kilograms per second. The material leaves the
chute vertically downward so that it has the same horizontal velocity as cart B, u. At the mome
PHYS 251 Problem Set 8
due date: Friday, November 6, 2015
1. A pendulum is made from two disks, each of mass M and radius R separated
by a massless rod. One of the disks is pivoted through its centre by a small pin.
The disks hang in the same plane and th
PHYS 251 Problem Set 3
due date: Friday, September 25, 2015
1. The gravitational force on a body located at a distance R from the centre of a uniform spherical
mass is due solely to the mass lying at a distance r R, measured from the centre of the sphere.
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2.20. Block under an overhang
Lets break up the forces into components parallel and perpendicular to the over
hang. Let positive F; point up along the overhang. Balancing the forces parallel
and perpendicular to the overhang gives, respectively,
F
PHYS 251 HONOURS CLASSICAL MECHANICS 2014
Homework Set 10 Solutions
1.
One can write the general standing wave solution as
q(t, x) = [A1 cos(ckt + ) + A2 cos(ckt + )] cos(kx + ) ,
(1)
2
where c /, is the string tension, and is the constant mass per unit l
PHYS 251 HONOURS CLASSICAL MECHANICS 2014
Homework Set 6 Solutions
6.25. Spring on a T
Let the -rod be horizontal (parallel to the x axis) at t = 0. Then, as it rotates with constant angular frequency
, its angle with respect to the x axis will be t. Thus
PHYS 251 HONOURS CLASSICAL MECHANICS 2014
Homework Set 5 Solutions
5.37. Heading to innity
By conservation of energy, we have
E =K +V =
1
mv(x)2 + V (x)
2
(1)
2
[E V (x)] .
m
= v(x) =
(2)
We are told that the potential is V (x) = A|x|n , A > 0, n > 0. Als
PHYS 251 Problem Set 10
due date: Friday, November 20, 2015
1. A uniform thin rod of length L and mass M is pivoted at one end. The pivot is
attached to the top of a car accelerating at rate A, as shown.
(a) What is the equilibrium value of the angle betw