ConcepTest 8.3 Up the Hill
Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? 1) the same 2) twice as much 3) four t
PHY 53
Summer 2010
Assignment 10
1.
Two identical point masses, each of mass m, are attached
by a massless horizontal rod of length as shown. They
are rotating at angular velocity about a xed axle
perpendicular to the rod, at distance d from its center.
a
PHY 53
Summer 2010
Assignment 9
1.
A heavy cylindrical container is being rolled up an
incline as shown, by applying a force parallel to the
incline. The static friction coefcient is s . The
cylinder has radius R, mass m and moment of inertia
about its sy
PHY 53 Summer 2010
Duke Marine Laboratory
1.
Some questions about the vector product C = A B .
a.
Assignment 8
Prove the rules given in the notes for the magnitude and direction of C
from the denition in terms of components. Let A and B lie in the x-y
pla
PHY 53
Summer 2010
Assignment 7
Reading: Systems of Particles
Key concepts: Center of mass, momentum, motion relative to CM, collisions.
1.
Two identical balls of mass m are
propelled at t = 0 from the same
starting point. Ball A moves on a
frictionless h
PHY 53
Summer 2010
Assignment 6
Reading: Energy 2
Key Concepts: Potential energy, total energy, conservation of mechanical energy,
equilibrium and turning points.
1.
Some statements about the law of conservation of mechanical energy. Comment
on their vali
PHY 53
Summer 2010
Assignment 5
Reading: Energy 1
Key Concepts: Scalar products, work, kinetic energy, work-energy theorem.
1.
Questions about the scalar product of two vectors.
a.
Use vectors to prove the law of cosines for a triangle. [Consider the
prod
PHY 53
Summer 2010
Assignment 4
Reading: Dynamics 2
Key concepts: Radial forces, effective gravity.
1.
A block of mass m slides at constant speed down an incline of angle .
a.
What is the coefcient of kinetic friction k ? Ans: k = tan .
b.
The same block
PHY 53
Summer 2010
1.
Three systems in static equilibrium.
a.
Assignment 11
A mobile hangs as shown.
The strings and crossbars are
massless. The strings supporting
the crossbars are attached at
distance / 4 from the left end.
4
3
The mass of ball #1 is m.
PHY 53
Summer 2010
1.
The king ordered a crown of solid pure gold, but what he got didnt feel right, so
he asked Archimedes to verify that it was really solid and all gold. Archimedes
realized he needed a way to measure the density of the crown, but he co
Physics 53
Dynamics 2
For every complex problem there is one solution that is simple, neat and wrong.
H.L. Mencken
Force laws for macroscopic objects
Newtons program mandates studying nature in order to discover general laws of force.
Newton showed how p
Physics 53
Dynamics 1
. from the same principles, I now demonstrate the frame of the System of the World.
Isaac Newton, Principia
Reference frames
When we say that a particle moves in a certain way, what we mean is that it is observed
to move that way. O
PHY 53
Summer 2010
Assignment 18
1.
For each of the cycles in Probs. 1-3 of Assignment 17, do the following.
a.
b.
Find the total work done and the efciency of an engine running on that
cycle.
c.
2.
Find the total heat taken in, for those steps where heat
PHY 53
Summer 2010
Assignment 17
1.
We take the expansion steps in the last problem of Assignment 16 and add steps
to make a cycle. The rst step starts with one mole of an ideal gas at pressure P0
and volume V0 (and therefore temperature T0 = P0V0 / R ).
PHY 53
Summer 2010
Assignment 16
1.
Some questions about air.
a.
b.
Explain the afternoon sea breeze.
c.
Explain why an air bubble in water grows in volume as it rises.
d.
2.
Explain why warm air rises.
Show that the upward acceleration of an air bubble i
PHY 53
Summer 2010
Assignment 15
1.
Take the usual reference intensity for the db scale for sound, I0 = 1012 W/m 2 .
a.
b.
2.
What is the intensity of a sound of loudness 120 db?
If this is the intensity of the sound at a rock concert at distance 90 m fro
PHY 53
Summer 2010
Assignment 14
1.
A harmonic wave in a string is described by y( x , t ) = 0.01 cos(0.6 x 60 t ) . [SI
units.]
a.
b.
What is the frequency f?
c.
What is the speed v of the wave?
d.
2.
What is the wavelength ?
What is the power transmitte
Supplementary Problems for Topics III
PHY 53 Summer 2010
1.
1.
Duke Marine Laboratory
An empty steel drum of mass M, height h and cross-section area A is floating
n in water. T 13
partially submerged as showAssignment he bottom of the drum is at depth d
PHY 53
Summer 2010
Assignment 3
Reading: Dynamics 1
Key concepts: Reference frames, inertia, mass, force, Newtons laws of motion, friction.
1.
A skilled oarsman rows his boat back and forth across a river of width w, and
then the same distance down and up
PHY 53
Summer 2010
Assignment 2
Reading: Kinematics 2
Key Concepts: Projectiles; circular motion.
[In problems with numbers, use g = 10 m/s2 .]
1.
Ball A and ball B are thrown with the same vertical component of initial velocity,
but ball A is thrown at a
Exam Taking Hints
Make sure that you budget your time wisely. If it is a 75 minute exam, a useful time allocation may be as follows: Spend 10-15 minutes combined on all multiple choice questions; Use 5 minutes to read the long problems; decide which two y
Problem Set 3 Solutions (Giancoli 4th ed.)
19. (a) Consider the free-body diagram for the crate on the surface. There is no motion in the y direction and thus no acceleration in the y direction. Write Newton's second law for both directions, and find the