N11: Oscillations
Problem: A mass m is suspended by a spring with spring constant k attached to
the ceiling. Find the frequency of small up and down oscillations of the mass
about its equilibrium position.
Problem: A pendulum consists of a mass m suspende
N10: Projectile Motion
battleship simultaneously fires two shells
Concept Test
enemy ships. If the shells follow the parA battleship simultaneously res shown, which
olic trajectories two shells at enemy ships. If the ship gets
shells follow the parabolic
N9: Accelerated
Reference Frames
Problem: A car is accelerating with constant acceleration A. A pair of fuzzy dice
hangs from the window at a constant angle. What is this angle?
Problem: An astronaut is in a rocket ship that is accelerating upward at 9.8
Reminders:
Exam 2 next Wednesday
HW7 corrections next Monday
N8: Circularly
Constrained Motion
Problem: A toy car of mass m goes around a vertical loop the loop of radius
R. What is the minimum speed it must have at the bottom in order to avoid
falling of
N7: Coupled Objects
Problem: A box of mass M is attached to a chain of mass m. A person pulls on
the chain with a constant force F. What is the force that the chain exerts on the
box?
m
Problem: A worker lifts a crate of mass m at constant speed using the
N6: Linearly Constrained
Motion
Problem: A box of mass m slides down an inclined plane that makes an angle
with the horizontal. The coefcient of sliding friction between the box and the
plane is . What is the acceleration of the box?
Concept Test
A physic
N5: Statics
Problem: A person of mass m walks across a beam of mass M. The beam is held
up by two supports, one at each end. What is the force exerted by the left
support as a function of where the person stands on the beam?
A 1-kg rock is suspended by a
N4: Motion from Forces
Problem: A owerpot falls downward past a window that has a vertical height
1.5 m. The owerpot is observed to take 0.2 seconds to fall past the window.
From how far above the top of the window did the owerpot fall?
Problem: A rocket
N3: Forces from Motion
Concept Test
A book sits at rest on a table. What explains the absence of a net force on the
book?
1. Newtons third law implies that the normal force equals the gravitational
force.
2. Force is caused by acceleration, so the absence
Concept Test
A painter on a platform pulls himself up by pulling on a rope as shown.
What is the correct free-body diagram for the system consisting of the
painter, the platform, and the weight on the platform?
1.
2.
3.
4. Other
cm
N2: Vector Calculus
Pro
N1: Newtons Laws
Concept Test
1.
2.
3.
4.
A puck is initially attatched to a horizontal rotating platform. At the
instant shown, the ball is released from the platform. Which line most
nearly shows the subsequent trajectory of the puck?
Neglect friction.
Formula Sheet
Velocity:
dr
dt
= vAB + vCD
v=
vAC
Momentum and center of mass:
1
(m1 r1 + m2 r2 + ) ,
M
p = M vcm
dp
Fnet =
dt
M = m1 + m2 +
rcm =
Energy:
E =K +V
K = 1 mv 2
2
dV
dx
GM m
=
mgh + const
r
= 1 k (r r0 )2
2
Fx =
Vgrav
Vspring
dE = Fnet dr
Ro
Final Exam
5 problems, 20 points each
1. (20 points) A ball of mass m is shot through a tube of length Z that is elevated
by an angle 0 as shown. The ball has initial speed 210 at the bottom of the tube. The
tube is aimed at a target a distance d away f
Final Exam
5 problems, 20 points each
1. (20 points) A canon on a horizontal surface res a cannonball with initial speed
v0 at an angle above the horizontal. There is a wind that gives rise to a constant
horizontal force opposing the cannonballs motion. T
Sample Midterm 2
1. (33 points) A bullet of mass m is red with a speed of vb at the center of a rod
of mass M = 3m and length L The trajectory of the bullet makes an angle of with
the horizontal. The rod hangs vertically from a pivot attached to the ceili
Midterm 1
There are three problems, worth 33 points each. You must justify your answer to
receive full credit.
1. Two planets of mass m and 2m have the same radius R. They start at rest with
their centers a distance ri apart (ri > 2R). The gravitational a
Review for Exam 1
Exam 1
Next Monday during class
Covers up to C9
3 problems, 33 points each
No calculator or notes
Formula sheet will be provided
Be on time!
Formula Sheet
Velocity:
dr
dt
= vAB + vCD
v=
vAC
Momentum and center of mass:
1
(m1 r1 + m
C14: Conservation of
Angular Momentum
Concept Test
A professor stands on a platform holding a rotating bicycle wheel. The bicycle
wheel is horizontal and is rotating clockwise as seen from the top. The platform
can freely rotate, but is initially at rest.
C13R.2
This is a conceptually tricky problem, and the books answer is incorrect. I will
instruct the grader to grade your problem on eort only.
To set the stage, let us rst consider the situation where the wheels of the jetliner
are locked, so there is no
C13: Angular Momentum
Problem: A comet of mass m is heading for a planet with much larger mass M.
At the instant shown, the comet has position
and velocity
in a coordinate system with the planet at the origin.
Find
and
at this instant.
Problem: A comet of