Exam 4 Solution!
Two carts are moving toward each other frictionlessly at constant speeds as shown. One cart has
a spring on it. The two carts collide elastically through the spring. During the collision, both carts
Chapter 9C Inelastic Collisions in 2-D!
Inelastic collisions are simpler for the reason that kinetic energy is not conserved. This means we
have only two equations but still four unknowns.!
m1(v1,f ,x v1,i,x ) + m2(v 2,f ,x v 2,i,x ) = 0 !
m1(v1,f ,y v1
Chapter 5C Working with Forces!
Here, I will introduce several forces and ways to deal with them in the context of using Newtons
second law of motion.!
A surface, like any object, applies one force on an object. However, a surface actual
Chapter 8B Power!
Power is the rate at which work is done by a source. This is its most general denition.!
You can also talk about the average power which is just the difference version of the equation.!
You can talk about a single
Chapter 8A Energy Conservation!
Conservation of Mechanical Energy!
Both the kinetic and potential energies are referred to as mechanical energies. They are energy
based on the mechanical variables of the object, velocity and position. Another way to loo
Chapter 6C Resistive Forces!
Fluid resistance (at low viscosity and low speed) is modeled as a force that is proportional to
the velocity in the opposite direction. This resistance exists in both directions, not just the
horizontal direction. The consta
Chapter 4A Motion in 2-D!
In vectors, additions to one of the components does not alter the value of the other components.
Force can be represented by vectors so that a force in the x direction can not produce a force in
the y direction. Finally, thro
Chapter 5B Force and Weight!
The denition of force is best expressed not as what it is but as how it affects motion. The way it
affects motion is described in Newtons second law of motion. Remember, this is applied to one
object. The net force on that o
Chapter 4D Relative Motion! !
When a measurement is made, it is important that you state who is making the measurement and
what the observer is doing. Most of the time, we assume what is called the lab observer which is
just a stationary observer relati
Chapter 4B Equations of Motion in 2-D!
Equations of Motion!
New that we know we can deal with the two directions independently, lets look at a 2-d problem
as two problems.!
In the x direction, we have a set of equations of motion.
pertain to the x direc
Chapter 6B Fictitious Forces! !
When you are standing on the ground and toss a ball straight up, you observe it going straight up.
If you are in a train that is traveling at a constant velocity and toss a ball straight up, you also
observe it going stra
Chapter 9A Linear Momentum!
In the previous chapter, we examined a variable called energy that is produced when work is done
on it. This work or transfer of energy is done when a net force acts on an object over some
Now, it is
Chapter 7A Work-Energy Theorem!
There are three parts to this. What is energy? What is work? And how are they related?!
Energy is the ability of an object to affect the motion of another object. This is a new way of
looking at an object. Instead
Chapter 10A Rotational Mechanics!
Rotational mechanics mirrors translational mechanics in most respects.
summarizes all of our physical concepts for these two types of motion.!
Newtons Second Law
F = ma
Moment of Inertia
Exam 3 Solutions!
A ball of mass m is attached to a pole through a string of length
L with negligible mass. The ball is made to travel in a horizontal
circle. The ball dips below the top of the pole by an angle . Use
the top of the pol
Exam 2 Solutions!
You want to re a cannonball with a velocity of 30 m/s at 60 above the
horizon. What is the magnitude of the constant force that is required to do
this. This force is applied over the 5.0 meter long cannon barrel. T
Exam 1 Solutions!
A car accelerates from rest along a 400 meters long track with a constant acceleration. You time
that the car takes 1.70 second to travel through the section from 100 m to 150 m. The car also
goes through a velocity chang
Chapter 11B Applying Angular Momentum!
A ball is shot at a hanging bar dangling that is dangling below a pivot. Upon contact, the ball
sticks to the bottom of the bar. Through what maximum angle does the bar swing up? Answer in
terms of the ini
Chapter 9D Elastic Collisions in 2-D!
Collisions in multiple dimensions is just applying the impulse-momentum theorem to each
direction plus the kinetic energy conservation of elastic collisions. In 2-D, we have this for
inelastic collision when the mom
Chapter 7B Potential Energy!
There are actually two kinds of forces that end up doing two kinds of work. Let me explain using
an example. I slide a block against a wall up 1 meter then back down 1 meter. !
Let me concentrate on two particular fo
Chapter 10C Work-Energy Theorem for Rotation!
The work-energy theorem for rotation is this. Notice that there is no potential energy for rotations.
Here are the parts of what make up this concept.!
Wnc = K !
Work is done on a rotational
Chapter 10B Newtons Second Law for Rotation!
Newtons second law for rotation is this. Here are the parts of what make up this concept.!
= I !
Torque is the analogue to force. Force changes the motion of objects and torque changes the
Chapter 10D Impulse-Momentum Theorem for Rotation!
The impulse-momentum theorem for rotation is this. Here are the parts of what make up this
concept. As long as you use the same axis of rotation for all objects within the system to calculate
Chapter 9E Center of Mass! !
The beginning of the impulse-momentum theorem was this statement.!
I = p !
We split this into internal and external impulses.!
Iext + I int = p !
The internal impulse are identically zero due to Newtons third law.!
Chapter 5A Newtons Second Law!
Lets Use the scientic method to relate force and motion!
Force makes things move.!
I drop a ball from some height.!
gravity, a force, makes the ball move down.!
Chapter 4C Circular Motion! !
Any curved path occurs in 2-d. A slice of a curve path can be treated as circular motion since any
small arc is circular in nature. Below, a section of the path matches the arc of the circle. This
means that the curvature o
Chapter 3 Vectors!
Scalar and Vector!
Scalars are numbers with unit.!
Vectors are scalar (magnitude) with directional information.!
A vector is represented by an arrow pointing from an origin to the vector va
Homework 5 Solution!
State the answer in term of the radial and tangential components, not x and y components.!
Homework 9 (Due 2/12/14)! !
Lets assume the bullet travels sideway. Duri
Homework 3 Solution!
For both runners, the position looks like this.!