Note 10 Two Acceleration Motion
Now we look at cases where an object is governed by two constant values of acceleration.
Example 1
A rocket is launched with an acceleration of 25 m/s2 upward.
engine of the rocket shuts off and the rocket goes into free fa
Note 23 Springs
Another type of force is produced by devices that act like a spring. A spring is a device what
produces a force that is dependent on the amount of compression or stretch of the spring. This
means that the spring force is not constant.
The
Note 24 Uniform Circular Motion
When an object moves in a circular arc, there is still an acceleration on the object due to the fact
that the direction of travel is changing. This is called circular motion. If the speed were constant,
it is called uniform
Note 27 Using Work-Energy Theorem
Example
A 1.0 kg block resting on a frictionless surface is pushed by a force of 5 N over a distance of 2
meters. How fast is the block traveling at the end of the push?
5N
final
velocity
5N
1 kg
2m
Here is the free-body
Note 30 Conservation of Mechanical Energy
Versions of the Work-Energy Theorem
We can write a version of the work-energy theorem using potential energy.
original version,
Starting with the
Wtotal = K
We can replace the total work with the work done by cons
Note 30 Potential Energy
There are two categories of force that do work. One category of forces does the same amount of
work no matter how it get from point A to point B. These are called conservative forces and the
work they do is path independent. The o
Note 32 Power
Power
Power the the rate at which energy is transferred. There can be different versions of power
depending on what you are interested in. Here is a version where the total energy input is of
interest.
The total average power is the energy s
Note 22 Connected Objects
Connected objects is a special class of multiple object situations where the objects move together
usually by way of direction contact or tension between the objects.
Example: Stationary Connected Objects
What is the normal force
Note 33 Impulse and Momentum
Impulse
There is another way that a force acting on an object can alter the motion of an object like work
does. It is when a force acts on the object over some amount of time, t. This is called the
impulse. It is a vector.
!
!
Note 34 Using Impulse and Momentum
Example
I drop a ball and it falls for 0.50 second, how fast is it traveling?
This is a straight-forward motion problem with time. Applying the impulse-momentum theorem to
the ball,
!
!
Iext = p
There is only one force o
Note 31 Using Potential Energy
Example
A block of mass 1 kilogram is dropped from rest through 0.50 meter onto a resting spring of spring
constant 400 N/m. How far does the spring compress before the block stops?
1 kg
0.5 m
1 kg
x
400 N/m
I will approach
Note 28 Work and Springs
Position Dependent Forces
With energy, we can now deal with forces that change. Specically, we can deal with forces that
change with position. Lets say there is a force acting on an object that is described by the
following graph.
Note 26 Work and Energy
Energy is a concept that is an abstraction of the concepts of force and motion.
Energy is the capacity to change the motion of another object.
It tells you the same things as force and motion but in a different way. Instead of a fo
Note 27 Work and Energy and Time
Notice that there is no time that appears explicitly in the work-energy theorem. The order with
which energy is put into or taken out of an object is not important.
Example
In a previous example, what if only the second ha
Note 11 Two Object Motion
There are times when more than one object interact with each other.
Example 1
Two cars are 192 meters apart at one moment in time. Car A is at rest but car B is already
traveling at 8 m/s toward car A. At this moment in time, the
Note 9 One Acceleration Motion
Here are some examples of motion in one-dimension for one object that has only one
acceleration. Again, we will deal only with accelerations that are constant.
Example: Straight-Forward Solution
A car accelerates from rest t
Note 13 Two Dimensional Motion
Motion in multiple dimensions is dealt with as a simple extension of motion in one dimension. The
principle that allows us to do this is the vector nature of motion. Motion in one direction does not
affect the motion in the
Note 16 Newtons Third Law
Newtons second law is about the forces and the acceleration of an object. Newtons third law
connects the forces between objects.
Experimenting with Newtons Third Law
Lets say I have two frictionless carts of the same mass on a tr
Note 14 Projectile Motion
Here are some example of projectile motion.
Example 1
I thrown a rock with a speed of 20 m/s at 50 above the horizon.
a. How much time does it take to arrives back at the same height?
b. How far does it travel horizontally when i
Note 17 Weight
Masses produce an attractive force between themselves. This is gravity. The amount of
gravitational force produced by the Earth that is applied to objects is called the weight of the
object. The weight requires gravity. Mass does not. Mass
Note 21 Tension
Tension is the force that is transmitted along a taut medium like a string or a rope. A force applied
at one end is transmitted to the other end. The tension force also allows the direction of an
applied force to be changed by the use of p
Note 15 Force
Force is a thing that is best dened by what it does rather than what it is. What it does is
governed by Newtons laws of motion. Specically, Newtons second law of motion is the
foundational principle of this course. It tells us how force and
Note 19 Ramps
The ramp is a simple machine that allows you to move an object upward without having to apply
the same force as the weight of the object.
Box on a Ramp
We placed a block on a ramp of angle with no friction on its surface (keeping it simple).
Note 18 Normal Force
The normal force is the force that is applied by a surface that is also perpendicular to that surface.
Example 1: Just a Box
A box of mass m is at rest on a table. What is the normal force on the box due to the table?
Here are the dia
Note 20 Friction
Friction is a force that opposes motion parallel to a surface. There are two types of friction, static
and kinetic. Static friction occurs between two surfaces that are not moving relative to each other
while kinetic friction occurs when
Note 36 Center of Mass
There is an application of the impulse-momentum theorem that is specically for the description of
a system of objects or masses.
!
!
Iext,system = psystem
Example
Two people are in space next to each other with no force acting on th
Note 37 Multiple Processes
Most of the processes that you observed in the real world require more than one step to analyze.
Now that you have the tools, ew will look at several examples of these processes.
Ballistic Pendulum
The ballistic pendulum is a ma
Homework 1 Soluiton
Practice Problems Chapter 3
6, 10, 11, 14, 20, 23, 24, 28, 29, 30, 31
38, 39, 40, 41, 42
49, 51, 52, 53, 57
79, 80, 81, 82
Graded Problem
We nd a treasure map in a hut. It tells you that to nd the treasure, you need to travel 3 km east
Homework 6 Solution
Graded Problem
A 10 kg block is on a 30 frictionless ramp. In the following situations, what are the net force and
the normal force on the block? Remember the direction.
a.
10 kg
30
b.
10 kg
40 N
30
c.
10 kg
40 N
30
d.
40 N
10 kg
30
e.
Homework 5 Solution
Practice Problems Chapter 5
2, 3, 4, 5, 6, 11, 13, 18, 19, 20, 21, 25, 27, 28, 29, 30, 32, 33, 34, 36, 38, 41, 42, 43, 44, 46, 49, 50
Graded Problem
Two people are pulling on a 300 kg rock. Person A is pulling from the east with a forc