introduction to mechanics. an overview of mechanics mechanics is the study of motion kinematics is a...
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Introduction to Mechanics
An Overview of Mechanics
Mechanics is the study of motionKinematics is a subtopic of mechanics dealing
with the description of motion without regard to outside influences
Dynamics is another subtopic of mechanics that deals with the forces behind the motion
Sometimes, we say that kinematics is the “how” and dynamics is the “why”.
What’s the difference between distance and displacement?
Distance: the total magnitude traveled For example, if you have to take the long way around
a traffic jam, your distance increases
Displacement: the shortest distance from the starting point to the ending point
Draw & label this picture on your notes
Circular Motion and Displacement
If a runner runs one lap in a certain amount of time, we can calculate his speed as distance/time
But, his velocity is zero…why?His displacement is zero because he
ended where he started.
What is average speed? Average Speed–The rate of change in distance
with respect to time.Even objects that are not moving have a speed = 0
m/sUnits: m/s, cm/s, mphSince speed is built from distance, a scalar
quantity, then speed is also a scalar quantity. Scalar Quantities carry no direction information
with them.
What is Average Velocity?The rate of change in displacement with respect
to time. Since displacement is a vector quantity, then
velocity is also a vector quantity. Vector Quantities have both magnitude and
direction.v=d/t
v= velocity (m/s)d= distance (m)t= time (s)
Fill in the triangle on your paper!
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Units For Speed and Velocity
In science, we use the metric system and distance and displacement are measured in meters
Time is measured in seconds no matter what measurement system you are using
Therefore, speed and velocity are both measured in meters/second (m/s)
Speed & Velocity Examples
Speed is distance divided by time2 cm/s
Velocity includes the direction2 cm/s west
West
More Velocity Examples
If the runner goes around a circular track 1 1/2 times, what is his displacement?
Did you guess that it is the diameter of the track?
What is the distance covered?Did you guess that it is 1 1/2 times the
circumference of the circle?
Try these Speed/Velocity Problems #1 and #2
A car travels 1000 m in 50 s. What is the car’s speed?
Speed = distance/time = 1000 m/50 s = 20 m/s
A car travels 1000 m north in 50 s. What is the car’s velocity?
Velocity = displacement/time = 1000 m/50 s = 20 m/s, north
Sample Problem #3
A car travels 500 m east, 1000 m west and then 2000 m east again. It does this in a time of 100 seconds. What is the car’s average speed?
Speed= distance/time = 3500 m/100 s = 35 m/s
What is the car’s average velocity?Velocity = displacement/time = 1500 m
east/100 seconds = 15 m/s, east
What is the difference between average velocity and instantaneous velocity?
Average Velocity: The longer the time period measured, the more it leads to calculating an average velocity.
Instantaneous Velocity: The shorter the time period measured the closer it brings you to calculating an "instantaneous velocity". Only if the time period becomes zero would we truly have an instantaneous velocity.
Using Graphs to Calculate Speed
We use graphical models to predict speedGraphical- mathematical model
Independent on x axis; what you change/test (MIX)Dependent on y axis; what you measure(DRY)
Position- where an object is, including direction, compared to where it was
Distance- length w/o regard to directionCan get speed from slope of position versus time
graphSlope = Rise/run