Introduction to Mechanics

An Overview of Mechanics Mechanics is the study of motion Kinematics 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/s  Units: m/s, cm/s, mph  Since 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! D V T

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 time  2 cm/s Velocity includes the direction  2 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 speed  Graphical- 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 direction Can get speed from slope of position versus time graph  Slope = Rise/run