motion - mrs. escobar - academir charter school...
TRANSCRIPT
MOTION
Chapter Four: Motion
Ø 4.1 Position, Speed and Velocity
Ø 4.2 Graphs of Motion
Ø 4.3 Acceleration
4.1 Position, Speed and Velocity Ø Position is a variable given relative to an
origin. Ø The origin is the place where position equals 0.
Ø The position of this car at 50 cm describes where the car is relative to the track.
4.1 Position, Speed and Velocity Ø Position and distance are similar but not
the same. Ø If the car moves a distance of 20 cm to the
right, its new position will be 70 cm from its origin.
Distance = 20 cm
New position
4.1 Position, Speed and Velocity Ø The variable speed describes how quickly
something moves. Ø To calculate the speed of a moving object
divide the distance it moves by the time it takes to move.
4.1 Position, Speed and Velocity Ø The units for speed are distance units over
time units.
Ø This table shows different units commonly used for speed.
4.1 Average speed Ø When you divide the
total distance of a trip by the time taken you get the average speed.
Ø On this driving trip around Chicago, the car traveled and average of 100 km/h.
4.1 Instantaneous speed Ø A speedometer shows
a car’s instantaneous speed.
Ø The instantaneous speed is the actual speed an object has at any moment.
How far do you go if you drive for two hours at a speed of 100 km/h?
1. Looking for: Ø …distance
2. Given: Ø …speed = 100 km/h time = 2 h
3. Relationships: Ø d = vt
4. Solution: Ø d = 100 km/h x 2 h = 200 km
= 200 km
Solving Problems
4.1 Vectors and velocity Ø Position uses positive and negative
numbers. Ø Positive numbers are for positions to the
right of the origin and negative numbers are for positions to the left the origin.
4.1 Vectors and velocity
Ø Distance is either zero or a positive value.
4.1 Vectors and velocity Ø We use the term velocity to mean
speed with direction.
4.1 Keeping track of where you are Ø Pathfinder is a small robot sent to
explore Mars.
Ø It landed on Mars in 1997.
Ø Where is Pathfinder now?
4.1 Keeping track of where you are Ø Pathfinder keeps track of its
velocity vector and uses a clock.
Ø Suppose Pathfinder moves forward at 0.2 m/s for 10 seconds.
What is Pathfinder’s velocity?
4.1 Keeping track of where you are Ø Suppose Pathfinder goes backward
at 0.2 m/s for 4 seconds.
What is Pathfinder’s change in position?
4.1 Keeping track of where you are Ø The change in position is the velocity multiplied by the time.
4.1 Keeping track of where you are Ø Each change in position is added up using positive and negative numbers.
Ø Pathfinder has a computer to do this.
4.1 Maps and coordinates Ø If Pathfinder was crawling on a straight
board, it would have only two choices for direction.
Ø Out on the surface of Mars, Pathfinder has more choices.
Ø The possible directions include north, east, south, and west, and anything in between.
4.1 Maps and coordinates Ø A graph using north−south and
east−west axes can accurately show where Pathfinder is.
Ø This kind of graph is called a map.
Ø Street maps often use letters and numbers for coordinates.
4.1 Vectors on a map Ø Suppose you run east for 10 seconds at
a speed of 2 m/s.
Ø Then you turn and run south at the same speed for 10 more seconds.
Ø Where are you compared to where you started?
4.1 Vectors on a map Ø To get the answer, you figure out your east−west changes and your north−south changes separately. origin = (0 , 0)
4.1 Vectors on a map Ø Your first
movement has a velocity vector of +2 m/s, west-east (x-axis).
Ø After 10 seconds your change in position is +20 meters (east on x-axis).
d = v x t d = 2 m/s x 10 s = +20 m
4.1 Vectors on a map Ø Your second
movement has a velocity vector of −2 m/s north−south (y-axis)
Ø In 10 seconds you move −20 meters (south is negative on y-axis)
d = 2 m/s x 10 s = -20 m New position = (+20 , -20)
A train travels at 100 km/h heading east to reach a town in 4 hours. The train then reverses and heads west at 50 km/h for 4 hours. What is the train’s position now?
1. Looking for: Ø …train’s new position
2. Given: Ø …velocity = +100 km/h, east ; time = 4 h Ø …velocity = -50 km/h, west ; time = 4 h
3. Relationships: Ø change in position = velocity × time
Solving Problems
4. Solution: Ø 1st change in position: Ø (+100 km/h) × (4 h) = +400 km
Ø 2nd change in position: Ø (−50 km/h) × (4 h) = −200 km
Ø Final position: Ø (+400 km) + (−200 km) = +200 km
Ø The train is 200 km east of where it started.
Solving Problems
4.2 Graphs of Motion Ø Constant speed means the speed stays
the same. Ø An object moving at a constant speed
always creates a position vs. time graph that is a straight line.
4.2 Graphs of Motion Ø The data shows the
runner took 10 seconds to run each 50-meter segment.
Ø Because the time was the same for each segment, you know the speed was the same for each segment.
4.2 Graphs of Motion Ø You can use
position vs. time graphs to compare the motion of different objects.
Ø The steeper line on a position vs. time graph means a faster speed.
4.2 Slope Ø The steepness of a line is measured
by finding its slope. Ø The slope of a line is the ratio of the “rise” to the “run”.
4.2 Graphs of changing motion Ø Objects rarely move
at the same speed for a long period of time.
Ø A speed vs. time graph is also useful for showing the motion of an object that is speeding up or slowing down.
4.2 Graphs of changing motion Ø Suppose we draw a rectangle on the
speed vs. time graph between the x-axis and the line showing the speed.
Ø The area of the rectangle is equal to its length times its height.
Ø On the graph, the length is equal to the time and the height is equal to the speed.
4.3 Acceleration Ø Acceleration is the rate at which your
speed (or velocity) changes. Ø If your speed increases by 1 meter per
second (m/s) for each second, then your acceleration is 1 m/s per second.
4.3 Acceleration Ø Acceleration is easy to spot on a speed vs. time graph.
Ø Acceleration causes the line to slope up on a speed vs. time graph. What is the bike’s acceleration?
4.3 Acceleration Ø If the hill is steeper, the acceleration
is greater.
4.3 Acceleration Ø There is zero acceleration at constant
speed because the speed does not change.
4.3 Acceleration Ø Speed and acceleration are
not the same thing. Ø You can be moving (non-
zero speed) and have no acceleration (think cruise control).
Ø You can also be accelerating and not moving!
Ø A falling object begins accelerating the instant it is released.
4.3 Acceleration Ø Acceleration describes how quickly speed changes.
Ø Acceleration is the change in speed divided by the change in time.
4.3 Speed and acceleration Ø An acceleration of 20
km/h/s means that the speed increases by 20 km/h each second.
Ø The units for time in acceleration are often expressed as “seconds squared” and written as s2.
Can you convert this rate using conversion factors?
Solving Problems
Ø A sailboat moves at 1 m/s.
Ø A strong wind increases its speed to 4 m/s in 3 s.
Ø Calculate acceleration.
1. Looking for:
Ø …acceleration of sailboat
2. Given:
Ø …v1 = 1 m/s; v2 = 4 m/s; time = 3 s
3. Relationships:
Ø a = v2 – v1/t
4. Solution:
Ø a = (4 m/s – 1 m/s)/ 3 s = 1 m/s2
Solving Problems
4.3 Acceleration on motion graphs Ø The word “acceleration” is used for any change in speed, up or down.
Ø Acceleration can be positive or negative.
4.3 Acceleration on speed-time graphs
Ø Positive acceleration adds more speed each second.
Ø Things get faster.
Ø Speed increases over time.
4.3 Acceleration on speed-time graphs
Ø Negative acceleration subtracts some speed each second.
Ø Things get slower.
Ø People sometimes use the word deceleration to describe slowing down.
4.3 Acceleration on position-time graphs
Ø The position vs. time graph is a curve when there is acceleration.
Ø The car covers more distance each second, so the position vs. time graph gets steeper each second.
4.3 Acceleration on position-time graphs
Ø When a car is slowing down, the speed decreases so the car covers less distance each second.
Ø The position vs. time graph gets shallower with time.
4.3 Free fall Ø An object is in
free fall if it is accelerating due to the force of gravity and no other forces are acting on it.
4.3 Free fall Ø Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2
Ø The letter “g” is used for acceleration due to gravity.
4.3 Acceleration and direction Ø Acceleration occurs whenever there
is a change in speed, direction, or both.
4.3 Acceleration and direction Ø A car driving around a curve at a
constant speed is accelerating because its direction is changing.
4.3 Acceleration and direction Ø Individual vectors can be drawn to
scale to calculate the change in direction.
4.3 Curved motion Ø A soccer ball is an
example of a projectile.
Ø A projectile is an object moving under the influence of only gravity.
Ø The path of the ball makes a bowl-shaped curve called a parabola.
4.3 Curved motion
Ø Circular motion is another type of curved motion.
Ø An object in circular motion has a velocity vector that constantly changes direction.