chapter 11 motion. chapter 11 sections 11.1 distance & displacement 11.2 speed & velocity...
TRANSCRIPT
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Chapter 11
Motion
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Chapter 11 Sections
• 11.1 Distance & Displacement• 11.2 Speed & Velocity• 11.3 Acceleration
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11.1 Distance & DisplacementKey Concepts
• What is needed to describe motion completely?
• How are distance and displacement different?
• How do you add displacements?
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11.1 Describing Motion
• To describe motion, you must state the direction the object is moving as well as how fast the object is moving.
• You must also tell its location at a certain time.• To describe motion accurately and
completely, a frame of reference is necessary.
• The necessary ingredient of a description of motion—a frame of reference—is a system of objects that are not moving with respect to one another.
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11.1 Describing Motion
• Relative motion is movement in relation to a frame of reference.
• As a train moves past a platform, people standing on the platform will see those on the train speeding by.
• When the people on the train look at one another, they don't seem to be moving at all.
• Choosing a meaningful frame of reference allows you to describe motion in a clear and relevant manner.
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11.1 Measuring Distances
• Distance is the length of a path between two points.
• When an object moves in a straight line, the distance is the length of the line connecting the object's starting point and its ending point.
• The SI unit for measuring distance is the meter (m).
• For very large distances, it is more common to make measurements in kilometers (km). One kilometer equals 1000 meters.
• Distances that are smaller than a meter are measured in centimeters (cm). One centimeter is one hundredth of a meter.
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11.1 Measuring Displacements
• To describe an object's position relative to a given point, you need to know how far away and in what direction the object is from that point.
• Distance is the length of the path between two points. Displacement is the direction from the starting point and the length of a straight line from the starting point to the ending point.
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11.1 Measuring Displacements
• If you measure the path along which a roller coaster car has traveled, you are describing distance.
• The direction from the starting point to the car and the length of the straight line from the starting point to the car describe displacement.
• After completing one trip around the track, the roller coaster car's displacement is zero.
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11.1 Vectors
• Displacement is an example of a vector. • A vector is a quantity that has magnitude and
direction. The magnitude can be size, length, or amount.
• Arrows on a graph or map are used to represent vectors. The length of the arrow shows the magnitude of the vector.
• Vector addition is the combining of vector magnitudes and directions.
• Add displacements using vector addition.
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11.1 Vectors• When two displacements,
represented by two vectors, have the same direction, you can add their magnitudes.
• In Figure 3A, the total magnitude of the displacement is 6 kilometers.
• If two displacements are in opposite directions, the magnitudes subtract from each other, as shown in Figure 3B.
• Because the car's displacements (4 kilometers and 2 kilometers) are in opposite directions, the magnitude of the total displacement is 2 kilometers.
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11.1 Vectors• When two or more
displacement vectors have different directions, they may be combined by graphing.
• Figure 4 shows vectors representing the movement of a boy walking from his home to school.
• The lengths of the vectors representing this path are 1 block, 1 block, 2 blocks, and 3 blocks.
• You can determine this distance by adding the magnitudes of each vector along his path.
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11.1 Vectors
• The vector in red is called the resultant vector, which is the vector sum of two or more vectors.
• In this case, it shows the displacement.
• The resultant vector points directly from the starting point to the ending point.
• Vector addition, then, shows that the boy's displacement is 5 blocks approximately northeast, while the distance he walked is 7 blocks.
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11.2 Speed & Velocity Key Concepts
• How are instantaneous speed and average speed different?
• How can you find the speed from a distance time graph?
• How are speed and velocity different?
• How do velocities add?
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11.2 Speed• Speed is the ratio of the
distance an object moves to the amount of time the object moves.
• The SI unit of speed is meters per second (m/s).
• You need to choose units that make the most sense for the motion you are describing.
• The in-line skater in Figure 5 may travel 2 meters in one second. The speed would be expressed as 2 m/s. A car might travel 80 kilometers in one hour. Its speed would be expressed as 80 km/h.
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11.2 Average Speed• Two ways to express the speed of an object are average speed and
instantaneous speed. • Average speed is computed for the entire duration of a trip,
and instantaneous speed is measured at a particular instant. • Sometimes it is useful to know how fast something moves for an
entire trip. • Average speed, , is the total distance traveled, d, divided by the
time, t, it takes to travel that distance.
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11.2 Instantaneous Speed
• Sometimes however, such as when driving on the highway, you need to know how fast you are going at a particular moment.
• The car's speedometer gives your instantaneous speed. Instantaneous speed, v, is the rate at which an object is moving at a given moment in time.
• For example, you could describe the instantaneous speed of the car in Figure 6 as 55 km/h.
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11.2 Graphing Motion• A distance-time graph is a good way to describe motion. • Recall that slope is the change in the vertical axis value divided by
the change in the horizontal axis value.• The slope of a line on a distance-time graph is speed. • In Figure 7A, the car travels 25.0 meters per second. In Figure 7B the
slope of the line is 250.0 meters divided by 20.0 seconds, or 12.5 meters per second.
• A steeper slope on a distance-time graph indicates a higher speed.
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11.2 Graphing Motion• Figure 7C shows the motion of a car that is not traveling at a constant
speed. • The times when the car is gradually increasing or decreasing its speed
are shown by the curved parts of the line. • The slope of the straight portions of the line represent periods of
constant speed. • Note that the car's speed is 25 meters per second during the first part
of its trip and 38 meters per second during the last part of its trip.
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11.2 Velocity• Sometimes knowing only the
speed of an object isn't enough. You also need to know the direction of the object's motion.
• Together, the speed and direction in which an object is moving are called velocity.
• Velocity is a description of both speed and direction of motion. Velocity is a vector.
• A longer vector would represent a faster speed, and a shorter one would show a slower speed.
• The vectors would also point in different directions to represent the cheetah's direction at any moment.
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11.2 Velocity• A change in velocity can be
the result of a change in speed, a change in direction, or both.
• The sailboat can be described as moving with uniform motion, which is another way of saying it has constant velocity.
• However, the sailboat's velocity also changes if it changes its direction.
• It may continue to move at a constant speed, but the change of direction is a change in velocity.
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11.2 Combining Velocities
• Sometimes the motion of an object involves more than one velocity.
• Two or more velocities add by vector addition.
• The velocity of the river relative to the riverbank (X) and the velocity of the boat relative to the river (Y) combine.
• They yield the velocity of the boat relative to the riverbank (Z).
• This velocity is 17 kilometers per hour downstream.
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11.2 Combining Velocities
• The relative velocities of the current (X) and the boat (Y) are at right angles to each other.
• Adding these velocity vectors yields a resultant velocity of the boat relative to the riverbank of 13 km/h (Z).
• Note that this velocity is at an angle to the riverbank and forms a right triangle.
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11.3 AccelerationKey Concepts
• How are changes in velocity described?
• How can you calculate acceleration?
• How does a speed time graph indicate acceleration?
• What is instantaneous acceleration?
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11.3 Acceleration
• The rate at which velocity changes is called acceleration.
• Recall that velocity is a combination of speed and direction.
• Acceleration can be described as changes in speed, changes in direction, or changes in both. Acceleration is a vector.
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11.3 Acceleration
• We often use the word acceleration to describe situations in which the speed of an object is increasing.
• Scientifically, however, acceleration applies to any change in an object's velocity.
• This change may be either an increase or a decrease in speed.
• Acceleration can be caused by positive (increasing) change in speed or by negative (decreasing) change in speed.
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11.3 Acceleration Due To
Gravity• An example of acceleration due to change
in speed is free fall, the movement of an object toward Earth solely because of gravity.
• The unit for acceleration is meters per second per second. This unit is typically written as meters per second squared (m/s2).
• Objects falling near Earth's surface accelerate downward at a rate of 9.8 m/s2.
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11.3 Acceleration From Changing Direction
• You can accelerate even if your speed is constant.
• You have experienced this type of acceleration if you have ridden on a carousel like the one in Figure 13.
• A horse on the carousel is traveling at a constant speed, but it is accelerating because its direction is constantly changing.
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11.3 Changing Speed & Direction
• Sometimes motion changes in both speed and direction at the same time.
• You experience this type of motion if you ride on a roller coaster.
• You are thrown backward, forward, and sideways as your velocity increases, decreases, and changes direction.
• Your acceleration is constantly changing because of changes in the speed and direction of the cars of the roller coaster.
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11.3 Constant Acceleration
• Constant acceleration is a steady change in velocity.
• The velocity of the object changes by the same amount each second.
• An example of constant acceleration is illustrated by the jet airplane shown in Figure 15. The airplane's acceleration may be constant during a portion of its takeoff.
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11.3 Calculating Acceleration
• Acceleration is the rate at which velocity changes. • You calculate acceleration for straight-line motion by
dividing the change in velocity by the total time. • If a is the acceleration, vi is the initial velocity, vf is the final
velocity, and t is total time, this equation can be written as follows.
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11.3 Graphing Acceleration
• You can use a graph to calculate acceleration.
• Figure 16 is a graph of the skier's speed.
• The slope of a speed-time graph is acceleration.
• This slope is change in speed divided by change in time.
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11.3 Speed-Time Graphs
• Constant acceleration is represented on a speed–time graph by a straight line.
• The graph in Figure 16 is an example of a linear graph, in which the displayed data form straight-line parts.
• The slope of the line is the acceleration.
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11.3 Speed-Time Graphs
• Constant negative acceleration decreases speed.
• A speed-time graph of the motion of a bicycle slowing to a stop is shown in Figure 17.
• The line segment sloping downward represents the bicycle slowing down. The change in speed is negative, so the slope of the line is negative.
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11.3 Distance-Time Graphs
• Accelerated motion is represented by a curved line on a distance-time graph.
• In a nonlinear graph, a curve connects the data points that are plotted.
• Figure 18 is a distance-time graph.
• Notice that the slope is much greater during the fourth second than it is during the first second.
• Because the slope represents the speed of the ball, an increasing slope means that the ball is accelerating.
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11.3 Instantaneous Acceleration
• Acceleration is rarely constant, and motion is rarely in a straight line.
• A skateboarder moving along a half-pipe changes speed and direction.
• At each moment she is accelerating, but her instantaneous acceleration is always changing.
• Instantaneous acceleration is how fast a velocity is changing at a specific instant.
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11.3 Acceleration As A Vector
• Acceleration involves a change in velocity or direction or both, so the vector of the skateboarder's acceleration can point in any direction.
• The vector's length depends on how fast she is changing her velocity.
• At every moment she has an instantaneous acceleration, even if she is standing still and the acceleration vector is zero.