Chapter 11 Motion Measuring Motion Motion an objects

Chapter 11 Motion

Measuring Motion • Motion: an object’s change in position to a reference point – Frame of reference: a system for specifying the precise location of objects in space and time • When an object changes position with respect to a frame of reference, the object is in motion – You can describe the direction of an object’s motion with a reference direction, such as north, south, east, west, up, or down – Displacement is the change of an object’s position • Measures how far it is between the starting and ending point • Must always indicate direction – Distance measures how far an object moves along a path

Measuring Motion • Speed: – Describes how fast an object moves – The distance traveled divided by the time interval during which the motion occurred • meters/second (m/s), miles/hour (miles/hr)

Measuring Motion

Measuring Motion • Velocity is described relative to a reference point • Velocity: the speed of an object in a particular direction – Speed and direction of motion • m/s North, miles/hr South

Measuring Motion • Combined velocities determine the resultant velocity

Measuring Motion

Measuring Motion • Instantaneous speed: speed measured in an infinitely small time interval – Car’s speedometer

Measuring Motion • The slope of a distance vs. time graph equals speed

Acceleration • Acceleration: the rate at which velocity changes over time – An object accelerates if its speed, direction, or both change

Acceleration

Linear Acceleration

Acceleration • Acceleration can also be a change in direction

Centripetal Acceleration • Constant speed in a circle – Speed same but direction always changing

Calculating Acceleration

Acceleration • Acceleration is negative when slowing down

Velocity-Time Graphs • • Given below is a strobe picture of a ball rolling across a table. Strobe pictures reveal the position of the object at regular intervals of time, in this case, once each 0. 1 seconds. Notice that the ball covers an equal distance between flashes. Let's assume this distance equals 20 cm and display the ball's behavior on a graph plotting its xposition versus time.

Velocity-Time Graphs • The slope of the position versus time graph shown above would equal 20 cm divided by 0. 1 sec or 200 cm/sec.

Velocity-Time Graphs • The following graph displays this exact same information in a new format, a velocity versus time graph.

Velocity-Time Graphs • This graph very clearly communicates that the ball's velocity never changes since the slope of the line equals zero. Note that during the interval of time being graphed, the ball maintained a constant velocity of 200 cm/sec. We can also infer that it is moving in a positive direction since the graph is in quadrant I where velocities are positive. •

Velocity-Time Graphs • To determine how far the ball travels on this type of graph we must calculate the area bounded by the "curve" and the x- or time axis.

Velocity-Time Graphs • As you can see, the area between 0. 1 and 0. 3 seconds confirms that the ball experienced a displacement of 40 cm while moving in a positive direction. •

Velocity-Time Graphs • Velocity is determined by the height of the graph (the yaxis coordinate • Acceleration is determined by the slope of the graph • Displacement is found by calculating the area bounded by the velocity-graph and the x-axis • Distance traveled would be the absolute value of each sectional area since it is a scalar quantity that does not depend on the direction of travel • Average speed during a time interval is defined as the total distance it traveled by the total time taken • Average velocity during a time interval is defined as the net displacement divided by the total time taken

Graphing Accelerated Motion • Moving in a negative direction and losing speed: no match • Moving in a positive direction and gaining speed at a slow rate: D • Traveling at a steady rate in a positive direction: C • At rest for an extended time: no match • Moving in a positive direction but losing speed: A • Moving in a positive direction and gaining speed at a rapid rate: B

Graphing Accelerated Motion • During which time interval(s) did it travel in a positive direction? • 0 -10 min / 10 -15 min / 1530 min • During which time interval(s) did it travel in a negative direction? • 30 -40 min / 40 -55 min

Graphing Accelerated Motion • How far did the cart travel in the first 10 minutes? – Area of triangle a = ½ (b x h) – ½ (d=s x t) – ½ (60 m/ min x 10 min) = 300 m • What was its average acceleration? • a = V 2 – V 1 / t 2 – t 1 = • a = 60 m/min – 0 m/min/10 min = 6 m/min 2

Graphing Accelerated Motion • What was its average acceleration between 10 and 15 minutes? • a = V 2 – V 1 / t 2 – t 1 = • 60 m/min/15 min 10 min= • 0 m/min/5 min = • 0 m/min 2

Graphing Accelerated Motion • • How far did it travel between 15 and 30 minutes? Area of triangle A=1/2 (b x h) ½ x (15 min x 60 m/min) = 450 m What was its average acceleration during this time interval? a = V 2 – V 1 / t 2 – t 1 = a = 0 m/min - - 60 m/min/ 30 min 15 min = -4 m/min 2

Graphing Accelerated Motion • How far did it travel between 30 and 40 minutes? • A = ½ (b x h) + • ½ (10 min x -40 m/ min) = • ½ (-400) = -200 m (200 m) • What was its average acceleration during this time interval? • • • a = V 2 – V 1 / t 2 – t 1 = a = -40 m/min – 0 m/min/40 min 30 min = a= -40 n/min / 10 min = -4 m/min 2

Graphing Accelerated Motion • • • How far did it travel between 40 and 55 minutes? A = ½ (b x h) ½ (15 min x -40 m/min) = ½(-600 m)= -300 m (300 m) What was its average acceleration during this time interval? a = V 2 – V 1 / t 2 – t 1 = a= 0 m/min - -40 m/min / 55 min 40 min = -40 m/min / 15 min = 2. 66 m/min 2 = 2. 7 m/min 2

Graphing Accelerated Motion • What was the total distance it traveled? • 0 -10 (300 m) • 10 -15 (300 m) (lxh) • 15 -30 (450 m) • 30 -40 (200 m) • 40 -55 (300 m) – 1550 m • What was its final displacement? • 550 m

Graphing Accelerated Motion • What was the cart’s average speed for the entire 55 minutes? • s = d/t • s = 1550 m / 55 min • s = 28. 18 m/mim = 28. 2 m/min • Its average velocity? • Net displacement / total time = • 1050 m – 500 m / 55 min = • 550 m/55 min = 10 m/min

Motion and Force • Fundamental Forces: – Are the forces of gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force • Vary in strength • Can act through a contact – Pushes and pulls of contact forces • Balanced and Unbalanced Forces – Whenever there is a net force acting, the object accelerates in the direction of the net force • Balance forces do not change motion • Unbalanced forces do not cancel completely

Motion and Force • The force of friction always opposes the motion: friction is a force that opposes motion between two surfaces that are in contact – Static: friction between surfaces that are stationary • Force that resists the initiation of sliding motion between two surfaces that are in contact and at rest – Kinetic: friction between moving surfaces • Friction that opposes the movement of two surfaces that are in contact and are moving over each other – Sliding – Rolling