Physical Science Chapter 11 Motion
Motion Definition An object is in motion when its distance from another object is changing.
Relative Motion Relative motion is movement in relation to a REFERENCE POINT. This is called Frame of Reference. Motion depends on the Frame of Reference Therefore an object is in motion if it changes position relative to a reference point.
Frame of Reference Example Look at the figures. In fig.1, the car is to the right of the tree. In fig.2, after 2 seconds, the car is to the left of the tree. As the tree does not move, the car must have moved from one place to another. Therefore, here the tree is considered as the frame of reference
Scalar Quantities Shows magnitude only (magnitude can be size, length, or amount) Examples: Speed, time, temperature, distance
Vector Quantities Show magnitude and direction Velocity, acceleration, force, displacement May be graphically represented Arrows
Vectors Vectors are a method used to visually show forces A vector is a quantity which has both magnitude (size) and direction. The length of the arrow shows the magnitude of the vector. The angle of the arrow shows the vector's direction. Just like numbers, we can add two or more vectors together and get a net force called the resultant
Adding 2 or More Vectors Fig 1 Fig 2 Fig 3 Add vectors A and B to get the Resultant C A + B = C Fig 1 - shows the magnitude & direction of the 2 vectors we are adding Fig 2 we move the beginning of vector B to the end of Vector A, making sure to keep the magnitude & direction exactly the same Fig 3 Connect the beginning of Vector A to the end of Vector B, this is your Resultant C.
Distance and Displacement
Distance vs. Displacement Distance is the length of a 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.
Combining Displacements You can add vectors using vector addition When two displacements have the same direction, you can add their magnitudes. If two displacements are in opposite directions, the magnitudes subtract from each other.
Displacement along a Straight Line
Displacement that isn t along a straight path Suppose a person moves 3 meters from A to B and 4 meters from B to C as shown in the figure. The total distance traveled by him is 7 meters. But is he actually 7 meters from his initial position? No, he is only 5 meters away from his initial position i.e., he is displaced only by 5 m, which is the shortest distance between his initial position and final position. Use Pythagorean s Theorem! a 2 + b 2 = c 2
Distance vs. Displacement David walks 3 km north, then turns and walks 4 km east. Amy runs 2 miles south, then turns around and runs 3 miles north. Jermaine runs exactly 2 laps around a 400 meter track. Derrick crawls 4 feet then turns 90 degrees and crawls 6 feet. Ray runs 30 feet north, 30 feet west, and then 30 feet south. Jamison turns around 5 times. Cassidee walks 1 mile then turns 90 degrees and walks 2 miles. Taja walks two miles from her door to the park, then returns home to her door.
Example problems What is the total distance of a person who over the course of a week ran a 5Km, 10Km, and biked a 150Km? Julia drove 2.56x10 5 m S to school today, and then drove 1.42x10 3 m N to Samantha s house after school. What was her total displacement?
Begins here!! Speed!!
Speed Comparison of time and distance Distance traveled per unit time S = d / t T = d / s D = s x t (speed = distance/time) What is the speed of a car that traveled 75 km in 1.5 hr? S = D / T = 75km / 1.5 hr = 50 km/hr
Speed Measured in m/s If you travel 2m in 1 sec, what is your speed? If you travel 15m in 12 sec, what is your speed? Car traveling at 80km/hr. What is this speed in m/s? 80 km x 1 hr x 1000m = 22.2 m/s hr 3600 sec 1 km
If the Algebra Stumps you!! V = d / t T = d / v D = v x t Divide here! Multiply here!
Velocity is speed with a direction Speed AND direction A vector quantity [magnitude & direction] Written like: 125 miles/hour east or 83 m/sec towards the house What is the velocity of a jet that traveled 1623 mi North in 83 min? V = D / T =1623 mi / 83 min =19.5 mi/min North You can add velocities just like you did displacements, with vector diagrams
Some Conversion formulas you may need: Write these in your notes!!!!! 1 mile = 1.609 km 1 km =.62 miles 1 mile = 5,280 feet 1 mile = 1,760 yards
Average speed - computed for the entire duration of a trip Instantaneous speed - measured at a particular instant, like when you check your speedometer
Average Speed Avg speed = total distance / total time V = d / t If an object moves at 104 km/hr for 12 hours, what distance has it traveled? If an object moves 640 km in 11 hours, what is its speed? If a car moves at an average speed of 60 mi/hr for 24 hours, what distance has it traveled? What is this distance in kilometers? (1 mile = 1.609 km)
Average Speed vs. Average Velocity Avg speed = total distance / total time V = D / t Avg velocity = total displacement / total time V = D / t
The slope of a line on a distancetime graph is speed
Average Speed Average Velocity) What is the average speed after two minutes? What is the average speed between 2 and 4 minutes? What is the average speed for the entire trip? Answers on next slide!! Let s see how you did!!
Answers for Average Speed or Average Velocity Average speed = total distance / total time What is the average speed after 2 minutes? total distance is 75m, total time is 2 minutes. S = D/T S = 75m / 2min S= 37.5 m/min What is the average speed between 2 & 4 minutes? total distance: 110m 75m = 35m total time: 4min 2min = 2minutes total time S = D/T S = 35m / 2min S= 17.5 m/min
Speed Constant Speed Speed that does not change Instantaneous speed that does not change
Bell ringer Who is Usain Bolt? His world record time is 9.58 s for the 100 meters. Speed = distance / time so what is his speed?
Begins here!! Acceleration!!!
Acceleration a change in speed, direction, or both. It is a vector We usually talk about positive acceleration, like a car speeding up or a rocket taking off. It can also be negative, like a car braking.
Acceleration The change in speed or velocity over time In the scientific community, the symbol for change is the triangle: Change in velocity is found by subtracting the initial speed from the final speed V f - V i = V The formula for acceleration is: A = V f - V i = V time time Therefore the units for acceleration are going to be a distance/time/time Example v f is final velocity v i is initial velocity ft/min/sec
Notice if v i > v f you will have a negative acceleration!
Acceleration For an object to accelerate it must: Speed up (positive acceleration) Slow down (negative acceleration a.k.a deceleration ) Change direction of travel 3 1 2 Each of these pictures depicts a type of acceleration: 1: the shuttle is speeding up every sec of the flight into orbit 2. the horse has come to a screeching halt (slowing down) 3. the baseball thrown to the batter is hit into the outfield (changed direction)
Change in direction Any time an object turns it has an acceleration Even though the speed may be constant, the direction is changing Constant acceleration is a steady change in velocity
Acceleration due to gravity Known as free fall As something falls its velocity increases by 9.8 m/s every second Acceleration due to gravity = 9.8 m/s 2
Review: DO NOT WRITE THIS DOWN Distance vs. Time graph The slope of a line on a distance-time graph is speed
Speed vs. Time graph Graph speed on y, time on x Slope equals acceleration.
The slope of the line represents The speed How does the slope during the first second compare to the slope during the fourth second? It is much greater during the fourth than the first What does this mean? An increasing speed means that the ball is accelerating.
What does it mean? What does a = 5 [m/sec 2 ] mean? If an object starts at rest, its velocity increases by 5 [m/sec] every second. Time (sec) Acceleration Velocity 0 5 m/sec 2 0 m/sec 1 5 m/sec 2 5 m/sec 2 5 m/sec 2 10 m/sec 3 5 m/sec 2 15 m/sec 4 5 m/sec 2 20 m/sec Therefore, an object accelerating at 5m/sec 2 will be travelling at 20 m/sec after 4 seconds.
Acceleration Problems: Calculate acceleration for the following data: A = 60km/hr - 20 km/hr = 4 km/hr 10 sec sec A = 150m/sec - 50 m/sec = 20 m 5 sec sec 2 A = 1200km/hr - 25 km/hr = 587.5 km/hr 2 min min
SASinschools Interactivity Linear Motion #1198 helps with reading speed and acceleration graphs!! Go to my website and click on SAS Acceleration Link Log in with username chargers and no password. Enter Code 1198 at the top where it says Quick Launch.
Bell ringer What are the formulas to calculate: velocity acceleration
Check this out??!! Virtual lab on velocity and acceleration in case you don t understand!! http://www.teachersdomain.org/resource/ phy03.sci.phys.mfw.accel/
Inquiry Activity p.327 How Does a Ramp Affect a Rolling Marble? 1. Form a ramp by placing one end of a long board on a stack of six identical books. 2. Have your partner release a marble at the top of the ramp. Use your phone to record the time. 3. Repeat this process 5 times for an average time.
Inquiry Activity p.327 How Does a Ramp Affect a Rolling Marble? 1. Form a ramp by placing one end of a long board on a stack of six identical books. 2. Have your partner release a marble at the top of the ramp. Use your phone to record the time. 3. Repeat this process 5 times for an average time.
Inquiry Activity p.327 4. Predict how many books it would take to double the time need for the marble to reach the ramp s end. Write this as a hypothesis 5. Test your hypothesis. 6. If you kept adding books to the stack, will the time needed for the marble to roll down decrease indefinitely?