Phantastic Physics: Linear Motion & Forces

• Linear motion is explored with corresponding forces
• The physical world and laws that govern it are understood through physics.
• Linear Motion and Forces is based on aspects of physics that were studied previously

Phantastic Physics Series

• A book series that contains the following subjects
• Linear Motion and Forces
• Electric Circuits
• Heat
• Energy and Momentum
• Waves
• Nuclear Models and Radioactivity

The 4F method

• A problem solving strategy for numerical problems within this book

Describing motion

• Moving objects can be described as slow or fast , and whether they are accelerating or slowing down
• The displacement of the fist, its velocity, and acceleration can all be calculated from each image
• A karate punch photograph shows the motion of a fist
• The distance between images indicates fist velocity, as the flashing light has a uniform flash rate
• The Bugatti Veyron and the EuroFighter are faster than the fist in the image shown
• The fist in the image is moving at 14ms-1 or 51kmhr-1 just before hitting its target

Average Velocity

• Two measurements are required to calculate average velocity: the displacement, s, of the object, and the time taken, t, for this displacement
• Displacement is the straight-line distance from a reference position
• The average velocity is given the symbol Vav
• The units for velocity are kilometers per hour in everyday situations
• S.I. units for velocity include metres per second or ms-1 as displacement is measured in metres (m) and time taken in seconds (s).
• You can rearrange the formula Vav = S/t to get s = tvav and t = S/Vav

Unit Conversions

• 1 kilometre is equal to 1,000 metres.
• 1 minute is equal to 60 seconds.
• 1 hour is equal to 60 minutes or 3,600 seconds.

Converting from kmhr-1 to ms-1

• A velocity of 20kmhr¹ converted to ms-1 is demonstrated: -20kmhr¯¹ = 20 <1,000mhr¯¹ = 20,000mhr¯¹ -20,000mhr¯¹ = 20,000m/3,600s = 5.55ms¯¹ -20kmhr¯¹ = 20 ↔ 1,000/3,600 or 20 < 1/3.6
• A conversion factor of 3.6 can be used -kmhr¯¹ ] 3.6 = ms¯¹ -ms¯¹ 3.6 = kmhr-1

Average vs Instantaneous Velocity

• Olympic sprinter covering 100m sprint in about 10s has an average velocity of 10ms-1.
• Sprinter is not moving at 10ms-¹ all the time, velocity will be zero at the start, and will be higher once they sped up after the 'gun'
• Moving objects do not travel at their average velocity all the time
• Instantaneous velocity is the velocity of an object at a particular time
• Speedometer in a car registers instantaneous velocity
• Average velocity is velocity calculated over a measured time interval
• Instantaneous velocity is the velocity of the object at an instant of time
• Approaching instantaneous velocity of moving object, the interval for average velocity calculation is decreased
• When an object moves with the same velocity at every instant of time, it is said to have constant/uniform velocity, average velocity equals instantaneous velocity

Measuring Velocity

• Measurements needed to determine velocity
• Displacement
• Time
• Displacement is easy to measure with precision
• Measurement of time is difficult time is more difficult

Measuring tape and stopwatch

• Stopwatch can be used if measuring time is sufficient
• Using stopwatch to time a friend riding a bicycle, a distance is measured (50m) to time the motion.
• 4s would lead to an average velocity of 12.5ms-1
• Problem: When measuring time with a stopwatch body needs to react to a stimulus is not immediate
• Body needs time for
• The nerves to carry messages to the brain
• The to decide a course of action
• Response to be transmitted to the muscles
• Muscles act
• Reaction time ranges from 0.2s - 0.5s
• If time interval small (1s) reaction times significant compared to time being measured
• Errors in the time measurement increase and other more accurate techniques should be used

Motion Sensors

• Used to measure -Fast Speeds -Very short time intervals
• Often use ultrasonic pulses that bounce off an object giving its position.
• Velocity calculated with the measurement of time between reflected pulses

Measuring tape and ticker timer

• Way of measuring speed using a ticker timer with short time intervals in a laboratory
• A length of ticker tape is attached to a moving object which passes under carbon paper and a hammer
• Hammer strikes the carbon paper and tape at regular time intervals, leaving a series of dots on the tape which gives information about the object's motion.
• Eliminates reaction time errors
• Introduces slight inaccuracies arising from friction between the ticker tape and the tape itself.
• Calculate average velocities with 4 or 5 tick intervals to improve accuracy
• A.C. ticker timer operates using an electro magnet. The electromagnet operates the alternating current from the power pack, causing the hammer to be attracted to it to move.

Distance, Displacement and Direction

• Direction of the motion has to be considered in all calculations if the moving body reverses direction
• Cyclist travels 100m to the east and turns around then travels travels back 60m (to the 40m mark) in 20s, then -The total distance travelled is 160 m -The displacement (straight-line distance from reference position) is only 40 m from the start
• Distance and displacement differ

Speed, Velocity and Direction

• Average Velocity and average speed are significantly different
• Motion in different directions needs to be distinguished, velocity is said to be positive when the motion is to the east, then motion to the west is to the west and the velocity negative(e.g. -5ms-1).
• Cyclist travels 100m to the east then turns around and travels back 60m (to the 40m mark) in 20s -Displacement is 40 m giving average velocity of-Vav=S/t=40/20 = 2ms-1 -Total distance traveled = 160m, and the displacement is only 40 m -Speed is distance travelled in unit time(160/20 = 8ms-1)

Graphing Motion

• Displacement-time graph shows displacement over time by sticking pieces of ticker tape on graphs such -Total displacement at any time is the distance from the start and equals the sum of all the ticker tape pieces up to that point. From this the displacement at any time can be seen. -A velocity-time graph shows motion over time

Velocity-Time graph and slope

• When the slope of a velocity-time graph is positive, the object is said to be speeding up.
• When the slope is zero the velocity is constant
• A negative slope indicates that the motion is said to be slowing down
• When the actual velocity is negative, the object is moving in the reverse direction
• Slope of the displacement-time graph equals average velocity
• Average velocity is constant along graph
• Average velocity is the slope of a displacement-time graph segment
• Instantaneous velocity is the slope of the tangent of a displacement-time graph. The slope of tangent to curve at point E = instantaneous velocity

Displacement and Velocity for a Ticker-tape

• Can determine motion by treating each piece separately
• Displacement is found to be 13.0cm, so the average velocity is Vav = S/t
• The speed has increased over the length of the tape to 20cms-1 and has remained constant at that value
• Two types of graph can be easily drawn using pieces of ticker tape: -Displacement-time graph -Velocity-time graph

Changing between kmhr-¹ and ms-¹

• Use the following conversions to change between kmhr-¹ and ms-¹: -1 kilometre = 1,000 metres -1 minute = 60 seconds -1 hour = 60 minutes = 60 x 60 = 3,600 seconds -Often, a conversion factor of 3.6 can be used to convert between kmhr-¹ and ms-¹
• The 4F method can be used to solve these problems

Describing motion

• Moving objects can be described as slow or fast, accelerating or slowing down.
• Displacement, velocity and acceleration can be derived from photographs of motion
• A flashing light has a uniform flash rate, the distance between images is an indication of fist velocity.
• Speed and Velocity is different, as the velocity negative when the motion is directed to the west

Examples of Velocity

• Snail: .003ms-1
• Walking: 2.2ms-1
• Running: 10ms-1
• Fast bird: 47ms-1
• Jet Plane 747: 235ms-1

Introduction to Motion

• Moving objects can be described -Fast or slow -Accelerating or slowing down
• The displacement of a fist, its velocity, and acceleration can all be calculated from the photograph
• Flashing light which creates image, has a uniform flash rate, the distance between images is an indication of fist velocity
• Bugatti Veyron and the EuroFighter travel a little faster than a fist during the act of delivering a karate punch

Calculating Acceleration

• Typically cars take about 10 seconds to accelerate from 0 to 100 kmhr1
• Under 7 seconds to accelerate from 0 to 100 kmhr1 is very good, and an under 4 seconds in extraordinary.
• Electric cars have produced some extraordinary results in 0-100kmhr-1 tests with Tesla's Model being one of the fastest cars in the world.

Defining Acceleration

• Acceleration is a change in velocity, either speeding up or slowing down.
• Acceleration is how quickly the velocity is changing

Equation for Acceleration

• Symbols needed for distinguishing velocities, for any calculation: -Final velocity is given as v -Initial velocity is represented by vo
• Acceleration symbol a
• Acceleration is the change in velocity divided by the time taken. a = v-vo/t
• Units for acceleration in the SI system are metres per second per second (ms-2).
• An acceleration of 5ms really means an increase of 5ms-1 in -2 velocity every -
• Often, the symbol △ (delta) is used to replace the expression 'change in

Deriving the Equations of Motion

• Velocity and acceleration is directed to the left with, Note: the negative signs.

Velocity-Time Graph with Acceleration

• The acceleration an object can be found the slope of a velocity-time graph
• Velocity = y step / x step= ( y2-y1) / (x2 - x1) = v-vo/t -slope = average acceleration -acceleration is the slope of a velocity-time graph -slope in a velocity-time corresponds to either an object speeding up or a positive acceleration and Negative slope corresponds to velocity-time graph slowing down