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Transcript

  • 1. Topic 2 Mechanics
  • 2. Contents
    • Kinematic Concepts: Displacement Speed vs. Velocity Acceleration Changing Units Instantaneous vs. Average
    • Frames of Reference Graphical Representation of Position
    • Graphical Representation of Velocity
    • Graphical Representation of Acceleration
    • Equations for Constant Acceleration
    • Vertical Motion of Objects
    • Air Resistance
    • Force and Mass: Springs
  • 3. Mechanics
    • Mechanics is the study of :
      • motion,
      • force and ,
      • energy.
  • 4. Kinematic Concepts
    • Kinematics is the part of mechanics that describe s how objects move.
    • The why objects move as they do is called dynamics .
  • 5. Kinematic Concepts
    • Displacement
    • When a person moves over a time interval,
      • they change their position in space.
    • This change in position is called the :
      • displacement .
    • It is a vector quantity .
  • 6. Kinematic Concepts
    • The further it moves from its starting position,
      • the greater it’s displacement.
  • 7. Kinematic Concepts
    • If the object moves in the opposite direction ;
    • as defined,
    • its displacement will be negative.
  • 8. Kinematic Concepts
    • Displacement is given the symbol s ;
      • or sometimes  x ,
      • it’s S.I. unit is the (m)etre.
  • 9. Kinematic Concepts
    • The term distance is a scalar :
      • the symbol is d .
    • Distance is more useful when purchasing a car.
      • The distance travelled is important ;
      • while the direction it travelled in is not.
  • 10. Kinematic Concepts
    • A person who walks 100 m east and then ;
      • 100 m west has travelled a distance of ,
      • 200 m.
    • Their displacement however is 0 m.
    • They have ended up at their starting point.
    • Distance vs Displacement
  • 11. Kinematic Concepts
    • Speed vs Velocity
    • Although speed and velocity are used interchangeably in everyday life,
      • both terms have specific meanings.
  • 12. Kinematic Concepts
    • Speed is defined as ;
      • the distance travelled by an object in a given time interval.
    • This will give us the average speed.
    • Mathematically, it can be represented by:
  • 13. Kinematic Concepts
    • As distance is one of the variables,
      • speed must be a scalar.
    • Velocity is used to signify both magnitude and direction hence ;
      • it is a vector.
  • 14. Kinematic Concepts
    • The average velocity is defined as :
      • the change in position of the object ;
        • in a given time interval.
    • Mathematically, it can be described as:
  • 15. Kinematic Concepts
    • The S.I. unit for both speed and velocity is m s -1 .
    • Always include a direction when giving the value of the velocity.
  • 16. Kinematic Concepts
    • Acceleration.
    • An object whose velocity is changing is :
      • accelerating.
    • Acceleration is defined as :
      • the rate of change in velocity.
  • 17. Kinematic Concepts
    • Which cars below are acceleration and which cars are traveling at constant velocity?
    • Which car accelerates fastest?
  • 18. Kinematic Concepts
    • The red car is traveling at constant velocity.
    • The blue car is accelerating fastest.
      • Its rate of change of velocity is greatest.
  • 19. Kinematic Concepts
    • Since an object always accelerates in a given direction,
      • acceleration is a vector quantity.
    • The S.I. units are m s -2
  • 20. Kinematic Concepts
    • Changing Units
    • When using kinematic equations,
      • the data given is not always given in S.I. units.
    • The data needs to be converted to S.I. Units;
      • before they can be substituted into an equation.
  • 21. Kinematic Concepts
    • An example is speed.
    • Very often speed is given in km h -1 .
    • The kilometres need to be converted to metres and the hours into seconds.
    • There are 1000 m in 1 km
      • 3600 s in 1 hr (60 x 60).
  • 22. Kinematic Concepts
    • There is doubt over whether the correct answer should be :
      • 30 m s -1 ,
      • 28 m s -1 or ,
      • 27.7 m s -1
        • due to the number of significant figures given.
  • 23. Kinematic Concepts
    • To avoid this problem, always give your data using scientific notation.
    • In the above example,
      • 1.00 x 10 2 m s -1 would eliminate the problem
      • hence the answer would be 27.7 m s -1 .
  • 24. Kinematic Concepts
    • Instantaneous vs Average
    • If you drive a car for 240 km in 3 hrs,
      • your average speed is 80 km h -1 .
    • It is unlikely that for every part of the journey,
      • you would be travelling at 80 km h -1 .
    • At each instant, your speed would change.
  • 25. Kinematic Concepts
    • The speedometer in the car gives ;
      • the instantaneous speed.
    • The instantaneous speed is defined as :
      • the average speed over an indefinitely short time interval .
  • 26. Kinematic Concepts
    • The same definition can be used for velocity.
    • The formula for velocity needs to be changed to :
      • accommodate the difference between average ,
      • and instantaneous velocity.
  • 27. Kinematic Concepts
    • Average velocity:
    • Instantaneous velocity:
  • 28. Kinematic Concepts
    • As  t becomes very small,
      • approaching zero,
      •  s approaches zero as well.
    • However, the ratio approaches a definite value.
  • 29. Kinematic Concepts
    • This definite value is known as the instantaneous velocity.
    • The symbol for instantaneous velocity is :
      • v no av or bar above the v .
  • 30. Kinematic Concepts
    • The same procedure can be used for acceleration and so the equations become:
    • Average acceleration:
    • Instantaneous acceleration:
  • 31. Kinematic Concepts
    • Relationship between Velocity & Acceleration
  • 32. Kinematic Concepts
    • Frames of Reference
    • The simple question ‘how fast are you moving’ is quite complex.
    • In your seat now, you are moving at :
      • 0 m s -1 relative to the room.
    • If the room were on the equator,
      • you would be moving at 1700 km h -1 .
  • 33. Kinematic Concepts
    • At the pole you would be spinning on the spot.
    • This however is not true relative to the Sun.
    • Two planes moving at 1000 km h -1 relative to the ground :
      • may be stationary relative to each other.
  • 34. Kinematic Concepts
    • All motion is relative .
    • We must choose our frame of reference in each description of motion we give.
    • Relative Motion (frame of reference)
  • 35. Kinematic Concepts
    • Usually the motion of objects is considered relative to the earth .
    • This is called:
      • the inertial frame of reference .
    • Unless otherwise stated,
      • this will be assumed.
    • Inertial Frame
  • 36. Graphical Representation of Motion
    • Graphical Representation of Position
    • Multiflash photographs of an object in motion ;
      • can be taken and ,
      • data collected from it.
    • An example of a multiflash photo is the toy car on the next slide.
  • 37. Graphical Representation of Motion
    • To take this photo ;
      • the film needs to be exposed for a period of time in darkness ,
      • with a strobe flashing at a known rate.
  • 38. Graphical Representation of Motion
    • From the data collected,
      • graphs can be drawn.
    • By plotting position on the vertical axis and ;
      • time on the horizontal,
      • the graph will look like:
  • 39. Graphical Representation of Motion
  • 40. Graphical Representation of Motion
    • A number of facts can be ascertained from this graph.
    • As the line is straight,
      • the change in position per unit time, is constant.
      • This means the velocity is constant.
  • 41. Graphical Representation of Motion
    • 2. The magnitude of the velocity can be obtained by the slope;
  • 42. Graphical Representation of Motion
    • If the graph is steep, it means :
      • there is a greater change in position ,
      • per unit time and the object ,
      • is moving relatively fast.
  • 43. Graphical Representation of Motion
  • 44. Graphical Representation of Motion
    • What happens when two cars traveling at different speeds but with constant velocity?
  • 45. Graphical Representation of Motion
    • If the graph is horizontal :
      • the object is stationary.
    • If the slope is negative :
      • the object is moving back towards its starting position with ,
      • constant velocity .
  • 46. Graphical Representation of Motion
  • 47. Graphical Representation of Motion
    • In graph a);
    • The person has moved at constant velocity over the interval t 1 to point p
    • They then remained stationary for the period t 2
    • The person then returned to the original starting position at a constant, but slower velocity over the interval t 3 .
  • 48. Graphical Representation of Motion
    • In graph b);
    • The person has moved at constant velocity over the interval t 1 to point p
    • They then remained stationary for the period t 2
    • The person then continued in the original direction for the same distance p as in interval t 1 at a constant, but slower velocity over the interval t 3 .
  • 49. Graphical Representation of Motion
    • Graphical Representation of Velocity
    • Consider graph a) from above.
    • From the information from the graph, a graph of the person’s velocity can be drawn.
  • 50. Graphical Representation of Motion
  • 51. Graphical Representation of Motion
    • The graph is slightly idealised as :
      • the person could not travel at the constant velocity ,
      • at every instant of the journey.
  • 52. Graphical Representation of Motion
    • In a real situation ;
      • velocity does not change in zero time and a more likely description is ,
      • the one shown above.
  • 53. Graphical Representation of Motion
    • What about v/t graphs for the two cars previously?
  • 54. Graphical Representation of Motion
    • V vs t graph animation
  • 55. Graphical Representation of Motion
    • Multiflash photography can be used to obtain :
      • direct values of average velocity.
    • This is because time intervals are :
      • very short and ,
      • constant.
  • 56. Graphical Representation of Motion
    • The distance from one image to the next is :
      • the change in position of the object in ,
      • a specific interval of time.
    • Changes in position in equal intervals of time are :
      • direct measures of the average velocity ,
      • over those intervals.
  • 57. Graphical Representation of Motion
    • The area under the Velocity vs. Time graph can :
      • be used to obtain further information.
    • This information relates to :
      • the change in position of the object.
  • 58. Graphical Representation of Motion
    • Rearranging this equation :
      • change in position is given by the product;
    • average velocity x time taken
    • The graph on the next slide deals with constant velocity .
  • 59. Graphical Representation of Motion
  • 60. Graphical Representation of Motion
    • As the velocity is constant ;
      • the average velocity must be v .
    • Hence, the change in position :
      • will be vt .
    • This is also equal to the :
      • area under graph in time interval t .
    • This relationship holds for all v/t graphs ;
      • as in the example on the next slide :
  • 61. Graphical Representation of Motion
  • 62. Graphical Representation of Motion
    • The motion in the graph above describes :
      • motion under non-zero constant acceleration
        • eg motion under the force of gravity.
  • 63. Graphical Representation of Motion
    • Since velocity changes in a regular way ;
      • the average velocity is ,
      • the average of the initial velocity and ,
      • the final velocity.
    • The horizontal line through P represents this.
  • 64. Graphical Representation of Motion
    • The areas a and b are equal :
      • one being under the graph and ,
      • the other, above the line.
  • 65. Graphical Representation of Motion
    • The product of v av t is :
      • the area under the graph and ,
      • gives the change in position.
  • 66. Graphical Representation of Motion
    • Another way to calculate the change in position is :
      • to divide the area under the graph into ,
      • a rectangle and triangle and ,
      • add the two solutions.
  • 67. Graphical Representation of Motion
    • Any area below the axis corresponds to :
      • motion in the opposite direction where ,
      • the change in position is opposite in sign.
  • 68. Graphical Representation of Motion
    • Graphical Representation of Acceleration
  • 69. Graphical Representation of Motion
    • In the example, the slope,
      • and therefore the rate at which velocity is changing,
      • is constant.
    • Constant Acceleration Graph
  • 70. Graphical Representation of Motion
    • Acceleration is defined as :
      • the rate of change of velocity.
    • Mathematically, this can be written as:
  • 71. Graphical Representation of Motion
    • The slope of the graph is given by: rise/run .
    • In the example , the rise =  v and the run as  t.
  • 72. Graphical Representation of Motion
    • This gives the formula:
    • This corresponds to our formula for acceleration.
  • 73. Graphical Representation of Motion
    • This corresponds to our formula for acceleration.
    • The slope of a v/t graph gives :
      • acceleration.
    • Acceleration is measured in m s -2 and ;
      • is a vector quantity so ,
      • direction must always be included.
  • 74. Graphical Representation of Motion
    • A car is stationary at the lights when the lights change to green.
    • Another car is moving when the lights turn green.
    • What is the displacement of each car after 3 seconds?
  • 75. Graphical Representation of Motion
  • 76. Graphical Representation of Motion
    • Red car
    • Area of triangle = ½ b x h
    • Displacement = ½ x 3 x 12
    • Displacement = 18 m
  • 77. Graphical Representation of Motion
    • Blue car
    • Area of rectangle = b x h
    • Displacement = 3 x 10
    • Displacement = 30 m
  • 78. Graphical Representation of Motion
    • Watch the animation again.
    • What is the acceleration of the red car after 3 seconds?
  • 79. Graphical Representation of Motion
    • Slope = ryse/run
    • Acceleration = 12/3
    • Acceleration = 4 m s -1
    • Watch the animation again and determine the displacement of both cars after 9 seconds.
  • 80. Graphical Representation of Motion
  • 81. Graphical Representation of Motion
    • Red Car
    • Displacement = area of triangle + area of rectangle.
    • Displacement = (½ x 3 x 12) + (9 x 12)
    • Displacement =18 + 72
    • Displacement = 90 m
  • 82. Graphical Representation of Motion
    • Blue Car
    • Displacement = area of rectangle
    • Displacement = 9 x 10
    • Displacement = 90 m
    • Watch the animation again.
    • When do the two cars pass each other?
    • Does it agree with your calculations?
  • 83. Graphical Representation of Motion
  • 84. Graphical Representation of Motion
    • Graphs of position, velocity and acceleration can be drawn for the same object.
  • 85. Graphical Representation of Motion
    • What happens if it is traveling backwards?
  • 86. Graphical Representation of Motion
    • What happens when it is being pushed forward?
  • 87. Graphical Representation of Motion
    • Traveling in the opposite direction?
  • 88. Graphical Representation of Motion
    • What happens when it is pulled backward?
  • 89. Graphical Representation of Motion
    • Traveling in the opposite direction?
  • 90. Graphical Representation of Motion
    • Very complicated motion can be studied using graphs.
    • Watch the two stage rocket as it is launched, run out of fuel and returns to Earth.
  • 91. Graphical Representation of Motion
  • 92. Graphical Representation of Motion
    • The Moving Man
    • Motion Graphs
    • If you would like more practice at drawing motion graphs diagrams, try this web site:
    • http://www.glenbrook.k12.il.us/gbssci/phys/shwave/graph.html
  • 93. Equations for Uniformly Accelerated Motion
    • The previous equations used can :
      • be applied to all types of motion.
    • However, when acceleration is constant :
      • our mathematical description can be taken further.
  • 94. Equations for Uniformly Accelerated Motion
  • 95. Equations for Uniformly Accelerated Motion
    • In the graph on the previous slide , as the slope is constant ;
      • the acceleration is also constant.
    • If we let u and v be the velocity at the start and end of the time interval t ;
      • average velocity can be described as;
  • 96. Equations for Uniformly Accelerated Motion
    • and from previously,
    • Comparing these equations, we can say:
  • 97. Equations for Uniformly Accelerated Motion
    • The average acceleration can also be given as:
    • Rearranging the equation gives:
  • 98. Equations for Uniformly Accelerated Motion
    • These two equations describe motion :
      • at constant acceleration ,
      • in terms of five variables;
      • u , v , t , s , a .
  • 99. Equations for Uniformly Accelerated Motion
    • Equation  does not use a and ;
      •  does not use s .
    • Using algebra, we can derive 3 more equations,
      • each one not using one variable listed above.
  • 100. Equations for Uniformly Accelerated Motion
    • rearranging gives;
  • 101. Equations for Uniformly Accelerated Motion
    • Equation 2: v = u + at rearranged becomes;
    • substituting for t we have:
  • 102. Equations for Uniformly Accelerated Motion
    • v 2 - u 2 = 2as 
  • 103. Equations for Uniformly Accelerated Motion
    • Equation  v = u + at
    • Substituting for v from  we get;
  • 104. Equations for Uniformly Accelerated Motion s=ut + ½at 2 
  • 105. Equations for Uniformly Accelerated Motion
    • Exercise:
    • Try and derive  , which is independent of u .
  • 106. Equations for Uniformly Accelerated Motion VARIABLES EQUATION u v t s a u v t s a v = u + at u v t s a v 2 - u 2 = 2as u v t s a u v t s a
  • 107. Vertical Motion of Objects
    • The Earth, near its surface, has a uniform gravitational field.
    • Objects that move perpendicular to the Earth’s surface,
      • move parallel to the gravitational field.
  • 108. Vertical Motion of Objects
    • The acceleration experienced by the object will be constant.
    • a = 9.81 m s -2 down.
    • If the object is moving towards the Earth,
      • the object’s speed will increase at the rate of,
      • 9.81 m s -1 every second.
    • This is assuming that air resistance is negligible.
  • 109. Vertical Motion of Objects
  • 110. Vertical Motion of Objects
    • True or False?
    • 1. The elephant encounters a smaller force of air resistance than the feather and therefore falls faster.
    • 2. The elephant has a greater acceleration of gravity than the feather and therefore falls faster.  
  • 111. Vertical Motion of Objects
    • 3. Both elephant and feather have the same force of gravity, yet the acceleration of gravity is greatest for the elephant.
    • 4. Both elephant and feather have the same force of gravity, yet the feather experiences a greater air resistance.
  • 112. Vertical Motion of Objects
    • 5. Each object experiences the same amount of air resistance, yet the elephant experiences the greatest force of gravity.
    • 6. Each object experiences the same amount of air resistance, yet the feather experiences the greatest force of gravity.
  • 113. Vertical Motion of Objects
    • 7. The feather weighs more than the elephant, and therefore will not accelerate as rapidly as the elephant.
    • 8. Both elephant and feather weigh the same amount, yet the greater mass of the feather leads to a smaller acceleration.
  • 114. Vertical Motion of Objects
    • 9. The elephant experiences less air resistance and than the feather and thus reaches a larger terminal velocity.
    • 10. The feather experiences more air resistance than the elephant and thus reaches a smaller terminal velocity.
  • 115. Vertical Motion of Objects
    • 11. The elephant and the feather encounter the same amount of air resistance, yet the elephant has a greater terminal velocity.
    • If you answered True to any of these questions, you need to review your understanding.
  • 116. Vertical Motion of Objects
  • 117. Vertical Motion of Objects
    • Objects which move vertically upwards:
      • will slow down at the rate of 9.81 m s -1 ,
      • every second until it is stationary.
    • It will then start to accelerate towards the earth at:
      • the rate of 9.81 m s -1 every second.
    • Vertical Motion
  • 118. Air Resistance
    • Objects falling in the Earth’s uniform gravitational field have two opposing forces acting on it.
      • Gravity acts towards the Earth, pulling the object downward.
    • Any resistance force opposes motion.
  • 119. Air Resistance
    • This means, in this case ;
      • air resistance acts upwards.
    • The faster the object falls ;
      • the greater the air resistance.
    • As the object accelerates under the force of gravity ;
      • the greater the air resistance.
  • 120. Air Resistance
    • This slows the rate at which the object ;
      • accelerates towards the earth.
    • Eventually, the two forces cancel each other out.
    • This means there is no acceleration and ;
      • the velocity becomes constant.
    • This is known as terminal velocity.
  • 121. Air Resistance
    • The terminal velocity is different :
      • for different objects.
    • Sky diver’s have a terminal velocity of :
      • about 150 to 200 km h -1 depending on ;
        • the mass of the sky diver and ,
        • their orientation.
  • 122. Air Resistance
    • Sky divers tend to try to:
      • increase the air resistance thereby ,
        • reducing the terminal velocity.
    • This gives them a longer free fall.
    • The parachute :
      • greatly increases air resistance and ,
      • cuts the terminal velocity to ,
        • between 15 and 20 km h -1 .
  • 123. Air Resistance
  • 124. Forces and Dynamics
    • To maintain the velocity of an object such as a wheelbarrow :
      • a push or pull is required.
    • To maintain acceleration :
      • either by changing the speed of an object or changing its direction,
      • a push or pull is required.
  • 125. Forces and Dynamics
    • The name we use for this push or pull is :
      • force .
    • A force is required to :
      • keep things moving or ,
      • change their motion.
    • A force can also be used to :
      • deform an object.
    • This happens when a tennis racquet hits a tennis ball.
  • 126. Forces and Dynamics
    • Using an air track, we can eliminate (or very nearly) ;
      • the force of friction on a glider.
    • This leaves the force of gravity and :
      • the force of the hand that pushes a glider.
  • 127. Forces and Dynamics
    • How can we determine the effect of a single force when ;
      • there are two forces acting?
    • We must make an assumption.
    • Gravitational forces being vertical :
      • have no effect on motion ,
      • in the horizontal plane.
  • 128. Forces and Dynamics
    • Recall the air track practical :
      • once the hand released the glider,
      • it moved with a constant velocity.
    • This indicates that the assumption is true.
  • 129. Forces and Dynamics
    • There are cases when more than one force acts on a object.
    • These forces may oppose each other:
      • Pushing an object forward and,
      • Friction backward
      • Or a tug of war
  • 130. Forces and Dynamics
    • Or they may act at some other angle:
      • Running for the football and,
      • being hip and shouldered.
    • A diagram can be drawn to show these forces.
    • It is called a Free-body Diagram.
  • 131. Forces and Dynamics
    • Consider a statue resting on a table.
    • What forces are acting on it?
    • As it is at rest:
      • there are no unbalanced forces.
    • Gravity ( F g ) is acting downwards.
    • What force balances gravity?
  • 132. Forces and Dynamics
    • The table exerts an upward force.
    • The table is compressed by the statue
      • Due to its elasticity it pushes upwards.
    • This is called a contact force.
      • As it occurs when two objects are in contact.
  • 133. Forces and Dynamics
    • When the contact force acts:
      • perpendicular to the common surface of contact, it is called,
      • the Normal Force ( F N ).
    • A diagram of the objects and their forces can be drawn.
  • 134. Forces and Dynamics
  • 135. Forces and Dynamics
    • We are interested in the forces and so:
      • we will only include vectors for the forces.
    F g F N
  • 136. Forces and Dynamics
    • Notice:
    • The vectors are of the same length:
      • Indicating same magnitude of force.
    • The vectors are in opposite directions:
      • Indicating the forces oppose each other.
    • The vectors have been labeled:
      • with appropriate symbols.
  • 137. Forces and Dynamics
    • What happens when you add a third force?
    • Consider a box at rest on a table.
    • What forces are acting on it?
      • F g and:
      • F N
  • 138. Forces and Dynamics F g F N
  • 139. Forces and Dynamics
    • What if you were to push down on the box with a force of 40 N?
    F N F g 40 N
  • 140. Forces and Dynamics
    • Notice that the combined length of:
      • the F g and 40 N vectors,
      • equal the F N vector.
    • This indicates the box is stationary.
    • What happens if you pull up with a force of 40 N?
  • 141. Forces and Dynamics F g F N 40 N
  • 142. Forces and Dynamics
    • Notice that the combined length of:
      • the F N and 40 N vectors,
      • equal the F g vector.
    • This indicates the box is stationary.
  • 143. Forces and Dynamics
    • What forces act on a shopping trolley?
  • 144. Forces and Dynamics
  • 145. Forces and Dynamics
    • As F N = F g
    • The force making the trolley move is equal to:
    • F p = Force supplied by the person.
    • This is an unbalanced force and:
      • it will cause an acceleration.
  • 146. Forces and Dynamics
    • What happens when the ( 10 kg) box in the earlier example is:
      • connected to another box (12 kg),
      • by a string and both,
      • are pulled along a table?
    • What do the Free Body Diagrams look like?
  • 147. Forces and Dynamics
  • 148. Forces and Dynamics Box 1 F N F g T F P
  • 149. Forces and Dynamics
    • Notice:
    • The vectors F g and F N are of the same length:
      • Indicating same magnitude of force.
      • No vertical motion
    • The vector F p is longer than T indicating:
      • acceleration to the right
  • 150. Forces and Dynamics Box 2 F N F g T
  • 151. Forces and Dynamics
    • Free Body Diagram
    • Another one
    • If you would like more practice at drawing free body diagrams, try this web site
    • http://www.glenbrook.k12.il.us/gbssci/phys/shwave/fbd.html
  • 152. Forces and Dynamics
    • Suppose you wanted to see what was in the box in the earlier example.
    • You pull it towards you:
      • using a string attached with,
      • a force of 40 N at,
      • an angle of 30 o above the horizontal..
  • 153. Forces and Dynamics
  • 154. Forces and Dynamics
    • This becomes more difficult to analyse .
    • Notice F N  F g
    • This is because some of the force supplied by the person is:
      • acting in an upward direction.
    • Forces can be resolved into components.
  • 155. Forces and Dynamics
    • Forces can be resolved into two components :
      • horizontal and vertical.
  • 156. Forces and Dynamics
    • This is useful when forces are applied at an angle but :
      • the effective force is in a particular direction ,
      • such as pushing a roller
  • 157. Forces and Dynamics
    • Forces can combine to give very different results.
    • A 10 N block hanging vertically from one horizontal string :
      • when measured by a spring balance would read ,
      • 10N.
  • 158. Forces and Dynamics
  • 159. Forces and Dynamics
    • As the block is stationary :
      • the force of the scale pulling up balances ,
      • the force downwards supplied by ,
      • the weight.
    • If 2 spring balances support the block :
      • the total weight will be the same.
  • 160. Forces and Dynamics
    • However each spring balance will support equal amounts :
      • ie 5N.
  • 161. Forces and Dynamics
    • Again the weight down is balanced by :
      • the two springs supplying a force up.
    • In all situations the two forces vectors :
      • one vertically downward and ,
      • the other vertically upwards ,
      • must balance.
  • 162. Forces and Dynamics
    • This looks logical for a vertical orientation but how do they work for non-vertical situations?
  • 163. Forces and Dynamics
    • The vertically up vector must still equal 10 N and so by vector addition :
      • the two scales will read more than 5 N each ,
      • perhaps 10 N.
    • If the angle is increased to 60 o from the vertical :
      • 120 o between the scales ,
      • The reading is much higher.
  • 164. Forces and Dynamics
  • 165. Forces and Dynamics
    • If we continue to do this until the angle is 90 o ,
      • the horizontal rope must support a force that is ,
      • much greater than the original weight.
  • 166. Forces and Dynamics
    • Gymnasts who hold their arms out horizontally from the rings :
      • must supply a force that is considerably greater than their own body weight.
    • This is an extreme test of strength.
  • 167. Forces and Dynamics
    • To determine exact values for the components:
      • Trigonometry must be used.
  • 168. Forces and Dynamics
    • F vert = opposite side
    • F horiz = adjacent side
    • F = applied force
    • sin  = opposite/hypotenuse
    • Opposite = F vert = F sin 
    • cos  = adjacent/hypotenuse
    • Adjacent = F horiz = F cos 
  • 169. Forces and Dynamics
    • Springs
    • If you hang a weight from a spring:
      • apply a force,
      • it stretches.
    • Add more weight:
      • It stretches more
    • Remove the weights:
      • It returns to its original length.
  • 170. Forces and Dynamics
    • The spring is said to be elastic.
    • By stretching a spring:
      • or compressing it,
    • The amount it is stretched is:
      • Directly proportional to the force applied.
    • This was first noticed by the British Physicist:
      • Robert Hooke
      • In the 17 th century
  • 171. Forces and Dynamics
    • It is now remembered as Hooke’s Law.
    • The applied force F and:
      • The extension (or compression) x
    • Can be represented mathematically.
    • F  x
    • A graph of this can be shown.
  • 172. Forces and Dynamics F x
  • 173. Forces and Dynamics
    • Compare the line to the equation of a straight line:
    • y = mx + c
    • y = F
    • x = x
    • c = 0 (as through the origin)
    • To turn the proportionality into an equation:
  • 174. Forces and Dynamics
    • F = mx
    • The slope is constant and so is given a special symbol:
      • k
    • All constants in Physics have special symbols.
    • The equation now becomes:
    • F = kx
  • 175. Forces and Dynamics
    • The full form of the equation is:
    • F = -kx
    • This is because the force is a restoring force.
      • It always acts to try an return the spring to the original length.
    • Hookes Law
  • 176. Forces and Dynamics
    • You will need to be able to:
    • draw a graph
      • Given data
    • Determine the spring constant k :
      • For a particular spring.
  • 177. Forces and Dynamics
    • Determine the force required to:
      • extend a spring by a certain amount
    • Determine the amount a spring is stretched by:
      • for a given force.
  • 178. Forces and Dynamics
    • An object that moves with constant velocity :
      • requires no force.
    • Although this is one experiment, it can be shown to be true :
      • in all situations
      • whether it is a person ice-skating or ,
        • a person slipping on a banana peel.
  • 179. Forces and Dynamics
    • Newton investigated this phenomenon,
      • which he embodied in his first law:
    • Provided no external force acts, the velocity of any object will remain constant unless an unbalanced force acts upon the object.
  • 180. Forces and Dynamics
    • A body is resistant to change.
    • This resistance of a body to change is called inertia .
    • Does this hold for a stationary object?
    • A stationary object has zero velocity :
      • and so it will remain at zero.
  • 181. Forces and Dynamics
    • Plates on a tablecloth are at rest.
    • If you pull the tablecloth quickly enough from under the plates :
      • t he small and brief force of friction ,
      • between the plates and the tablecloth is ,
      • not significant enough to ,
      • appreciably move the dishes.
  • 182. Forces and Dynamics
    • Does this hold for tug of war contest?
    • When the two sides are even :
      • the forces are equal in magnitude and ,
      • opposite direction.
    • The resultant force will be zero.
    • This implies that the two sides will not move.
  • 183. Forces and Dynamics
    • Does this apply to a car moving on a straight road ;
      • at a constant velocity?
    • The car will slow to a stop unless :
      • the force applied by the engine continues.
  • 184. Forces and Dynamics
    • This appears to disobey the law :
      • until friction is taken into account.
    • We can ignore gravity because :
      • it is acting in a vertical direction.
    • Friction however is a retarding force acting :
      • in the opposite direction to the motion.
  • 185. Forces and Dynamics
    • This is an example of translational equilibrium.
    • Two forces are being applied in opposite directions.
    • As the forces cancel each other out,
      • no acceleration occurs.
    • The object continues to move at:
      • a constant velocity.