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Our Dynamic Universe

Higher Physics. Our Dynamic Universe. Our Dynamic Universe :. Contents. Speed, acceleration and vectors - Revision Equations of motion Forces, energy and power Collisions and explosions Gravitation Special relativity The expanding universe Big Bang Theory.

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Our Dynamic Universe

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  1. Higher Physics Our Dynamic Universe

  2. Our Dynamic Universe: Contents Speed, acceleration and vectors - Revision Equations of motion Forces, energy and power Collisions and explosions Gravitation Special relativity The expanding universe Big Bang Theory

  3. Our Dynamic Universe: Speed, acceleration and vectors Average Speed Average speed is a measure of the distance travelled in unit time. To measure an average speed you must: • measure the distance travelled with a tape or metre stick • measure the time taken with a stop clock • calculate the speed by dividing the distance by the time

  4. Our Dynamic Universe: Speed, acceleration and vectors d = v t time (s) distance (m) average speed ( ms-1)

  5. Our Dynamic Universe: Speed, acceleration and vectors Instantaneous Speed Instantaneous speed at a given point can be measured by finding the average speed during as short a time as possible.

  6. Our Dynamic Universe: Speed, acceleration and vectors length of card instantaneous speed = time to cut beam

  7. Our Dynamic Universe: Speed, acceleration and vectors Acceleration – - - Revision Acceleration is the change in speed in unit time. a acceleration (ms-2) t time (s) v - u a = t u starting speed (ms-1) v final speed (ms-1)

  8. Our Dynamic Universe: Speed, acceleration and vectors Measuring Acceleration Acceleration can be measured using a double card, a light gate and a motion computer.

  9. Our Dynamic Universe: Speed, acceleration and vectors • Measure the length of card and enter the length into the motion computer. • Let the car run down the slope with the card cutting the light beam. • The time for length 1 to pass is recorded and used to find u. • The time for length 2 to pass is recorded and used to find v. • The time t between the lengths is recorded and the computer uses the equation to calculate the acceleration.

  10. Our Dynamic Universe: Speed, acceleration and vectors Scalars and vectors Speed , distance, energy, pressure, force are examples of quantities that can be measured. Quantities can be split into two groups, scalars and vectors. A scalar is a quantity that has magnitude (size) only. A vector is a quantity that has magnitude and direction.

  11. Our Dynamic Universe: Speed, acceleration and vectors A vector can be represented by a straight line with an arrow. The length of the line gives the magnitude of the vector. The direction of the arrow gives the direction of the vector. e.g. 10 N

  12. Our Dynamic Universe: Speed, acceleration and vectors The sum of two or more vectors is called the resultant. Vectors are always added ‘nose to tail’. resultant

  13. Our Dynamic Universe: Speed, acceleration and vectors Distance and Displacement Distance is a scalar. Displacement is a vector and is the shortest distance between the start and the finish .

  14. Our Dynamic Universe: Speed, acceleration and vectors N North b) 1 km Example. A girl walks 4 km due North then 3 km due South. Find a) the distance from the start. b) the displacement from the start. a) 7 km 3 km 4 km

  15. Our Dynamic Universe: Speed, acceleration and vectors Speed and velocity Speed is a scalar. Velocity is a vector. Speed = Velocity =

  16. Our Dynamic Universe: Equations of Motion Equations of motion The equations of motion can be applied to objects with a constant acceleration moving in a straight line. Start with and re-arrange to give v = u + at -1 v final velocity ms u initial velocity ms a acceleration ms t time s -1 -2

  17. Our Dynamic Universe: Equations of Motion displacement = area under graph velocity s = ½(v-u)t + ut s = ½ (at )t + ut s = ½ at + ut v u 2 time t 0 2 s = ut + ½at

  18. Our Dynamic Universe: Equations of Motion The first two equations can be combined to give a third equation of motion v = u + 2as 2 2

  19. Our Dynamic Universe: Equations of Motion Example -1 A car moving is moving at 20 ms . The car accelerates at 4 ms for 5 s. Calculate the magnitude of its final velocity. -2 Step 1 list the information u = 20 a = 4 t = 5 v = ? Step 2 choose an equation of motion v = u + at v = 20 + 4×5 v = 20 + 20 v = 40 ms -1

  20. Our Dynamic Universe: Equations of Motion Measuring the acceleration of a falling object (1) attemptacceleration (ms-2) double mask 1 2 3 4 5 average computer light gate

  21. Our Dynamic Universe: Equations of Motion Measuring the acceleration of a falling object (2) attempt time ( s ) electromagnet 1 2 3 4 5 average metal ball timer switch 2 s = ut + ½at

  22. Our Dynamic Universe: Equations of Motion Measuring the acceleration of a falling object (3) motion sensor ball computer

  23. Our Dynamic Universe: Motion-time graphs Measuring the acceleration of a popper toy • Use a metre stick to measure the height the popper rises. • Calculate the speed the popper leaves the bench using an equation of motion. • Measure the thickness of the popper. • Use an equation of motion to calculate the upward acceleration of the popper.

  24. Our Dynamic Universe: Motion-time graphs Velocity -Time Graphs v v v 0 0 0 t t t constant velocity positive acceleration negative acceleration The area under a velocity-time graph is displacement. The gradient is acceleration.

  25. Our Dynamic Universe: Motion-time graphs 8 - 0 -2 (a) = 0∙8 ms = 10 Example The velocity-time graph for a car travelling along a straight road is shown. velocity (ms-2) 8 time (s) 0 10 30 40 Calculate • The acceleration of the car during the first 10 s. • The displacement after 40 s. (b) Displacement =area = (½8x10) + (8 x 20) + (½8x10 ) = 240 m

  26. Our Dynamic Universe: Motion-time graphs Velocity - time graph of a bouncing ball motion sensor ball

  27. Our Dynamic Universe: Motion-time graphs velocity time 0

  28. Our Dynamic Universe: Motion-time graphs Displacement -Time Graphs s s s 0 0 0 t t t constant velocity positive acceleration negative acceleration The gradient of a displacement-time graph is velocity.

  29. Our Dynamic Universe: Motion-time graphs -1 0-2 s v = 8 ÷ 2 = 4 ms Example The displacement-time graph for the movement of an object is shown. displacement (m) 8 0 time (s) 3 1 2 4 Draw the corresponding velocity-time graph for this object. -1 2-3 s v = -8 ÷ 1 = - 8 ms

  30. Our Dynamic Universe: Motion-time graphs velocity (ms-1) 4 0 time (s) 3 1 2 4 -8

  31. Our Dynamic Universe: Motion-time graphs Acceleration -Time Graphs a a a 0 0 0 t t t positive acceleration constant velocity negative acceleration

  32. Our Dynamic Universe: Motion-time graphs Example The graph shows how the acceleration of an object, starting from rest, varies with time. acceleration (ms-2) 4 2 0 time (s) 30 10 20 Draw the corresponding velocity-time graph for the motion of this object. 20 – 30 s v = u + at = 80 + (2 x 10) = 100 ms-1 0 – 20 s v = u + at = 0 + (4 x 20) = 80 ms-1

  33. Our Dynamic Universe: Motion-time graphs velocity (ms-1) 100 80 0 time (s) 30 10 20

  34. Our Dynamic Universe: Balanced and unbalanced forces Balanced Forces When forces act on an object the combined effect depends on their size and direction. Balanced forces are equal in size but opposite in direction. 5 N 5 N 5 N 5 N balanced forces unbalanced forces

  35. Our Dynamic Universe: Balanced and unbalanced forces weight Newton’s First Law An object will remain at rest or move at constant velocity unless acted upon by an unbalanced force.

  36. Our Dynamic Universe: Balanced and unbalanced forces To find the relationship between force, mass and acceleration. Experiment - - -Newton’s Second Law to computer light gate trolley weight

  37. Our Dynamic Universe: Balanced and unbalanced forces Force (N) Mass (kg) Acceleration (ms-2)

  38. Our Dynamic Universe: Balanced and unbalanced forces As the force increases the acceleration increases. As the mass increases the acceleration decreases. F = ma acceleration (ms-2) unbalanced force (N) mass (kg)

  39. Our Dynamic Universe: Balanced and unbalanced forces Example A force of 30 N pulls a box of mass 2 kg along a frictionless surface. Calculate the acceleration of the box. F a = m 30 = 2 = 15 ms-2

  40. Our Dynamic Universe: Balanced and unbalanced forces Example The forces acting on an object of mass 2 kg are shown. Calculate the acceleration of the object. 20 N 4 N 2 kg F a = m 16 = 2 = 8 ms-2 to the left

  41. Our Dynamic Universe: Balanced and unbalanced forces 6∙0 kg Tension Tension is the pulling force exerted by a string or cable on another object. Example A string is used to suspend a mass of 6∙0 kg as shown. Calculate the tension in the string. mass is stationary → tension (up) = weight (down) = mg = 6 x 9·8 = 58∙8 N

  42. Our Dynamic Universe: Balanced and unbalanced forces Example Two boxes on a frictionless horizontal surface are joined together by a string. A constant horizontal force of 12 N is applied as shown. 12 N 2·0 kg 4·0 kg Calculate the tension in the string joining the two boxes. F 12 a = = = F = ma = 2 x 2 = 4 N 2 ms -2 m 6

  43. Our Dynamic Universe: Balanced and unbalanced forces Example A train engine of mass 15000kg has a pulling force of 35 000 N. It is used to pull two carriages each of mass 10 000 kg. What is the tension in couplings A and B ? Coupling B Coupling A For Coupling A F = ma F = 20000 x 1 F = 20000 N For Coupling B F = ma F = 10000 x 1 F = 10000 N F = ma 35000= 35000 x a a = 1 ms-2

  44. Our Dynamic Universe: Balanced and unbalanced forces F a = = = m 20 10 2 ms -2 Internal Forces Example Two boxes are pushed with a horizontal force along a frictionless surface. Calculate the force acting on the 6 kg block. 6∙0 kg 20 N 4·0 kg F = ma = 6 x 2 = 12 N to the right

  45. Our Dynamic Universe: Balanced and unbalanced forces Friction Friction is the force that acts when two surfaces slide or try to slide over each other. Friction acts in a direction to oppose motion.

  46. Our Dynamic Universe: Balanced and unbalanced forces When a parachutist jumps from an aircraft she will accelerate downwards. As the speed increases so will the air friction, until it exactly balances out her weight. She will then be travelling at a constant speed – called the terminal velocity. When the parachute opens the air friction suddenly increases and the parachutist decelerates to a lower terminal velocity.

  47. Our Dynamic Universe: Balanced and unbalanced forces velocity / ms-1 60 10 0 time / s 15 10 5 20

  48. Our Dynamic Universe: Balanced and unbalanced forces Paper Helicopters An investigation of air resistance and surface area. Surface area (cm2) Average time (s) 60 54 48 42 36 30 24

  49. Our Dynamic Universe: Balanced and unbalanced forces 6 cm Fold one wing backwards and the other forwards along the dashed line. 10 cm 12 cm 1∙5 cm 8 cm Fold upwards along the dashed line and attach a paper clip 2 cm

  50. Our Dynamic Universe: Balanced and unbalanced forces Lifts If the lift is moving with constant velocity reading on scale = weight If the lift accelerates upwards reading on scale = weight + ma If the lift accelerates downwards reading on scale = weight - ma m = mass of person on the scale a = acceleration of lift

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