Download Motion Lesson 1: Review of Basic Motion

Motion in one and two dimensions: Lesson 1 Semi-notes
Motion Lesson 1: Review of Basic Motion
Note. For these semi notes we will use the bold italics convention to represent vectors.
Complete the following table :
Term
Symbol
Unit
Definition
ms-1
The rate of change of distance
Distance
Displacement
x
Speed
Velocity
Acceleration
ms-2
Displacement Vectors
The vector x = 39 km East is shown below.
Draw the vectors 2x, -x and 2x in the space below and give the magnitude and direction of each.
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Motion in one and two dimensions: Lesson 1 Semi-notes
Vector Addition
Vectors add “head to tail”.
Solution
Solution
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Motion in one and two dimensions: Lesson 1 Semi-notes
Solution
Vector Subtraction
To subtract a vector simply .............. the ............... vector.
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Motion in one and two dimensions: Lesson 1 Semi-notes
Some Basic Facts
•
•
•
•
•
The SI unit for speed is ..............................
An everyday unit for speed is...............................
-1
Conversion factor, 1 ms = ....................km/h
Instaneous speed is......................................................................................................................................
Instantaneous velocity is .............................................................................................................................
Change in Velocity
∆v =
Average Acceleration
Where a =
∆v
v=
u=
∆t
Solution
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Motion in one and two dimensions: Lesson 1 Semi-notes
Solution
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Motion in one and two dimensions: Lesson 1 Semi-notes
Solution
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Motion in one and two dimensions: Lesson 1 Semi-notes
Centre of Mass
The centre of mass is ..........................................................................................................................
Locate the centre of mass for each of the following and mark it with a asterix *
Additional Notes
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Motion in one and two dimensions: Lesson 1 Semi-notes
You should now be able to complete questions from your Heinemann text Physics 12 (3rd edition), Chapter section
1.1, page 11, questions 1 and 2.
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Motion in one and two dimensions: Lesson 2 Semi-notes
Motion Lesson 2: Further Review of Basic Motion
Three types of graphs commonly used to describe motion are:
Describe in your own words, the motion of the walker indicated on the displacement – time graph below.
The graph below shows the motion of a swimmer travelling 50m in a pool, then turning and swimming back to the
starting position.
Find
a. The total displacement of the swimmer.
b. The distance travelled by the swimmer.
c. The velocity for the first 50m lap in ms-1
d. The velocity for the return 50m lap in ms-1
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Motion in one and two dimensions: Lesson 2 Semi-notes
Describe in your own words, the motion of the walker indicated on the velocity – time graph below.
The graph below represents the motion of a dancer moving back and forth across a stage.
Find
a.
b.
c.
d.
e.
f.
The velocity at t = 0 seconds (ms-1)
The velocity at t = 2 seconds (ms-1)
Acceleration for first 4 seconds (ms-2 )
Displacement after 4 seconds (m)
Displacement after 6 seconds (m)
Average velocity over the 6 seconds (ms-1)
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Motion in one and two dimensions: Lesson 2 Semi-notes
Complete the following summary of motion graphs by filling in the blanks.
Write the words “slope” or “area under” to complete the following summary of motion graphs.
Extra Notes
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Motion in one and two dimensions: Lesson 2 Semi-notes
Worked Example
Solution
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Motion in one and two dimensions: Lesson 2 Semi-notes
Constant Acceleration Equations.
Write down the five equations that can be used in problems involving constant acceleration.
Where
x = displacement (m)
t = time (s)
u = initial velocity (ms-1)
v = final velocity (ms-1)
a = acceleration (ms-2)
Worked Example
Solution
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Motion in one and two dimensions: Lesson 2 Semi-notes
You should now be able to complete questions from your Heinemann text Physics 12 (3rd edition), Chapter section
1.1, page 11, questions 3,4,5,7 and 9.
Extra Notes
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Motion in one and two dimensions: Lesson 3 Semi-notes
Motion Lesson 3: Newton’s Laws of Motion and Forces
Describe in your own words the difference between Aristotle’s definition of the word force, and Newton’s definition
of force.
What is the “natural state of motion”? ........................................................................................................................
Newton’s Three Laws of Motion are:
Newton’s First Law of Motion
Newton’s Second Law of Motion
Net force can be written as ...................... or .....................................
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Motion in one and two dimensions: Lesson 3 Semi-notes
Newton’s Third Law of Motion
The horse and buggy below are moving with constant velocity motion.
a) Draw in and label all the individual forces acting on the buggy.
b) Add the force vectors head to tail to show that the net unbalanced force equals zero in this case.
Show vector addition below
Forces can be classified as either Contact or Action-at-a-distance.
List four action-at-a-distance forces.
....................................................................................
....................................................................................
....................................................................................
....................................................................................
Which of these is most important in studying the motion topic? Explain why?
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Motion in one and two dimensions: Lesson 3 Semi-notes
Complete the table to summarise contact forces.
Name of Force
Pushing and pulling forces
Description or example of this type of force
Pushing a car
Tensile Force
Normal Reaction Force
Thrust
Friction
Air Resistance
Draw in the individual forces acting in each of the situations illustrated below. Give each force a label and show how
the vectors add to give the net force, Fnet in each case.
Explain why can’t Newton’s Third Law action reaction pairs of forces be added together.
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Motion in one and two dimensions: Lesson 3 Semi-notes
Worked Example
Solution
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Motion in one and two dimensions: Lesson 3 Semi-notes
Solution
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Motion in one and two dimensions: Lesson 3 Semi-notes
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Motion in one and two dimensions: Lesson 3 Semi-notes
You should now be able to complete questions from your Heinemann text Physics 12
(3rd edition), Chapter section 1.2, page 17, questions 2, 3,4,5,7, 8 and 9.
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Motion in one and two dimensions: Lesson 3 Semi-notes
Extra Notes
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Motion in one and two dimensions: Lesson 4 Semi-notes
Motion Lesson 4: Normal Force and the Inclined Plane
A normal force acts at right angles to a surface. It is often labelled as either FN or N.
Draw in and label the normal force for each of the situations below.
In the context of a physics question, the word smooth means ....................................................
The normal force is sometimes called the normal reaction force.
What happens to the normal reaction force when Joe (above) pushes harder on the wall?
..................................................................................................................................................
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Motion in one and two dimensions: Lesson 4 Semi-notes
An object (below) accelerates down a smooth inclined plane. The two forces acting are Normal Reaction N and the
force of gravity or weight force, W.
Resolve the Weight force, W, into components parallel and perpendicular to the slope and draw these on the
diagram above.
Indicate the size of each of these components in terms of m, g and θ.
Hence write an expression for the net unbalanced force, Fnet, acting on the object.
Fnet =
Use Newton’s second law to write an expression for the acceleration.
a=
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Motion in one and two dimensions: Lesson 4 Semi-notes
In the context of a physics question, the word rough means ....................................................
Shown below is an object moving down a rough inclined plane. The forces acting are Normal Reaction N, the force of
gravity or weight force, W, and the friction force Fr.
Resolve the Weight force, W, into components parallel and perpendicular to the slope and draw these on the
diagram above.
If the object moves down the slope with constant velocity motion, find;
a) The Net Force Fnet acting on the object.
b) An expression for the size of normal reaction N.
c) An expression for the size of the friction force Fr.
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Motion in one and two dimensions: Lesson 4 Semi-notes
Worked Example
Solution
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Motion in one and two dimensions: Lesson 4 Semi-notes
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Motion in one and two dimensions: Lesson 4 Semi-notes
Summary
•
The normal force is the force that a ...................... exerts on an
object. Normal force is usually designated N or FN
• The normal force act at ............................ to a surface .
• Its size changes depending on the size of the force exerted on a
surface.
• To solve inclined plane questions, the weight force is usually
resolved into components ...................... and ......................... to the
plane.
• The magnitude of the normal force, N, acting on an object on an
inclined plane is the same as the component of the weight force
perpendicular to the incline.
• The steeper the incline, the .................... the normal force.
• The acceleration of an object on a smooth inclined plane is given
by a = ........................
You should now be able to complete questions from your Heinemann text Physics 12
(3rd edition), Chapter section 1.3, page 22, questions 1, 2, 3, 4, 5, 9 and 10.
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Motion in one and two dimensions: Lesson 5 Semi-notes
Motion Lesson 5: Projectile Motion
What type of force produced the motion of the tennis ball?
The trajectory of a projectile motion is ...................................... in shape.
The diagram below shows a projectile motion, ignoring the effects of air resistance.
On this diagram sketch in different colours
a) The net force that produces this motion.
b) The velocity vectors throughout the motion.
c) The trajectory of the projectile.
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Motion in one and two dimensions: Lesson 5 Semi-notes
Here is a another diagram showing a projectile motion projected horizontally to the right. Successive
images show the projectile’s position after equal time intervals.
The horizontal component of a projectile motions is .........................................................
The vertical component of a projectile motion is .................................................................
Write down some motion equations which apply to the horizontal component of the motion.
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Motion in one and two dimensions: Lesson 5 Semi-notes
Write down some motion equations which apply to the vertical component of the motion.
Sketch motion graphs below for the
horizontal component of the motion.
Sketch motion graphs below for the
vertical component of the motion.
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Motion in one and two dimensions: Lesson 5 Semi-notes
The strobe photo below show a ball dropped vertically and another projected horizontally at the same
time.
Explain why both balls hit the ground at the same time.
The time in the air, or time of flight, is determined by what?
Additional Notes
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Motion in one and two dimensions: Lesson 5 Semi-notes
Worked Example
Solution
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Motion in one and two dimensions: Lesson 5 Semi-notes
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Motion in one and two dimensions: Lesson 5 Semi-notes
Oblique Projection
Here is a another diagram showing a projectile motion projected obliquely, that is , at an angle to the
horizontal to the right. Successive images show the projectile’s position after equal time intervals. Again,
air resistance is ignored.
On this diagram (above) sketch in different colours
a) The net force that produces this motion.
b) The velocity vectors throughout the motion.
c) The trajectory of the projectile.
For an oblique projection;
The Horizontal component of the motion is.......................................................................
The Vertical component of the motion is.......................................................................
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Motion in one and two dimensions: Lesson 5 Semi-notes
For an object (below) projected at a speed v at an angle θ;
a)
b)
c)
d)
Horizontal velocity = .............................throughout.
Initial vertical velocity = ................................
Vertical velocity at maximum height = .......................
Final vertical velocity = ....................................
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Motion in one and two dimensions: Lesson 5 Semi-notes
Worked Example
Solution
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Motion in one and two dimensions: Lesson 5 Semi-notes
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Motion in one and two dimensions: Lesson 5 Semi-notes
The Range Equation
The horizontal distance travelled by a projectile is called the ........... The range equation is a quick way of
finding the range.
Where:
R=
R = Range (m)
v = initial speed (ms-1)
θ = angle of projection (degrees)
g = acceleration due to gravity = 9.8 ms-2
The range is maximum
when θ = ........................
The Effcts of air Resistance
Describe the effects of air resistance on projectile motion.
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Motion in one and two dimensions: Lesson 5 Semi-notes
Summary
The trajectory of a projectile motion is ............................
Projectiles can be understood by analysing the ....................and ...................components
of the motion.
If we ignore air resistance,
The horizontal component of a projectile motion is constant ..........................
The vertical component of a projectile motion is constant ...................................
The net force is supplied totally by gravity or the weight force, W = mg.
Hence the .................................. is 9.8 ms-2 downwards.
An object dropped or projected horizontally from the same height will take the ................
.............. to reach the ground.
When air resistance is not negligible, the net force will no longer be constant and directed
downwards, and the trajectory will not be parabolic.
You should now be able to complete questions from your Heinemann text Physics 12
(3rd edition), Chapter section 1.4, page 29, questions 1, 3, 4, 5, 6, 7, 8 and 10.
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