PHYSICS 231 Lecture 9: Revision

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PHYSICS 231Lecture 9 Revision

• Remco Zegers
• Walk-in hour Thursday 1130-1330
• Helproom

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The slides about friction are in lecture 8!!
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TRIGONOMETRY
SOH-CAH-TOA sinopposite/hypotenuse cosadjacent/
hypotenuse tanopposite/adjacent
Pythagorean theorem
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Units

• Convert all units in your problem to be in the SI
  system
• When adding/subtracting two quantities check
  whether their units are the same.
• If you are unsure about an equation that you want
  to use, perform the dimensional analysis and make
  sure that each part of the equation that is set
  equal/subtracted/added have the same dimensions
• When 2 quantities are multiplied, their units do
  not have to be the same. The result will have as
  unit the multiplied units of the quantities being
  multiplied.
• Sin, cos and tan of angles are dimensionless

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Solving a quadratic equation
At2Btc0

• Use the equation
• CHECK THE ANSWER
• OR just calculate it!
• t2(B/A)tC/A0 and use (td)2t22dtd2
• t(B/2A)2-B2/4A2C/A0
• t-B/2A??(B2/4A2-C/A)

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Constant velocity
Constant acceleration
Constant motion
x(t)x0v0t½at2
x(t)x0
x(t)x0v0t
x(m)
x(m)
x(m)
t
t
t
v m/s
v m/s
v m/s
v(t)0
v(t)v0at
v(t)v0
t
t
t
a m/s2
a m/s2
a m/s2
a(t)0
a(t)0
a(t)a0
t
t
t
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x
v
t
time
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Vector operations in equations
(xab,yab)
y
(xb,yb)
B
(xa,ya)
A
x
XaAcos(?) YaAsin(?) length/magnitude of A
?(Xa2Ya2)
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Parabolic motion decompose x and y directions
t0
t4
t3
t2
t1
t5
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Parabolic motion
X(t)X0V0cos?t Y(t)Y0V0sin?t-1/2gt2
t0
t4
t3
t2
t1
t5
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2D motion

• When trying to understand the motion of an object
  in 2D decompose the motion into vertical and
  horizontal components.
• Be sure of your coordinate system is the motion
  of the object you want to study relative to
  another object?
• Write down the equations of motion for each
  direction separately.
• If you cannot understand the problem, draw motion
  diagrams for each of the directions separately.
• Make sure you understand which quantity is
  unknown, and plug in the equation of motions the
  quantities that you know (givens). Then solve the
  equations.

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Newtons Laws

• First Law If the net force exerted on an object
  is zero the object continues in its original
  state of motion if it was at rest, it remains at
  rest. If it was moving with a certain velocity,
  it will keep on moving with the same velocity.
• Second Law The acceleration of an object is
  proportional to the net force acting on it, and
  inversely proportional to its mass Fma
• If two objects interact, the force exerted by the
  first object on the second is equal but opposite
  in direction to the force exerted by the second
  object on the first F12-F21

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General strategy for problems with forces

• If not given, make a drawing of the problem.
• Put all the relevant forces in the drawing,
  object by object.
• Think about the axis
• Think about the signs
• Decompose the forces in direction parallel to the
  motion and perpendicular to it.
• Write down Newtons first law for forces in the
  parallel direction and perpendicular direction.
• Solve for the unknowns.
• Check whether your answer makes sense.

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A snowball is launched horizontally from the top
of a building at v12.7 m/s. If it lands 34 m
away from the bottom, how high was the building?
V012.7 m/s
h?
d34m
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A red ball is thrown upward with a velocity of
26.8 m/s. A blue ball is dropped from a 13.3 m
high building with initial downward velocity of
5.00 m/s. At what time will the balls be at the
same height.
Vo-5.00
h13.3m
V026.8
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A car starts at rest and travels for 5.09 s with
uniform acceleration of 1.48 m/s2. The driver
then brakes, causing uniform acceleration of
-1.91 m/s2. If the brakes are applied for 2.96 s
how fast is the car going after that?
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A 2000 kg sailboat is pushed by the tide of the
sea with a force of 3000 N to the East. Because
of the wind in its sail it feels a force of 6000
N toward to North-West direction. What is the
magnitude and direction of the acceleration?
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T
T
900
1kg
A mass of 1 kg is hanging from a rope as shown in
the figure. If the angle between the 2 supporting
wires is 90 degrees, what is the tension in each
rope?
ThorR