Energy, Kinematics, and Buoyant Forces Lab

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Energy, Kinematics, and Buoyant Forces Lab

• Andrew Roth, Evan Levine, Eric Rohrs, Keya Vash

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Explanation

• We will release a ball onto a track
• It will be projected off the table, into a
  graduated cylinder full of water
• Using conservation of energy, into kinematics,
  into buoyant forces, we will be able to determine
  the acceleration of the ball as it is falling in
  the water, and the final velocity of the ball
  before it hits the bottom

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Measurements

• Height of ball on track______
• Mass of ball______
• Density of liquid_____
• Radius of loop_____
• Volume of ball_____
• Height from floor to track_____
• Height of graduated cylinder_______
• Height from table to top of graduated
  cylinder______
• Time it takes for ball to sink (using stopwatch)
  ______

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Ball on track

• PEi KEf PEf
• mghi 1/2mv2 mghf
• Using the initial height of the ball, we will
  calculate the velocity of the ball at the highest
  point of the loop.

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Ball after loop

• PEi KEf
• mghi 1/2mv2
• Using the initial height of the ball, we will
  determine what the final velocity of the ball
  will be just before it is projected off the table

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Ball flying into cylinder

• YViyt .5gt2
• Using the y-displacement of the ball as it
  travels from the table to the cylinder, we will
  determine the time it takes for the ball to reach
  the cylinder.

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Placing the graduated cylinder

• Vix x/t
• Using the initial velocity of the projected ball,
  and the time it takes to reach the cylinder, we
  will calculate a distance at which to place the
  cylinder

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Ball hitting water

• Vfy Viy gt
• Using the time previously calculated, and
  plugging in Viy 0m/s, we can figure out the
  velocity of the ball as it hits the water

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Ball falling in water

• Fb mg ma
• pgV mg ma
• Using the mass of the ball, the density of the
  liquid, and V, the volume of the liquid, solve
  for the acceleration of the falling ball
• Vfy Viy at
• Using the time acquired by the stop watch, the
  initial velocity at the top of the water, and the
  acceleration as it is falling, calculate the
  final velocity of the ball at the bottom of the
  cylinder

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Measurements

• Height of ball on track__.57m_
• Mass of ball___.01 kg____
• Density of liquid__1000 kg/m3____
• Radius of loop___.15 m___
• Volume of ball__9 mL____
• Height from floor to track__.94 m__
• Height of graduated cylinder__.44 m_____
• Height from table to top of graduated
  cylinder__.5 m_
• Time it takes for ball to sink (using stopwatch)
  1.9 sec

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Calculations

• mghi 1/2mv2 mghf
• (9.8 m/s2)(.57 m) v2/2 (9.8 m/s2)(.3 m)
• v 2.3 m/s
• mghi 1/2mv2
• (.01 kg)(9.8 m/s2)(.57 m) ½(.01 kg)(v)2
• Vix 3.3 m/s
• ?YViyt .5gt2
• -.50 m (0 m/s)(t) .5(9.8m/s2)(t2)
• t .32 seconds

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Calculations continued

• Vix ?x/t
• ?x Vixt
• ?x (3.3m/s)(.32 seconds)
• ?x 1.05 meters
• Vfy Viy gt
• Vfy 0 m/s (-9.8 m/s2)(.32 seconds)
• Vfy -3.1 m/s (velocity of ball as it
  hits water)

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Even more calculations

• pgV mg ma
• (1000 kg/m3)(9.8 m/s2)(9e-6) (.01 kg)(9.8
  m/s2) (.01 kg)(a)
• a -.98 m/s2
• Vfy Viy at
• Vfy -3.1 m/s (-.98 m/s)(1.9 seconds)
• Vfy -4.9 m/s

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Results

• Acceleration (a) ___-.98 m/s2____
• Final velocity (Vfy) __-4.9 m/s__

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Sources of Error

• Viscosity (fluid friction) changes the
  acceleration as the ball falls, and we did not
  take that into account
• Track friction, as well as air friction effect
  how the ball moves and where it is projected, and
  that also was not taken into account
• Human error also plays a part
• Using a stopwatch to get the time it takes the
  ball to sink
• Measuring the meniscus line, or starting the ball
  from the exact spot on the track