Conservation of Energy Through the LoopDLoop into Projectile

1
Conservation of Energy Through the Loop-D-Loop
into Projectile

• By Eric Lum, Matt Ryan, and Tim Carroll

2
The Apparatus
3
The Walkthrough

• We will be dropping a car from the top of the
  ramp.
• It will then travel through the loop-d-loop and
  finally undergo projectile motion.

• We will be doing.
• Computation centripetal force at the top of the
  loop.
• Proving conservation of energy throughout the
  experiment.
• The horizontal displacement of the car during
  projectile motion.

4
Data Collection

• Velocity at the top and bottom of the loop
• Take photogate reading as the car passes through
  each point.

• Initial Velocity before projectile motion
• Calculate using the conservation of energy
  equation.

• Height of track
• Find by adding the measurements of the height of
  track off the table with the height of the table

5
Equations

• Energy Before
• PEi mghapparatus height of table
• PEi ____
• Energy at the top of loop
• EnergyKEtop of loop PEtop of loop PEi
• E1/2mv2 mghloop height of table PEi
  _______
• v was found by using the photo gate
• Energy after the loop but before projectile
  motion
• Energy KEon flat track after loop PEon flat
  track after loop 1/2mv2of car mghof table
  _______
• V was found by using the photo gate
• Centripetal Force at top of loop
• Fcmacm(v2/r)
• Horizontal Displacement
• Kinematic Vix ?X/t

6
Data
7
Data w/ Substitutions

• Energy Before
• PEi (.035 kg)(9.8 m/s/s)(1.5 m)
• PEi .51 J
• Energy at the top of loop
• Energy (1/2)(.035 kg)(2 m/s)2 (.035 kg)(9.8
  m/s/s) (1.15 m) .46 J
• Energy after the loop but before projectile
  motion
• Energy (1/2)(.035 kg)(2.65 m/s)2 (.035 kg)(9.8
  m/s/s)(.92 m) .44 J
• Centripetal Force at top of loop
• Fcmac (.035 kg)(2 m/s)2 / (.115 m) 1.2 n
• Horizontal Displacement
• Kinematic 2.65 m/s ?X/(.32 sec)
• ?X .848 m

8
Results

• Energy Before .51 J
• Energy At Top Of Loop .46 J
• Energy After .44 J
• Centripetal Force 1.2 n
• Horizontal Displacement .848 m

9
Sources Of Error

• Friction
• Measuring
• Estimations
• Rounding