7/28/2019 Mit 2001 Contest Table Calculations
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MITandPendulum contest calculations
By Alex Slocum
Last modified 8/20/01
These are NOT official numbers, verify via the contest
website!
Assumptions: Ball bearing supports make pendulum 95%+ efficient
(ignore friction)
Strategy Calculations: Impart enough velocity to pendulum to
make it rise and dump balls
Pendulum inertia calculations
Length below pivot, Lp_1 (m) 1.150
Length above pivot, Lp_2 (m) 1
Cross-section, w (m) 0.075
Thickness, t (m) 0.0015
Denisty, rho (kg/m^3) 1400
Moment of inertia of beam, Jbeam (kg-m^2) 0.4258
Mounting shaft inertia calculations
Shaft diameter, Ds (m) 0.04
Shaft Length, Ls (m) 0.5
Shaft density, rhoshaft (kg/m^3) 4900
Moment of inertia of beam, Jshaft (kg-m^2) 0.0006
Plate length, Lp (m) 0.25
Plate width, wp (m) 0.05
Plate thickness, tp (m) 0.012
Moment of inertia of plate, Jplate (kg-m^2) 0.0038
Ball inertia calculations
Balls below pivot, NBb 6
Balls above pivot, NBa 9
Diameter of balls, Db (m ) 0.05
Mass of balls, mb (kg) 0.055
Moment of inertia of balls, Jballs (Kg-m^2) 0.0040
Total pendulum moment of inertia, jp (kg-m^2) 0.43
Total pendulum mass, mp (kg) 2.18
Location of center of mass from pivot, rcm (m) -0.018
Displacement and velocity calculations
Angle from hanging vertical to raise, thetadump (deg) 110
Angle at which drive system loses contact, thetapush (deg)
20Increase in potential energy, PE (kg-m^2/sec^2) 0.50
Required angular velocity, wpend (rad/sec) 1.52
Required tip velocity, Vcar (m/sec) 1.74
Concept 1 Calculations: Push from standing start
Distance between pendulum tip and arc surface, dpa (m) 0.010
Distance available for travel, dtravel (m) 0.405
Acceleration to achieve velocity in distance, areq (m/sec^2)
3.75
"g's" acceleration required 0.38
Coefficient of friction between wheels and ground, mu 0.38
Max attainable coefficient of friction, mureal 0.50
Min distance required for Vcar given mureal, dreal (m) 0.31
Concept 2 Calculations: Conservation of energy and
momentumDistance to travel to impact, dtravel2 (m) 0.405
Vehicle mass, mvehicle (kg) 4
Reasonable acceleration, areal (m/sec^2) 4.9
Velocity at impact, vimpact (m/sec) 1.99
Equivalent linear point mass of pendulum, mpend (kg) 0.328
Resulting tip velocity after impact, Vtipimpact (m/sec) 3.68
Concept 3 Calculations: Castle-based spring launchers
Constant force spring force, Fspring (N) 11
Constant force spring travel, Xspring (m) 0.25
