Understanding Energy and Momentum in Softball Hitting

Energy and Momentum in Hitting a Softball Shaina Mann

Objects Used Softball: can vary in size and weight Used a 6 oz (170 g) softball Bat: can vary in size and weight Used a 23 oz (652 g), .84 m bat

Question Are energy and momentum conserved when hitting a softball off a tee?

Energy Kinetic: energy of motion Linear: due to translational motion Angular: due to rotation of object Potential: energy of position Total energy: Kinetic energy + Potential energy In an isolated system, energy is conserved. This, however, is not an isolated system. In hitting a softball, potential energy of bat kinetic energy of bat kinetic energy of ball

Momentum Linear: measure of an object s translational motion Angular: rotational analog of linear momentum Total momentum: Linear + Angular In an isolated system, momentum will be conserved. However, this is not an isolated system. In hitting a softball, momentum of bat momentum of ball

Forces at play Potential energies of bat and ball Kinetic energies of bat and ball (angular and linear) Momentum of bat and ball (angular and linear) Energy and momentum of hitter Elasticity of bat and ball Heat generated by friction

Equations Needed Linear Kinetic Energy=1/2*m*v^2 (Joules) Potential Energy=m*g*h (Joules) Angular Kinetic Energy=1/2*I*w^2 (Joules) Linear Momentum=m*v (kg*m/s) Angular Momentum=I*w (kg*m^2/s) Moment of inertia of rod (I)=m*L^2/3 or m*L^2/12 (kg*m^2)

Time vs. Linear Kinetic Energy 160 150 140 130 Bat 120 Kinetic Energy (J) 110 100 Moment of contact 90 80 70 60 50 40 30 Ball 20 10 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 0.85 Time (sec) Kinetic Energy at moment of contact: 151 J Kinetic Energy at end of swing: 91.8 J Difference: 59.2 J

Time vs. Potential Energy 16 15 14 13 Potential Energy (J) 12 11 10 Bat 9 8 7 Moment of contact 6 5 4 3 2 Ball 1 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 0.85 Time (sec) Potential Energy at moment of contact: 8.7 J Potential Energy at end of swing: 18.4 J Difference: 9.7 J

Time vs. Angular Kinetic Energy of Bat 160 Moment of contact Angular Kinetic Energy of Bat (J) 140 120 100 80 60 40 20 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 Time (sec)

Time vs. Angular Kinetic Energy of Hitter 400 Moment of contact Angular Kinetic Energy of Hitter (J) 350 300 250 200 150 100 50 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 Time (sec)

Time vs. Total Energy of Bat and Ball 350 Moment of contact 300 Total Energy of Bat and Ball (J) 250 200 150 100 50 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 Time (sec) 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 Total Energy at moment of contact: 305 J Difference: 165 J Total Energy at end of swing: 140 J

Time vs. Linear Momentum 15 14 13 12 Bat Momentum (kg*m/s) 11 10 Moment of contact 9 8 7 6 5 4 Ball 3 2 1 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 0.85 Time (sec)

Time vs. Total Linear Momentum of Bat and Ball 16 15 14 Total Momentum (kg*m/s) 13 12 11 10 Moment of contact 9 8 7 6 5 4 3 2 1 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 Time (sec) 0.7 0.725 0.75 0.775 0.8 0.825 0.85 Total momentum at moment of contact: 14.8 kg*m/s Total momentum at end of swing: 11.2 kg*m/s Difference: 3.6 kg*m/s

Time vs. Angular Momentum of Bat 30 Angular Momentum of Bat (kg*m^2/s) Moment of contact 25 20 15 10 5 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 Time (sec)

Time vs. Angular Momentum of Hitter 100 Moment of contact 90 80 Angular Momentum (kg*m/s) 70 60 50 40 30 20 10 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 Time (sec)

Time vs. Total Momentum of Bat and Ball Total Momentum of Bat and Ball (kg*m/s) 30 Moment of contact 25 20 15 10 5 0 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 Time (sec) 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 Total Momentum at moment of contact: 24.7 kg*m/s Total Momentum at end of swing: 14.5 kg*m/s Difference: 10.2 kg*m/s

Was total energy conserved? Energy was not conserved Friction forces Partially inelastic collision Tee might have absorbed some of the energy

Were linear and angular momentum conserved? Momentum was not conserved Partially inelastic collision Tee might have absorbed some of the force Person swinging had momentum as well, which was hard to measure

Problems Angular velocity and momentum of hitter were difficult to calculate, and thus total energy and total momentum calculations may have been off as well The softball tee absorbed energy as well, making it difficult to determine if more energy may have been conserved had the tee not been there

Next Steps Determine a better way to measure energy and momentum of the hitter Determine a way to measure the energy and momentum absorbed by the tee Compare hitting softball off a tee to hitting a pitched ball

References http://library.thinkquest.org/11902/physics/mom entum.html http://www.real-world-physics- problems.com/physics-of-hitting-a-baseball.html http://www.racquetresearch.com/angmom.htm http://www.swing-smarter-baseball-hitting- drills.com/physics-of-hitting-a-baseball.html