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 Potential: energy of position 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 Bat Moment of contact Kinetic Energy (J) Ball Time (sec) Kinetic Energy at moment of contact: 151 J Difference: 59.2 J Kinetic Energy at end of swing: 91.8 J
Time vs. Potential Energy Bat Potential Energy (J) Moment of contact Ball Time (sec) Potential Energy at moment of contact: 8.7 J Difference: 9.7 J Potential Energy at end of swing: 18.4 J
Time vs. Angular Kinetic Energy of Bat Moment of contact Angular Kinetic Energy of Bat (J) Time (sec)
Time vs. Angular Kinetic Energy of Hitter Moment of contact Angular Kinetic Energy of Hitter (J) Time (sec)
Time vs. Total Energy of Bat and Ball Moment of contact Total Energy of Bat and Ball (J) Time (sec) Total Energy at moment of contact: 305 J Difference: 165 J Total Energy at end of swing: 140 J
Time vs. Linear Momentum Bat Moment of contact Momentum (kg*m/s) Ball Time (sec)
Time vs. Total Linear Momentum of Bat and Ball Moment of contact Total Momentum (kg*m/s) Time (sec) Total momentum at moment of contact: 14.8 kg*m/s Difference: 3.6 kg*m/s Total momentum at end of swing: 11.2 kg*m/s
Time vs. Angular Momentum of Bat Moment of contact Angular Momentum of Bat (kg*m^2/s) Time (sec)
Time vs. Angular Momentum of Hitter Moment of contact Angular Momentum (kg*m/s) Time (sec)
Time vs. Total Momentum of Bat and Ball Moment of contact Total Momentum of Bat and Ball (kg*m/s) Time (sec) Total Momentum at moment of contact: 24.7 kg*m/s Difference: 10.2 kg*m/s Total Momentum at end of swing: 14.5 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/momentum.h tml 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