CONSERVATION OF ENERGY
The purpose of this experiment is to calculate the gravitational potential energy through experimental values, to calculate the theoretical potential energy given the experimental kinetic energy in an isolated system while also using the kinetic energy to find the spring constant, and to compare kinetic energies and potential energies in an isolated system to see if they are equivalent.
To calculate the gravitational potential energy through experimental values, we dropped a racquetball from a height of one meter and measured the height at which the ball bounced back up from the ground. These values were used to find the total mechanical energy that was lost.
In order to calculate the theoretical potential energy of an object, we shot a “superball” from a ballistic launcher at three different settings and measured the height the ball traveled as well as the velocity of the ball when it left the launcher.
Using the values of the velocities at different settings and measuring the different distances the spring was compressed, we calculated the spring constant of the spring inside the ballistic launcher.
Finally, to compare the potential and kinetic energies within an isolated system, we pushed an air-cart along a frictionless air-track and measured the velocity and vertical distance traveled. We used these values to calculate the potential and kinetic energies and see if these calculations fell within the range of uncertainty.
Part A: Gravitational Potential Energy
Mass of racquetball: 0.0392 kg
Height at Bounce-Back (m)
Average Height at Bounce-Back: 0.742 m
Formula needed to find Initial Potential Energy:
Given mass is .0392 kg, and gravitational acceleration is 9.81 m/s2, and the height at which the ball was located preceding release was 1 m, we can solve to find the initial potential energy of the racquetball.
U= 0.0392 × 9.81 × 1.0
U= .385 J
Formula needed to find the potential energy at bounce-back:
Given mass is .0392 kg, and gravitational acceleration is 9.81 m/s2, and the average height at which the ball was located after bouncing back was .742 m, we can solve to find the new potential energy of the racquetball.
U= 0.0392 × 9.81 × .742
U= .285 J
The amount of mechanical energy lost can be found by the formula:
UA+ KA= UB+ KB
Since at both positions, there is zero kinetic energy, the formula will be reduced to:
By substituting the values from the previous calculations, we can find the difference in mechanical energy.
.385 J= .285 J
Due to simple mathematics, we can easily see that there is a difference of .1 J in mechanical energy from initial to final positions. Because the value at the second position is lower, .1 J of mechanical energy is lost.
This mechanical energy may possibly be lost due to air resistance or a transfer of energy from the ball to the floor because of friction.
Part B: Conservation of Energy in Vertical Motion
Short Distance (m)| Short Velocity (m/s)| Medium Distance (m)| Medium Velocity (m/s)| 0.52| 3.41| | 1.31| 5.32| |
0.5| 3.28| | 1.43| 5.64| |
0.54| 3.47| | 1.3| 5.51| |
0.61| 3.52| | 1.18| 5.22| |
0.44| 3.23| | 1.41| 5.44| |
0.522| 3.382| Average| 1.326| 5.426| Average|
0.061806149| 0.110526015| Std Dev| 0.100149888| 0.163340136| Std Dev|
Long Distance (m)| Long Velocity (m/s)|
2.4| 7.32| |
2.26| 7.01| |
2.33| 7.26| |
2.29| 7.15| |
2.19| 6.97| |
2.294| 7.142| Average|
0.078294317| 0.15221695| Std Dev|
To calculate the height the ball should have reached given the experimental averages of velocity, we must apply the following formula:
UA+ KA= UB+ KB
U=mgh, and K=12mv2
When the ball is moving out of the ballistic launcher and passing...