Omolara Atinuke Physic Lab 1061 Projectile Motion and the Conservation of Energy Charles Swartz
Objective: We will predict the position of a ball that is shot at an angle using project motion and observe if the total mechanical energy is conserved. Introduction:
Energy conservation is the principle that describes the transformation of energy from one form to another: for a given system, as long as all the types of energy within the system are accounted for, the total energy of the system (closed) must be constant. This experiment is a demonstration of energy conservation in that the gravitational potential energy at the start of the launch is partially converted to kinetic energy
Procedure: Part 1 Calculating the Initial velocity of the ball from its range 1. Put the ball in the launcher and turn it to the middle position. Push the ball in one click. Fire the ball and observe where it lands. This is where a piece of white paper should be taped. Place a piece of carbon paper, carbon side down, on the white paper. 2. Fire 5 shots and record where they land. 3. The measured vertical distance should be from the mark on the barrel to the spot where the ball is released. 4. The horizontal distance should be measured from the release point to the edge of the paper. Then measure from the edge of the paper to the dots on the paper. Record this data in the table. Part 2 Find the initial velocity using the computer and photogates 1. Repeat Part 1 using the gate timing-projectile computer program and the two photogates. 2. Conduct 5 runs and record the initial velocities in the table. Compare to initial velocity calculated in Part 1 Part 3 Predicting the range of the ball when it is launched at an angle
1. Set the launcher at an angle between 30 and 60 degrees. Write down the set angle 2. Predict the time of flight and the horizontal distance using the data that was previously obtained 3. Shoot the ball six times and measure the distances and find the average. Record all in table provided. Part 4a the total mechanical energy of a ball and measuring height of trajectory 1. Keep the same settings of the launcher and photogates except change the direction of the launcher so that it fires straight up. 2. Run the timing program and measure the time between the ball blocking the two gates 3. Shoot three times. Record and retrieve the average 4. Shoot the ball and use a meter stick to measure the balls height. maximum Record the results. Find the mass of the ball and record the results. Analysis and Data: Table 14.1 Trial Number 1 2 3 4 5 Average Standard Deviation Total Distance Vertical distance = 123 cm Distance from Paper edge (cm) 8.8 11.1 11.4 14.1 27.8 14.64 146.64
Horizontal Distance to paper edge = 132 cm Initial Velocity = gx22y = 9.8(146.64)22 (123) = 3603. 7 cm/s = 3.6 m/s Calculated Initial velocity
Table 14.2 Trial Number 1 2 Initial Velocity (m/s) 2.9465 2.8216
3 2.9286 4 2.8959 5 2.8498 Average standard deviation 2.8828 How close are the values of the initial velocities obtained in Part 1 and Part 2? % error = 2.8828-3.62.8828 * 100%= 24.9% Table 14.3 Trial Number 1 2 3 4 5 6 Average Standard deviation Total Distance Vertical Distance =123 cm Initial Velocity = 2.8828 m/s paper edge = 150.4 cm Distances (cm) 8.5 9.3 9.3 9.2 9.7 9.6 9.3 159.7 Angle = 40 Horizontal distance to
Calculated time of flight = V0V02sin-4ghg = 2.8828(2.8828)2sin(40)49.82(0.123)(9.82) = 0.3663 s Predicted Range: (v0cos) tmax = (2.8828)(cos 40)(0.3663) = Percent error: Does the height of the release point change when the launcher is aimed at angle? Estimate the precision of the predicted range. From the precision of the y and q values used does this estimate agree with your measured values? How many of the final ten shots landed within this range? Table 14.4 Trial Number 1 2 Time (s) .0385 .0386
3 Average time Initial Speed Maximum Height Ball Mass Initial Speed/ Initial KE Final PE % Difference
.0385 .0385
70 cm 9.6 g
We have ignored friction throughout this experiment. How does friction affect the value in Table 14.5 for the KE? How does friction affect the value in Table 14.5 for the potential energy Conclusion:
In order to truly demonstrate energy conservation in the real world, one must take into account losses of energy due to friction as well. Therefore, change in total energy of a closed system is defined as the sum of the changes in kinetic and potential energies minus the work done by friction, and this must equal zero. In this experiment, the work done by friction was measured by trial and error; different height settings were used so that as the ball (projectile) traveled through the launch track it came to a rest just before exiting and track. At this height setting, there is no kinetic energy change, and therefore work done by friction must equal the change in potential energy.