Exercise 6: The conservation of energy and momentum

Transcription

1 Physics 221 Name: Exercise 6: The conservation of energy and momentum Part 1: The projectile launcher s spring constant Objective: Through the use of the principle of conservation of energy (first law of thermodynamics), you will determine the spring constant of the spring in the projectile launcher. Introduction: In Lab 5, you will be using the projectile launcher and the ballistic pendulum to demonstrate the conservation of energy. However, there is another way in which the principle may be shown without the ballistic pendulum. Consider the system to be the projectile launcher only. When you load the projectile, you are storing potential energy in the spring of the launcher. When you fire the projectile, the stored energy of the spring translates into the kinetic energy of the projectile. This can be tested. Relevant equations: 1. What is the equation governing the potential energy in the spring of the projectile launcher? Within the equation, identify clearly what variables are to be measured (and their units) and what variables are to be determined. 2. What is the equation governing the kinetic energy of the projectile in motion, immediately as it leaves the muzzle of the launcher? Again, clearly identify the variables that are to be measured and their units.

2 3. Finally, apply the conservation of energy principle, and write an equation that isolates the spring constant of the projectile launcher variable on one side. Procedure: 4. Draw a sketch of the equipment setup to be used to measure all the variables in questions 1 and 2. Some variables may require a couple different measurements (hint: velocity).

3 Data and analysis: 5. Set up the experiment and run it as a class demonstration. Record the information in the table below, then perform the calculations that yield the spring constant of the projectile launcher. Run the demonstration ten times, using different initial conditions.

4 Results and conclusion: 6. Report the mean and standard deviation of the spring constant of the projectile launcher. Pay attention to significant figures and units. 7. What was the very large assumption about this experiment? Hint: see section 7.3 of the text. Design/explain a way to test this assumption. Part 2: Testing the conservation of momentum in this experiment 8. In this experiment, you discovered that the amount of potential energy gained by the pendulum and ball was not very close to the amount of kinetic energy lost by the ball. What type (elastic or inelastic) of collision does this illustrate? How can you tell? Consider the collision between the fired ball and the pendulum this way: initially, there is a yellow or steel plastic ball with a constant initial velocity and the pendulum is at rest. A moment after the collision (literally as the ball enters the cavity in the pendulum), the

5 pendulum and ball are moving in the same direction as the ball initially. Clearly, the final velocity of the ball and pendulum is less than the initial velocity of the ball. 9. Draw the before and after picture of Lab 5, as described above. Label masses as appropriate, and add (and label) velocity vectors, using our usual notation. 10. Set up the conservation of linear momentum equation between the initial and final states of the collision in Lab 5. Note that the final state is not when the pendulum has reached its greatest height; it s just after the collision with the ball.

6 11. Using your team s values from Lab 5, determine the value of the initial momentum and the value of the final momentum. Be careful about sig figs and units! Note that you can figure out the final velocity from conservation of energy (that is, the gravitational potential energy of the final measured angle had to come from somewhere). 12. Does the experiment show that linear momentum is conserved (at least to within 10% or so)? How does this support your answer to question 8?

7 Random example of conservation of momentum and frames of reference 13. a. In a fully elastic collision, an object of mass 5.0 kg, travelling horizontally on a frictionless surface at 16 m/s, strikes a stationary object of mass 3.0 kg. After the collision, the larger object is observed to have a velocity of magnitude 12 m/s at 30 to its original direction of motion. What is the velocity (magnitude and direction) of the smaller object? b. Describe quantitatively where the center of mass of the two particles in problem 2 is, initially.

8 c. Rewrite the initial conditions of problem 2a from a center of mass frame of reference, then re-solve the problem. Show that the solution is equivalent to the solution in problem in part a. Hint: drawing vectors may help.