GUIDE QUESTIONS 1. Suppose the ball with half the mass is used and is projected out of the launcher with the same speed. How does the increase in height of the system now compared with that when the original ba ll was used? Defend your answer. Answer: (Reference System: System: Pendulum) If the half-weighed ball was was used in this same-speed simulation, the observable height will be much smaller than the observable height when the original ball was used. Consider this scenario: m1: 10 grams
m1/2: 5 grams
m2: 15 grams
v: 20 m/s
Consider the equation used in the experiment:
:
( ) 2 2
Rearranging the given equation in terms of y:
: ( ) (2) Substitutions of the given to equation:
:
()() (+) +)(∗.)
y if the m1 used is the original
:
() )() (+) +)(∗.)
y if the m1 used is the half-weighed Answer (y): 1.275510204 m
Answer (y): 3.265306122 m
(Reference System: Launcher alone with the “pendulum”; assuming that air -resistance -resistance is negligible) If the half-weigh ball used in this same-speed simulation, the observable height will be much larger than the observable height when the original ball was used. The force of the ball will be relatively large compared to the force exerted by gravity on the ball; hence, the height of the half-weighed ball will be much larger. 2. Suppose the launcher is positioned higher above the table top. How does this change affect the computed initial speed of the ball? Defend your answer. Answer: There will be no change in the initial speed; In Kinematics , the horizontal component of the velocity remains constant while the vertical component of the velocity is the only component changing. When the height increases, the range also increases, making the velocity constant as long as that the x-component range is not that d eviated;
3. A 50-gram bullet is fired horizontally into a 5 -kilogram block of wood suspended by a long cord. The bullet sticks in the block. Determine the velocity of the bullet if the inelastic collision causes the block to swing 0.10-meters above its initial level. Given: m1: 50 grams ~ 0.05 kilograms
m2: 5 kilograms
dy: 0.10 meters Unknown: velocity of the bullet Working Equation:
:
( ) 2
Substitution:
: Answer: Velocity of the bullet: 141.4 m/s
(0.055) √ 2 ∗ 9.8 ∗ 0.10 0.05
ANALYSIS 1. Which method (ballistic method or trajectory method) is more accurate in determining the initial speed of the ball? Defend your answer. Answer: Ballistic method; the farthest distance that the pendulum will swing is the point where its potential energy is at its peak. Observing the conservation of mechanical energy (concept of the pendulum), the potential energy on the maximum angle that the pendulum covered is also its kinetic energy after collision. Also using the law of conservation of momentum, the velocity can then be extrapolated by using the following conditions. 2. In Part 1 of the experiment, is the total momentum of the system conserved? Explain. Answer: Yes; by definition, the total momentum of the system is conserved if and only if the net external force on the system is zero. Since there are no external force acting on the system, hence, total momentum is conserved. 3. In Part 1 of the experiment, when is the total energy of the system not conserved? When is the total energy of the system conserved? Answer: It is a fundamental law of physics that the total energy of the system must be conserved at all times. Within the system, however, energy can transform into any other form of energy. Since the collision is inelastic, it follows that the kinetic energy of the system is not conserved (some of the kinetic energy is converted into heat energy, some were also converted to sound energy). Since the system also follows the principle of a p endulum, the potential energy at the maximum angle is equivalent to its kinetic energy before collision.
CONCLUSION 1. What causes the total momentum of the system to change? Answer: (Defining the total momentum and the conservation of the total momentum) The total momentum of the system is the vector summation of individual momenta occurring in the system. It is a fundamental law of physics that the total momentum of the system should always be conserved unless an external force is acting on the system. External forces are responsible for the changes in the momentum of the system. 2. When the total momentum of the system is conserved, is the total energy of the system conserved as well? Answer: Yes; Fundamental laws of Physics states that momentum and the energy of the system should always be conserved. However, in the system, energy can transform from one form to the other; in an inelastic collision, it follows that the kinetic energy of the system is transformed into other forms energy, while in an elastic collision kinetic energy of the system is always conserved; 3. Is the total momentum of the system conserved in all kinds of collisions? Explain. Answer: Yes; In an elastic collision and inelastic collision, momentum and energy is always conserved; however, for an inelastic collision the kinetic energy of the system is not conserved because the energy is transformed from one form to the other (i.e. sound energy, heat energy, and energy expelled during the deformation process).
