CONSERVATION OF ENERGY LAB REPORT

1 CONSERVATION OF ENERGY Felecia Hassan, Lab Partner: Ariela Rodriguez Section:007, 10/30/2023

2 I. DESCRIPTION / OBJECTIVE The main purpose of this lab was to explore the total energy in multiple mechanisms including free fall, and springs. The total energy of and mechanism can be described by the equation E total = KE + PE . The law of Conservation of energy states that energy is neither created nor destroyed. In other word, the total energy ( E total ¿ of any mechanism should be the same throughout the mechanism. With this law any changes in KE should be offset by changes in PE and vice versa. This lab included the use of a Capstone, motion sensor II, photogate sensor, small bench clamp, double clamp, 90 cm rod, 40 cm rod, brass spring (taped to horizontal rod 25 cm from vertical rod), hook masses, index cards, 30 cm string with loops at both ends, calipers, rubber tube, paper tube about 2.5 cm in diameter, 2 meter ruler, 6 inch ruler, 12 inch ruler, and tape. II. THEORY During the lab my lab partner and I reviewed examined the mechanisms with both conservative and non-conservative forces. When a force is applied onto a mass and the path taken by the mass influences the force, this force is a non-conservative force. If the path taken by mass does not influence its force, this force is a conservative force. Conservative forces apply to mechanisms such as the force in a spring or the uniform force due to gravity. The conservative force is defined by this integral : During Section 3 of the lab my lab partner and I aslso explored the relationship between total energy and the velocity of a free falling mass using the equation V = √ 2 gh . We get this equation by first considering two equations : 1. the equation for total energy of the tube near the

4 Percent Eror = 2.1856 − 2.215 2.215 X 100% Percent Eror = 1.33 PART IV DATA/ CALCULATIONS / GRAPHS VELOCITY OF TUBE AT VARYING HEIGHTS TRIAL Velocity (m/s) at h= 7 cm Velocity (m/s) at h= 15 cm 1 1.0629 1.5269 2 1.1978 1.5250 3 1.1208 1.4601 4 1.1445 1.4802 5 1.1467 1.4190 Mean 1.1345 1.48224 Standard deviation 0.043749221707363 0.040783751666564 a. When h= 7 cm = 0.07 m a. v ( theoretical value ) = √ 2 gh b. v ( theoretical value ) = √ 2 ( 9.18 m / s 2 ) ( 0.07 m ) c. v ( theoretical value ) = 1.173 m s Percent Eror = mean experiemental velocity − theoretical velocity theoreticalvelocity X 100% Percent Eror = 1.1345 − 1.173 1.173 X 100% Percent Eror = 3.85% a. When h= 15 cm = 0.15 m a. v ( theoretical value ) = √ 2 gh b. v ( theoretical value ) = √ 2 ( 9.18 m / s 2 ) ( 0.15 m ) c. v ( theoretical value ) = 1.17155 m s Percent Eror = mean experiemental velocity − theoretical velocity theoreticalvelocity X 100% Percent Eror = ( 1.1345 − 1.7155 ) 1.7155 X 100% Percent Eror = 33.86%

5 PART V (PENDULUM ) LAB DATA POSITION (m) VELOCITY (m/s) ACCELERATION ( m s 2 ) Lowest point 0.2449 - 1.02357 -4.5645 Zero Crossing (1) - 0 0 Highest Point 0.8484 1.1537 4.57241 Zero Crossing (2) - 0 0 *My lab partner and I were unable to determine values for Zero Crossing (1) and Zero Crossing (2) due to timing. Based on the graph produced, Zero Crossing (1) should be some value between 0.2449 m and 0.8484 m. Similarly, Zero Crossing (2) should be some value between 0.8484 m and 0 m. PART V CALCULATIONS k ( Spring Constant ) = F ( force ) h ( distance ) k ( Spring Constant ) = mg h ( distance ) DISTANCE V. POSITION ACCELERATION V. POSITION VELOCITY V. POSITION

7 a. From the data that my lab partner and I have collected I would assume that there is no friction in the experiment. However, air friction may be an effector of the velocity. 4. Is the conservation of energy observed? Why or why not? EXPLAIN ( pg. 4 ) a. According to our data energy is conserved, since there is little variation between the experimental and theoretical velocity values ( with the exception of one portion of the lab ) we assumed that the energy is conserved. 5. As the pendulum swings down the string exerts a force on the mass. Does this force contribute to PE? Why or why not? a. The mass of the string is negligible. As a result the tension created by the string is equal ( and opposite in magnitude) of the normal force of the mass . They would essentially cancel each other out, and have no effect on the potential energy. 6. Compare your measured velocities to the theoretical values. What contributes to the change in PE for the pendulum? a. Based our calculations my lab partner and I concluded that the height in which the tube is dropped contributes to the change in PE for the pendulum. 7. Does your intuition about the motion correspond to what the graphs are displaying? For example, is the acceleration maximum or minimum when the velocity is zero? When the velocity is maximum is the acceleration maximum or minimum? (pg. 7) a. Yes, when the velocity is 0, the acceleration is at its maximum, and when acceleration is 0 velocity is at its maximum . 8. Is there kinetic energy that is not given by 1 2mv2 ? If so, this would be worthwhile mentioning in your error analysis. (Hint: There are at least two items one might notice here.)

8 a. Elastic potential energy of the spring and vertical potential energy of the mass must also be taken into account. 9. Compare the total energy at these 4 points. Why would energy vary at each point? Is energy conserved? What factors might introduce error into your measurements and calculations? a. The energy varies at each point because energy is “lost”( transformed into other forms of energy). These other forms of energy include the drag force when oscillating. 10. Initially we assumed no friction in this experiment. Will friction affect your experimental results? Is there any evidence of friction in the curve of position vs time graph? Explain. ( pendulum velocity curve)? a. Yes friction will affect my results. The velocity curve and acceleration curve do not perfectly line up with each other. The amplitude of each graph also appears to vary, where friction may be going against the kinetic energy. PART VII. CONCLUSION Overall, the experiment was successful in proving the law of conservation of energy, and we can conclude that the total energy of a system is equal to the sum of the total kinetic energy and the total potential energy. We observed that energy is conserved when there are no other forces acting on the object. However, it is important to note how these forces affect the conservation of energy.