Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

no text concepts found

Transcript

PHY211 LAB 10 Simple Harmonic Motion Abstract The purpose for this lab is to demonstrate the effects of mass, length, and angle upon a pendulum, and to compare the calculated gravitational effect to actual gravity effect. Through a series of weights of 50 -150 g and m lengths of the same numeric, the average time was calculated to find the period of a 10-cycle swing. By changing the angle of the beginning swing, this displacement will also be used to calculate the e ffect of starting momentum on the mass. Sanabria, Helen (PPCC) Data Data Table 1: Amplitude and Period for L = 1.50 m, m = 50 g Angle (°) Time 1 (s) Time 2 (s) Time 3 (s) 5 10 20 25.7 25.5 25.2 24.8 25.2 25.1 24.7 24.9 25.3 Average time (s) 25.1 25.2 25.2 Period (s) Observations 2.51 2.52 2.52 Fast Slow Slower Data Table 2: Length and Period for θ = 10°, m = 50 g Length (m) Time 1 (s) Time 2 (s) Time 3 (s) 1.50 1.00 0.50 25.5 20.1 14.7 25.2 19.9 14.7 24.9 20.1 14.8 Average time (s) 25.2 20.0 14.7 Period (s) Observations 2.52 2.00 1.47 Slow Low times Lowest Data Table 3: Mass and Period for θ = 10°, L = 1.0 m Mass (g) Time 1 (s) Time 2 (s) Time 3 (s) Period (s) Observations 20.1 Average time (s) 20 50 20.1 19.9 2.00 20.7 20.6 20.7 2.07 20.9 20.7 20.8 2.08 Average times Slightly slower Slowest 100 20.6 150 20.9 Data Table 4: Acceleration Due to Gravity for θ = 10°, m = 50 g Length (m) 1.50 1.00 0.50 Period squared (m/s2) 6.4 4.0 2.2 g (calculated) (m/s2) 9.3 9.85 8.9 Δg % Error (calculated) (calculated) (m/s2) 2.8 5.1 2.9 0.5 4.5 9.2 g (graph) (m/s2) % Error (graph) 9.2 12.2 Graph 1: L versus T2 Excel graph, should have L on y-axis, Time2 on x-axis, remember to include units Data Table 5: Energy for θ = 10°, m = 100 g, L = 1.00 m Amplitude (m) 0.174 Umax (J) 0.15 Kmax (J) 0.15 % Difference 0 Calculations 4π2 L = 𝑠𝑙𝑜𝑝𝑒 · 4π2 T2 0.2998 ∗ 4𝜋 2 = 11.0 𝑚/𝑠 2 |11.0 − 9.8| ∗ 100% = 12.2% 9.8 𝐴=𝜃∗𝐿 10 ∗ 𝜋 =( ) ∗ 1𝑚 = 0.174𝑚 180 1 𝑚𝑔 𝑈𝑚𝑎𝑥 = ( ) 𝐴2 2 𝐿 100 ∗ 9.81 = .5 ( ) 0.1742 = 0.15𝐽 100 2πA 2 𝐾𝑚𝑎𝑥 = .5𝑚 ( ) T 2π0.174 2 . 5(100) ( ) = 0.15𝐽 20 𝑔= 25.7 + 24.8 + 24.7 = 25.1𝑠 3 25.1 = 2.51s 10 𝑚 𝑇 2 = 2.522 = 6.35 ( 2 ) 𝑠 4𝜋 2 𝐿 𝑔= 2 𝑇 4𝜋 2 (1.50) 𝑔= = 9.25 𝑚/𝑠 2 6.4 2𝛥𝑇 𝛥𝐿 𝛥𝑔 = 𝑔 [( ) + ( )] 𝑇 𝐿 2(0.1) 0.4 9.3 [( )] = 2.8 𝑚/𝑠 2 )+( 6.4 1.50 |9.3 − 9.8| ∗ 100% = 5.1% 9.8 (0.15 − 0.15) | | · 100 = 0% 0.15 + 0.15 ( ) 2 Summary of error Within the experiment, there are some sources of error due to human error and possible miscalculations. Within Data Table 1, 2 and 3, the slowing momentum could affect loss in time measurements, which can explain slower times or even incomplete swings of the pendulum. In Data Table 4, the error calculations shown are low enough to confirm that the gravitational acceleration of the mass is measured correctly to match up to the actual gravitational pull of 9.81 m/s2. By used of the simulated system in Graph 1, the slope calculated with component 4π2 gives us the estimated gravitational pull within the given average length and period2. With all these components in mind, a potential and kinetic energy Max can be given for each one, both with 0% error due to similar calculation methods. In conclusion, the calculations of each data table show little to unavoidable error due to imperfect setting and incorrect time measurements from lost momentum by air friction. Exercise 1 1. 2. 3. 4. Determine the position in the oscillation where an object in simple harmonic motion: (Be very specific and give some reasoning to your answer.) a. has the greatest speed i. The mean position is where the velocity is at a maximum. b. has the greatest acceleration i. The extreme position is where the acceleration is at its max. c. experiences the greatest restoring force i. The extreme position is where the restoring force is at maximum as well. d. experiences zero restoring force i. The mean position is where an object experiences zero restoring force. Describe simple harmonic motion, including its cause and appearance. (Make sure to use your own words and be very specific. And few examples would be helpful.) a. Simple harmonic motion is an oscillatory motion where restoring force that is acting on a body is directly proportional to displacement from a mean position. Use the information listed in Data Tables 1 to 3 to describe how the change in, using complete sentences: a. amplitude (angle) b. length c. mass affect the period of the pendulum i. The angle, length, and mass have a varying effect on the period of a pendulum. The period is independent of mass and amplitude but is proportional to the square root of the length. Compare your calculations of g using individual measurements and using the graph in Graph 1, listed in Data Table 4. Do your measurements including uncertainty fall within the accepted value? Which method is more accurate? List possible sources of error in your data and calculations. 5. 6. a. The most accurate measurement based on the table is when the length of the pendulum is 1 m. It falls within 0.4% of the accepted value. The possible sources of error are the inaccurate length of strength, the angle at which the pendulum is swung, and how the stopwatch is timed. Was energy conserved during the motion of your pendulum? If not, list some possible ways energy could have been lost from the pendulum system, making sure to use complete sentences. a. Without friction, energy would have been conserved as mechanical energy. With the friction, the energy is converted into heat or other forms. Energy is lost from the air and the swing from the pendulum and the attached points. Why did you measure 10 periods of the pendulum instead of just 1? Would your measurements be improved by measuring 100 periods instead of 10? Why or why not? How many periods do you think is the optimal number to measure? a. I measured 10 periods instead of 1 in order to get more consistent results. With just one period, the pendulum is exerting max energy, and not being as slowed down from friction as it would be from 10 periods. My measurements from 100 periods would not be as accurate, as the amount of energy needed to reach 100 periods would not be possible from a 5 or ten degree drop. I think the optimal number to measure is 10-15. Extension Question 1. How would the motion of a pendulum change at high altitude like a high mountain top? How would the motion change under weightless conditions? (Make sure to use your own words.) a. On a mountain top, a reduced gravity will result in longer periods of oscillation. With weightless conditions, the pendulum would not work because what keeps the pendulum oscillating is gravity. Citations Halliday, D., Resnick, R., & Walker, J. (2018). VitalSource bookshelf online. In online.vitalsource.com (11th ed.). WileyPlus. https://online.vitalsource.com/#/books/9781119306856/cfi/6/44