LM CH 6 Lab

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Ball State University *

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110

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Physics

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Jun 8, 2024

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6

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Lab Report for Ch 6-Lab: Masses and Springs PhET Colorado Simulations: https://phet.colorado.edu/en/simulation/mass-spring-lab Name: Logan Mercuri Goals Determine the factors that affect the period of oscillation. Correlate the relationship between the velocity and acceleration vectors, and their relationship to motion, at various points in the oscillation. Examine conservation of Mechanical Energy using kinetic, elastic potential, gravitational potential, and thermal energy Calculate the spring constant of the springs using Hooke's Law. Determine the mass of an unknown object Theoretical Background Hooke's Law: F = k ∙∆ x F is the magnitude of the elastic force k  is a spring constant ∆ x is a stretch or change in a length of the spring Simple Harmonic Motion: The period (T) of the oscillations is the time it takes an object to complete one oscillation. T = 2 π m k T 2 = 4 π 2 k m Part I [2 pts]: Select INTRO 1. Put a 100 g mass on the first and the second springs. They should hang at the same level and move similarly. Always carefully place the mass on the spring, NEVER PUSH UP OR STRETCH Remove the mass from spring 2 Increase the SPRING CONSTANT 2 (make large, aka make the spring stiffer) Put the 100 g mass back on the second spring 2. What happens when the stiffness (constant) of spring 2 is increased? The spring stretches not as far but moves up and down more rapidly. 3. Remove the second mass, make the value small for Spring Constant 2, and place the mass back on. What happens when the stiffness (constant) is decreased? The spring stretches further but less rapidly. Part II [7 pts] : Select LAB 1
1. Procedure Set the initial point at zero of scale. Set the Spring Constant. Set the Damping to None. Set the Mass as below. Find the displacement. 2. Observations and Calculations No. Mass ( m ) kg Force(F) = mg (N) Displacement(d) m Spring constant( k ) = F/d (N/m) 1 0.1 kg 0.42 . 20 2.1 2 0.15 kg 0.66 0.34 1.9 3 0.2 kg 0.85 0.43 2.0 4 0.25 kg 1.04 0.52 2.0 5 0.3 kg 1.21 0.61 2.0 6 Unknown mass 1.50 0.75 2.0 Make a graph for force vs displacement using above 5 mass data and Excel, and find a slope that is a spring constant. a) Graph b) spring constant ( k ) = 1.97N/m 2
Choose one of the unknown masses and do simulation. After you find a displacement, find an unknown mass using a graph above and the obtained spring constant. Unknown mass (m) = __ 0.74 _ kg 3. Procedure Set the initial point at zero of scale. Set the Spring Constant. Set the Damping to None. Set the Mass as below. Take the stopwatch from your cellphone. Now oscillate the spring and measure time of ten oscillations. Repeat the above step for unknown mass. 4. Observations and Calculations No. Mass ( m ) kg Time for 10 oscillation (t) s Periodic time (T =t/10) s Square the period (T 2 ) 1 0.1 kg 6.39 0.693 0.48 2 0.15 kg 7.72 .772 .60 3 0.2 kg 8.96 0.896 .80 4 0.25 kg 9.96 0.996 0.99 5 0.3 kg 10.88 1.088 1.18 6 Unknown mass 12.11 1.211 1.47 Make a graph for T 2 vs mass using above 5 mass data and Excel, and find a slope which is 4 π 2 / k . a) Graph 3
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b) Show your work for calculating a spring constant. Spring constant ( k ) = 8.22 _ Choose one of the unknown masses and do simulation. After you find a periodic time (T), find an unknown mass using a graph above and the obtained spring constant. Write an expression mass m in term of T, k , and constants. m = K(2 π (T^2)) 4
Unknown mass ( m ) = __ 0.31 __ kg Part III [3 pts]: Select ENERGY Set the damping to none and put a 100 g mass. 1. Draw the ENERGY BAR GRAPH diagrams when the mass is at the identified positions 2. When you put the 100 g mass on the spring, describe what happens to the a. KE as the spring bounces: Kinetic energy increases as the weight goes downward (spring stretches) and decreases once the spring is fully extended. The kinetic energy increases again as the spring retracts and then reduces to zero. b. PE gravity as the spring bounces: PEgravity decreases when the spring stretches and increases as it retracts. c. PE elasity as the spring bounces: PEincreases as the spring stretches and decreases as it decreases. d. E total as the spring bounces: As the spring steatches the Etotal increases, decreases as it retracts. Part IV [3 pts] : POST QUIZ 1. The main difference between kinetic energy, KE, and gravitational potential energy, PE g, is that Ans: _ B __ 5 Energies at LOWEST point (full stretch) Energies at MID point Energies at HIGHEST point (no stretch)
A. KE depends on position and PE g depends on motion B. KE depends on motion and PE g depends on position. C. Although both energies depend on motion, only KE depends on position D. Although both energies depend position, only PE g depends on motion 2. As any object free falls, the gravitational potential energy Ans: C __ A. vanishes B. is immediately converted to kinetic energy C. is converted into kinetic energy gradually until it reaches the ground Questions 3-6: A spring is hanging from a fixed wire as in the first picture on the left. Then a mass is hung on the spring and allowed to oscillate freely (with no friction present) . Answers A-D show different positions of the mass as it was oscillating. 3. Where does the spring have maximum elastic potential energy? Ans: _ C __ 4. Where is the gravitational potential energy the least? Ans: __ B _ 5. Where is the kinetic energy zero? Ans: _ B and C _ 6. Where is the elastic potential energy zero? Ans: _ A __ 6
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