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PHYSICS 111 Experiment # Conservation of Energy Name: Grade: Instructor: Partners: Date Performed: Comments: Date Submitted: OBJECTIVE Conservation of energy will be demonstrated in this lab by comparing the potential energy lostby a falling mass to the potential energy gained by a spring to which the mass ig attached. EQUIPMENT Meter stick & masking tape Hooked Masses Set Spring support & stand Spring All thiswill be found in the following site: https://phet.colorado.edu/sims/htm/masses-and-springs/latest/masses-and-springs _en.html INTRODUCTION The law of conservation of energy is one of the most important principles of Physics. It requires that in energy transformations (for a closed system ), it is possible to account for all energy gains and losses. Lifting a mass to some height requires a force through a distance (W=Fs). In other words, work must be done on the mass. At its new height, the mass has an increase in its potential energy (P.E=mgh). To stretch a spring, a force must be exerted through a distance. The stretched spring then has gained a potential energy equal to the work done to stretch the spring (W=Fs). To calculate this work, the average and losses. Lifting a mass to some height requires a force through a distance {(W=Fs). In other words, work must be done on the mass. At its new height, the mass has an increase in its potential energy (P.E=mgh). To stretch a spring, a force must be exerted through a distance. The stretched spring then has gained a potential energy equal to the work done to stretch the spring (W=Fs). To calculate this work, the average force between two points of stretch for the spring must be used. The average force is the middle force, or the initial force plus the final force divided by two. This occurs because of Hooke's Law, which states that the stretch of a material such as that used in a spring and the force to stretch a spring are uniform and proportional over a range of values. Average force (F/2) times the distance (s) then 1s Fs/2, or work, which is the area under a force-distance graph. The energy for the fallen mass can then be comparedto the energy of the stretched spring found from the areaunder the spring's force-distance graph. PROCEDURE 1. Suspend the spring from the support stand. 2. Locate a zero position or reference position for the spring in the unstretched position. Use the same point of reference for all following measurements. {The very bottom of the spring should serve as a congistent reference point.) Record the zero position here 3. Hang a 50g mass on the spring. Determine the new position of the reference point and record that in Table I in the column \"Reading on the ruler.\" The elongation is the difference between this value and the zero position of the unstretched spring. as determinedin step 2. Convert the massesto forces and enter the force and distance values in Table I below. 2 4. Repeat step 3 using 100g, 150g, 200g, and 250g masses. 5. Plot the force and elongation values from Table I on a graph with the elongation as the independent variable. The area under the curve represents the work done to stretch the spring (Fs/2). 6. Put a 250g mass on the unstretched spring and allow it to fall. Record the lowest point to which the mass falls. Perform several trials to determine the lowest point with fair certainty. Average these trials in Table II. 7. Determine and record below the distance through which the mass fell in stretching the spring. (DO NOT USE THESE TABLES), they are just a sample of what you should do in Excel. Mass 100 Spring Constant 1 Displacement Small Large 0 50 300 Natural Length Mass Equilibrium O Movable Line Period Trace Gravity 9.8 m/s? 30Normal 100g E O Slow ----- Height = 0 m PHET : Intro Energy ah Table I Table II Mass Force Ruler Elongation (kg) (N) Reading (m ) (m Trial # Distance Fallen 1 3 AverageCalculations: 1. Calculate the potential energy lost by the falling mass using the data from table II. Do not forget the correct units for this calculation. 2. Find the energy gained by the stretched spring at the distance of the fallen mass. This energy is the areaunder the graph up to the distance stretchedfor the fallen mass. It will be necessary to extrapolate the graph to include this point. (Note: For small masses, the spring is not linear. However, this non-linearity near zeromay be ignored when finding the area by assuming a straight line for the triangular areaunder the curve.) Show this calculation. 3. Calculate the energy gained by the spring by using data trom table I and compare this value with the one obtained in #1 4. Compare the values of the energies from #1, #2 and #3. Questions: 1. Does the work found as the area under the graph equal the loss in potential energy of the falling mass? What happened to the work done on the spring by the falling mass? 2. Explain how this experiment demonstrates conservation of energy