Copy of Lab 6 Conservation of energy.docx

LAB 6: CONSERVATION OF ENERGY Date 4/1/2021 Lead Author Tyaija Hicks Lead Experimentalist Tyaija Hicks Associate Experimentalist Tyaija Hicks Introduction Work We define work done by a force as the amount of force applied along the direction of motion multiplied by the distance moved. Algebraically, this results in ............................................ (6.1) 𝑊 = ? → | | ???θ ∆? → | | Where is the applied force, θ is the angle between the applied force and direction of motion, ? → and is the distance moved by the object. ∆? → If the applied force is in the same direction as the object's motion, the work done by that force is positive . If the force is in the opposite direction as the motion, then the work done is negative . A force perpendicular to the direction of motion does no work - you can verify this by putting θ = 90 ◦ in the above equation. For a force measured in Newtons and distance measured in meters, the work unit is Joules (J). Kinetic Energy The kinetic energy of an object is the measure of an object’s energy due to its motion. Mathematically it is defined as ................................... (6.2) 𝐾? = 1 2 ?𝑣 2 where m is the mass of the object and v is its speed. The kinetic energy will also have units of Joules (J). When mass is measured in kg and speed in m/s. Potential Energy Potential energy is a measure of the capacity of an object to do useful work. There are multiple potential energy types, but the two most common are gravitational potential energy and spring potential energy . An object has gravitational potential when it is raised some height ∆ h above a predetermined reference point. This reference point is arbitrary, but it must remain fixed once it is picked for a particular scenario. We determine the gravitational potential energy of an object using PE GRAV = mg ∆ h ................................... (6.3) where m is the object's mass, and g is the acceleration due to gravity = 9.8 m/s 2 . Spring potential energy occurs when a spring is compressed or stretched. We write this type of potential energy as ................................... (6.4) 𝑃? ???𝑖?? = 1 2 ? (? ? 2 − ? 𝑖 2 ) where k is the spring constant (a measure of how stiff the spring is), x i is the initial compressed distance (= 0 if you are starting with a spring at equilibrium), and x f is the final compressed

distance. Work-Energy Theorem In any closed system, total energy must be conserved. This means that the sum of kinetic energy, potential energy, and other forces' work will always add up to the same number. A specific application of this conservation law states that the change in kinetic energy of an object is equal to the work done on that object by forces acting on it, i.e. Discussion Question 1. Several forces are acting on the box in the diagram below as it moves 5 m to the right. Calculate the amount of work done by each of the forces and the net work done on the box. Be sure to include the correct units and sign. [ 5 pts ] Force Work done by the force FN 2N *0 m= 0 J Fg 2 N * 0 m= 0 J Ff 4N * 5 m= -20 J F app 8N * 5 m = 40 J NetWork = 40 J + (-20 J)=20 J 2. Suppose a moving object has a kinetic energy of = 100 J. What will be the object’s 1 2 ?𝑣 2 kinetic energy if a. its speed is doubled? [3 pts] ½ m(2v)^2 = 4/2 mv^2 = 4(½ mv^2) = quadruple the kinetic energy b. its mass is doubled? [2 pts] ½(2m)v^2 = 2/2 mv^2= 2(½ mv^2 )= double the kinetic energy 3. If a force does a positive amount of work on an object, does the object's speed increase, decrease, or remain the same? Explain. [5 pts] If the positive amount of work is on an object, which means in this case the net force is also positive then the object's speed would increase.

5. a. What is the speed of the skater at the highest vertical point of the track? [5 pts] Speed: KE= ½ mv^2 25 J= ½(75kg)(v^2) 25 J = 37.5 kg (v^2) 0.6667= v^2 v=0.8 m/s b. What is the skater’s kinetic energy at the highest vertical point of the track? [5 pts] Kinetic energy: 25 J 6. Using the 6.3 equation in the introduction, calculate the skater's potential energy at the lowest vertical level? [5 pts] PE GRAV = mg ∆ h PE= (75kg)(9.8 m/s^2)(1 m) PE=735 J Value on simulator: 733 J 7. Using the 6.3 equation, calculate the skater's potential energy at the highest vertical level (at 4 meters). [5 pts] PE GRAV = mg ∆ h PE= (37.5kg)(9.8 m/s^2)(1 m)

PE=367.5 J ● Fill Table 1 with the respective energies calculated in question 4c, 5b, 6, and 7. Calculate the total mechanical energy of the skater at each position and complete the table 1. 8. Calculate the percent difference between the total energy at the highest level and the lowest level of the track and record in the Data Table. Show your calculations below. [5 pts] ??????? ?𝑖???????? = ???𝑎? ?????? 𝑎? ???𝑖?𝑖?? 1− ???𝑎? ?????? 𝑎? ???𝑖?𝑖?? 2 | | ???𝑎? ?????? 𝑎? ???𝑖?𝑖?? 1+ ???𝑎? ?????? 𝑎? ???𝑖?𝑖?? 2 | | ? 100% Table 1: Energy comparison [10 pts] Skater’s position Potential energy (J) Kinetic energy (J) Total energy (J) Highest level (4m above zero level) 2800 J 1470 J 4270 J Lowest level (zero level) 0 J 36 J 36 J Percent difference = 42.34% 9. What would you expect the percent difference between the total energy at two positions to be in a perfect system? How close were your results to this? [5 pts] No, I wouldn't expect that and they weren't close at all. 10. Friction effect on energy Click the track friction icon and set the friction to be some value (none zero). Simulate a 75 kg skater. Based on your results, does it look like energy was conserved in this experiment? Explain your answer using the terms and values from the simulator, such as kinetic energy, potential energy, thermal energy, and total energy of the system. [5 pts]

Results and Conclusions (10 pts) Briefly summarize the objective of today’s lab as well as the results of your experiment. State any applicable errors you calculated and give AT LEAST two possible reasons your results deviated from theoretical values. If the experiment was purely qualitative (i.e. you did not calculate a % difference or % error), you may replace the two sources of error with two SPECIFIC concepts from lecture that the experiment demonstrated. Objective: The objective of today’s lab was to study conservation of energy using the skate park method. Results: We observed the total energy values to be KE: 4422 J and PE: 5235 J In a real lab, usually, we get about 10-15% error percentage. If your calculated % difference or % error values are closer to zero, what could be the sources of error. The deviation of our measurements from theory could be attributed to 1. the amount of energy being used 2. positions of the graphs Note - the following are never acceptable sources of error: • “human error” • rounding/calculation errors • mysterious equipment malfunction