Conservation of Energy Lab Packet Unit # 3 Main Topic: Pendulum Duration: 10 days NAME:
Contents/Page Number Day 2 (2/1/16): The Pendulum Lab Day 1 (2/2/16): The Physics of Pendulum Day 3 (2/3/16): The math and Physics of Pendulum Day 4 (2/4/16): Tri # 2 Essay Writing Optional: The calculus of Pendulum (Lunch time & during 8th Period) Day 5 (2/5/16): The Roller Coaster Lab Day 6 (2/9 /16) : The Physics of Roller Coaster Day 7 (2/10/16) : The Conservation of Energy Lab Day 8 (2/11/16): Physics of Conservation of Energy Law Optional: The calculus of Roller Coaster (Lunch time & during 8th Period) Day 9 (2/12/16): Unit # 3 Final 1
Booklet # 63 Day # 2 (2/1/16) (The Simulation of Pendulum ) 1 What is a Pendulum? What is the connection between Pendulum and Conservation of energy? 2 What is its equilibrium position? 3 What is Restoring force. 4 What is Period? 2
5 Force analysis of Pendulum. What forces act upon a pendulum bob? 6 Pendulum Lab Introduction: Old grandfather clocks have large pendulums that swing back and forth to keep time. A Foucault pendulum is a huge pendulum that swings in two axes as the earth rotates to also keep time. The time a pendulum takes to swing back and forth ( one cycle ) is referred to as one. The period of a pendulum is measured in seconds and is given by the formula shown below. The inverse of period is, the number of complete cycles each second. The equilibrium position is the point below the pivot, at a. The amplitude of the pendulum s swing is the displacement from the equilibrium. The top of each swing is referred to as maximum displacement or maximum amplitude. Important Formulas 3
7 Procedure: 1. Write Following line on the Google: Bari Science Lab > Conservation of Energy> Pendulum Lab 2. Spend some time learning about pendulums. The simulated pendulum is frictionless, so it will attain the same amplitude in every swing. That is, it will lose no energy to friction (heat). 3. Using a 1.00 kg pendulum, adjust the length of the pendulum and determine the period. (In this lab, you may use the photogate timer to determine the period ) 8 Complete the table below (Different Length) Write hypothesis: Mass (kg) Length (m) Period (s) gravity 1.00 kg Earth 1.00 kg Earth 1.00 kg Earth 1.00 kg Earth 9 Repeat the investigation but adjust only the mass of the pendulum, leaving all other variables constant. Write hypothesis: Mass (kg) Length (m) Period (s) gravity Earth Earth Earth Earth 10 Repeat the investigation but adjust only the Degree of the pendulum, leaving all other variables constant. Write hypothesis: 4
Mass (kg) Length (m) Degree Period 1 kg 2 m 1 kg 2 m 1 kg 2 m 1 kg 2m 11 Velocity and Acceleration Vectors Turn on the velocity and acceleration vectors. Observe the magnitudes and directions of the vectors as the pendulum moves. The green vector represents and the yellow vector. 12 Lab Questions 1. What force causes the pendulum to speed up on the way down and slow down on the way up? 2. As pendulum length increases, the period of harmonic motion increases / decreases / remains the same. 3. As pendulum mass increases, the period of harmonic motion increases / decreases / remains the same. 4. As gravity (Jupiter) on the pendulum increases, the period of harmonic motion increases / decreases / remains the same. (Click on Show Energy ( More about PE and KE tomorrow) 5. A pendulum attains maximum velocity at the equilibrium position / at maximum amplitude. 6. A pendulum attains minimum velocity at the equilibrium position / at maximum amplitude. 7. A pendulum attains maximum acceleration at the equilibrium position / at maximum amplitude. 8. A pendulum attains minimum acceleration at the equilibrium position / at maximum amplitude. 9. A pendulum attains maximum PE (potential energy) at the equilibrium position / at maximum amplitude. 10. A pendulum attains minimum KE (kinetic energy) at the equilibrium position / at maximum amplitude. 11. Consider a playground swingset. Is it possible for a kid to swing over the middle bar? 12. Why / Why not? 13. In real devices that use pendulums (clocks, Foucault pendulums in museums) a force must be added to counteract friction. When should that force be applied? Constantly / at the same period as the pendulum / it doesn t matter. 5
14. A pendulum that completes a cycle in 4 seconds has a period of seconds. 15. That same pendulum has a frequency of cycles per second (Hz) 16. If a pendulum completes 25 cycles in a minute, its period is seconds. 17. and its frequency is Hz. 18. What is the period (on earth) of a.25 kg pendulum with a length of.45 m? 19. What is the period (on earth) of a 7.5 kg pendulum with a length of.45 m? 14 Homework: In order to swing with a period of exactly 2.0 s, a grandfather clock s 1.5 kg pendulum must have a length of m. 6
Booklet # 64 Day # 2 (2/2/16) (Physics of Pendulum ) 1 Fill the blank below. 2 What is the period on Earth of a pendulum with a length of 2.4 m? 7
3 How long should a pendulum be in order to swing back and forth in 1.6 s? 4 A grandfather clock needs to have a period of one second. What length of pendulum should be hung for the clock to keep good time? 5 If the clock from question 1 was taken to the moon where gravity is 1.7 m/s 2, what length should the pendulum have? 8
6 A playground swing is 3 meters long. What is the period of the swing? 7 9
Booklet # 65 Day # 3 (2/3/16) (Math and Physics of Pendulum ) 1 A grandfather clock swings back and forth in two second. a. What is the frequency in Hz of this papa clock? (b) How long is the clock s arm assuming it follows simple harmonic motion? What would be the period if the mass of the clock arm was doubled? (d) How long should the arm be if we want it to work with the same period while on Mars? (g= 4m/s2 ) 2 A one meter long pendulum with a mass of 1kg is let go at θ= 70. a. Draw a picture and determine the change in height. How much energy does it have when it is let go? How fast is it traveling when the pendulum is at θ= 00?d. what it its period? How much time did it take to go from θ= 70 to θ= 00? 10
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Booklet # 66 Day # 4 (2/4/16) (Trimester # 2 Essay Writing) 1 A heavy pendulum called a charpy impact pendulum is used to test the strength of m = 10,0000 kg materials by breaking them! How much energy was needed to break the steel pieces above if a 2m long pendulum had to be dropped from at least at θ = 100 to fracture and break the steel? 2 Take out the laptop and complete your Trimester # 2 Essay. 12
Booklet # 67 Day # 6 (2/5/16) (The Simulation of Roller Coaster) Do now 1 Why mechanical energy is conserved? 2 Take out the laptop and go to the sim page: 3 Procedure: d) Put a check mark on the Measuring Tape box and measure the height of the ramp from the highest point to the GPE = 0 Reference Line. This is the h 1 height measurement a) Choose Energy Skate Simulation and press Run Now button. b) Modify the track configuration and place the skater at the top of the track as shown on the picture below. c) Put a check mark on the Potential Energy Reference box and position the GPE = 0 Reference Line at the bottom of the slide. At that height level, e) Position the measuring tape as shown on the picture and measure the height of the bottom of the slide in relation to the ground. This is the h 2 height measurement. f) Calculate the speed v 2 of the skater when he comes off of the bottom of the slide. g) Calculate the distance d that the skater will travel when he hits the ground. h) Position the measuring tape on the ground aligned with the bottom of the slide and open it to a length equal to the expected distance d. i) Run the simulation and verify the accuracy of your measurements and calculations. 13
we assume gravitational positional energy to be zero. 4 14
5 Data collection Solve the following problems: 6 Comparing the simulation with our design we did yesterday. Solve the problem: 1. Find the GPE at the position A 2. Find the height of the table (hints: Use kinematic equation) 3. Find time (t) 4. Find the horizontal velocity? 5. Find the KE at the edge of the table 6. Why GPE > KE? Explain... 15
7 Assessment 8 Homework (Watch the video tutorial to solve the following questions) 16
Booklet # 68 Physics & Math of Roller Coaster Day # 6 (2/9/16) Do now (10 mins) 1 Conceptual Understanding (Mechanical energy) 1. A 3 kg block is sliding down a 25 degree incline at a constant speed. (a) Sketch three primary vectors(weight, normal force and friction) acting on the block (b) Find the weight of the block FInd magnitude of NF (d) Find FF (e) Find coefficient of FF. 2. A 50 N block is placed on a frictionless 20 degree incline (a) Find the net force acting on the block (b) Find block rate of acceleration down the plane. 3. Calculate the amount of force needed to move a 2.5 kg object up to 30 degree frictionless incline at constant speed. 17
2 Conceptual Understanding (Roller coaster) Find the speed of the track at the bottom of the Roller coaster. Imagine a cart on a roller coaster. Think about using Newton s laws to determine how fast the cart is going at the end of the ride. At every instant there are two forces, and. You need to know the direction and magnitude of each vector to determine the total force. Once you know the total force, you can use Newton s second law. Acceleration is not, so you can t use the equations of kinematics under constant acceleration. So how can you find the speed of the track at the bottom of the coaster? This is a nightmare problem. Explain why you can solve the problem on the left by applying Conservation of mechanical energy? Mathematics of Conservation of mechanical energy. 3 Proof the following hypothesis: If there are only conservative forces acting on a system, then its mechanical energy is conserved. (Hint: Conservation of mechanical energy can be derived from the definitions of kinetic and potential energy and the work kinetic energy theorem) 18
Mathematics of Roller Coaster: 4 Find velocity at position A, find velocity at position B and find the total energy at position B. Mathematics of Roller Coaster: 5 Find GPE at position # 1, find velocity at position #2 and find heights at position # 3 of the following roller coaster. 19
6 Engineering aspect of Roller Coaster: Designing Roller Coaster Collecting data 1. Find GPE at position 1 2. Measure the time (how long the ball spin in the red track 3. Measure the amount of distance it travel on the red track 4. Ball will launch off at the edge of the table and hit the ground. Measure how far ball landed from the table. Solve the problem: 1. 1Find the GPE at the position A 2. Find the height of the table (hints: Use kinematic equation) 3. Find time (t) 4. Find the horizontal velocity? 5. Find the KE at the edge of the table 6. Why GPE > KE? Explain... 20
7 Assessment Homework (Watch the video tutorial to solve the following question) 21
Booklet # 66 Conservation of Energy Lab Day # 6 (2/10/16) 1 22
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2 The Skate Park Intro to Conservation of Energy Lab Introduction: When Tony Hawk wants to launch himself as high as possible off the half pipe, how does he achieve this? The skate park is an excellent example of the conservation of energy. The law of conservation of energy tells us that we can never create or destroy energy, but we can change its form. In this lab, we will look at the conversion of energy between gravitational potential energy, work, and kinetic (or moving) energy. This conversion is work. (Realize though, that in real life, skateboard wheels have friction. In our experiments, we ignore friction) Energy is measured in units of Joules. Important Formulas: 3 Procedure: Go to Simulation > Play With Sims à Energy Skate Park > download >open Take some time and play with the skater and his track. Click on the buttons to show the energy graphs and the pie graphs. These graphs show the conversion between kinetic energy (green) and potential energy (blue). If any energy is lost, it will be shown with a red bar ( thermal energy lost ). Reset the skater to the standard half pipe and observe the energy bars as he moves back and forth (without friction). Reset the skater to the standard half pipe and observe the energy bars as he moves back and forth (without friction). 4 24
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5 6 Conclusion Questions: use g = 10. m/s 2 1. At the highest point kinetic energy is zero / maximum while the potential energy is zero / maximum. 2. At the lowest point kinetic energy is zero / maximum while potential energy is zero / maximum. 3. Mass affects / does not affect the conservation of energy. 4. How much potential energy does the 60. kg skater have before she starts her ride, 12 m above the ground? 5. How much kinetic energy does a 60.0 kg skater have traveling with a velocity of 4 m/s? 6. How fast must a 20. kg skater travel to have a kinetic energy of 360 Joules? 7. How high must a 2.0 kg basketball be thrown so it has a potential energy of 160 J? 8. How fast must the 2.0 kg basketball be thrown upward to achieve the same 160 J? 9. If a 75kg skater starts his skate at 8.0m, at his lowest point, he will have a velocity of 26
Booklet # 70 Math & Physics of Conservation of Energy (Day 8 : 2/11/16) 1 Do now: 1. Explain why you can use conservation of mechanical energy when all the forces acting on a system are conservative forces. 2 You can use conservation of mechanical energy to understand even very simple systems. When you drop a superball onto a hard surface, for example, conservation of energy tells you that Any discrepancy between the initial and final heights reflects a of energy somewhere in the system. This energy loss might occur because or 27
3 Here is a problem that would be extremely difficult to solve using Newton's laws. What is the final speed of the roller coaster? Why this problem would be extremely difficult to solve using Newton's laws? What is the final speed of the roller coaster? 28
4 Let s add a spring to the Roller Coaster! Let's modify the problem slightly by adding a giant spring to the end of the track? (a) What is the final speed of the roller coaster? (b) Is the problem harder than before? The only difference is that now, instead of traveling at a speed f v at the end of the track, the roller coaster compresses the spring and comes to a halt. Its final kinetic energy is therefore zero, while it has an additional potential energy of 1 /2 kx^2 (where x is the distance that the spring is compressed). Set the total initial energy equal to the total final energy and solve for x. 29
5 Let s make it more complicated! Really! Suppose now that instead of compressing a spring, the roller coaster just flies off the track. What is its speed at the instant before it hits the ground? 30
6 Assessment: 31
Booklet # 71 (Unit # 3 Exam) CLOSED BOOK Part # 1: Unit # 3 Exam Review Questions: 32
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Part B: 34
Part # C 1. What is the period on Earth of a pendulum with a length of 2.4 m? 2. How long should a pendulum be in order to swing back and forth in 1.6 s? 3. A grandfather clock needs to have a period of one second. What length of pendulum should be hung for the clock to keep good time? 4. If the clock from question 1 was taken to the moon where gravity is 1.7 m/s 2, what length should the pendulum have? 5. A mountain climber, who has had physics in high school, figures out the gravity at his location in the mountains. He used a 4.0 m length of string and found that with a rock tied at its end, its period as a pendulum was 4.1 seconds. What was g at his location? 6. A ride at 6 Flags straps you in and you swing like a pendulum. The length of the cord that holds you is about 20 meters. How much time does it take to swing back and forth once? 7. A playground swing is 3 meters long. What is the period of the swing? 8. A playground swing is 3 meters long. What is the period of the swing? 9. If we colonized Mars and took the swing set from question 5 there, it would swing back and forth with a period of 5.7 seconds. What is the acceleration due to gravity on mars? 10. The desk toy with the swinging ball bearings has a length of 12 cm. What is the period of their swing? 35
Part D: 36
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