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Spring Problems

Examples of . Frequency and Period Problems. Spring Problems. Pendulum Problems. Equations for Equation sheet for Springs and Pendulum Problems. Examples of Period Frequency Problems. Frequency and Period Problem (Without Period or Frequency given).

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Spring Problems

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  1. Examples of Frequency and PeriodProblems Spring Problems Pendulum Problems Equations for Equation sheet for Springs and Pendulum Problems

  2. Examples of Period Frequency Problems

  3. Frequency and Period Problem(Without Period or Frequency given) Terry Jumps up and down on a trampoline 30 times in 55 seconds. What is the frequency with which he is jumping? 30 times 55 seconds 0.55 Hz

  4. Frequency and Period Conversion problem Terry Jumps up and down on a trampoline with a frequency of 1.5 Hz. What is the period of Terry’s jumping? 1.5 Hz 0.67 sec

  5. Examples of Pendulum Problems

  6. Problem: • At the California Academy of Sciences the length of the pendulum is:90m = L • The acceleration of gravity at this location is:9.8 m/s/s = g • What is the Period? T=???? seconds

  7. Solution Solve: “Plug and Chug” List: L = 90m g = 9.8 m/s/s T=???? seconds Choose equation: 90 m 9.8m/s/s 9.18s2 (3.03 s) (19.0 s)

  8. A problem where you Find the period or frequency 1st A pendulum has a length of 3 m and executes 20 complete vibrations in 70 seconds. Find the acceleration of gravity at the location of the pendulum.

  9. A pendulum has a length of 3 m and executes 20 complete vibrations in 70 seconds. Find g. 1. f = cycles / seconds = 20 cycles / 70 seconds = 0.286 hz = 0.286 / sec 2. T = 1 / f = (1 / 0.286) seconds = 3.5 seconds What short cut could I have used? # vibrations # seconds is the time for all the oscillations

  10. L = 3m and T= 3.5 secondsFind the acceleration of gravity at the location 3.5 s = 2π√(3/g) 3.5 s = 6.28 √(3/g) Square both sides 12.25 = 39.43 (3/g) 12.25 = 118.3/g 12.25(g) = 118.3 Divide by 12.25 g = 9.658 m/s/s Heads up!! If you÷ by 2π Use (2π ) !!

  11. A problem Where "g" = 9.8 m/s/s is “understood”Know you use g=9.8 m/s/s if:“g” not given or asked for used 9.8 m/s/sPart 1:A simple pendulum has a period of 2.400 seconds where "g" = 9.810 m/s/s. Find the length?Part 2:Find "g" where the period of the same pendulum is 2.410 seconds at a different location.

  12. Why are the items green on this problem??Pendulum is not a variable, why is it marked?? • A simple pendulum has a period of 2.400 seconds where "g" = 9.810 m/s/s. Find the length? • Find "g" where the period of the same pendulum is 2.410 seconds at a different location.

  13. 1st find the LengthA simple pendulum has a period of 2.400 seconds where "g" = 9.810 m/s/s. T2=4π2 (L/g) 2.4002=4 π2 (L/9.810) 2.4002= 39.44(L/9.810) 2.4002(9.810) = L 39.44 L=1.433 m • Write equation • Substitute #’s • Square 4 π2 • ÷ 39.44 And X 9.810 • Answer with label

  14. Part 2: Use Length from 1st part of problemSame Pendulum, same length NOW:Find "g" where the period of the pendulum is 2.410 seconds. T2=4π2 (L/g) 2.4102= 4π2(1.433/g) 2.4102=39.44(1.433/g) g 2.4102=39.44(1.433) g =39.44(1.433)/2.4102 g = 9.73 m/s/s Equation Substitute #’s 4 π2 =39.44 X by “g” ÷2.4102 Answer and label

  15. Examples of Spring Problems Hooke’s Lawgraphing

  16. Examples of using the graph to find the Slope and the value of “k” for springs

  17. What is the spring constant for the data graphed below? Δx(m)

  18. (0,0) y2 - y1 x2-x1 Slope = (6,147) 147N– 49N 6 m – 2m k = (2,49) 98 N 4 m k = Δx(m) k = 24.5 N/m How do I know the Label?? Labels on axes: Rise (N) & Run (m) So: rise/run is N/m !!

  19. Examples of Spring Problems UsingEquations

  20. Examples ofHooke’s Law problemsStretch or compress – at rest In anticipation of her first game, Alesia pulls back the handle of a pinball machine a distance of 5.0 cm. The force constant is 200 N/m. How much force must Alesia exert?

  21. Examples of Hooke’s Law problems In anticipation of her first game, Alesia pulls back the handle of a pinball machine a distance of 5.0 cm. The force constant is 200 N/m. How much force must Alesia exert? List: Δx = 5.0 cm = .05 m k = 200 N/m Fsp=??? Equation Substitute #’s Answer with label Fsp= k Δx Fsp= 200N/m(0.05 m) Fsp= 10N

  22. Example of Oscillation spring ProblemsOscillating or bouncing • Bianca stands on a bathroom scale which has a spring constant of 220 N/m. The needle is bouncing from side to side. Bianca’s mass is 180 kg. What is the period of the vibrating needle attached to the spring?

  23. Example of Oscillation Spring Problem List: k = 220 N/m m = 180 kg T = ?? • Bianca stands on a bathroom scale which has a spring constant of 220 N/m. The needle is bouncing from side to side. Bianca’s mass is 180 kg. What is the period of the vibrating needle attached to the spring? 0.818 s2 180 kg (0.904 s) 220N/m 5.7 sec

  24. Spring Problems Use Both EquationsExample of Combination of Hooke’s Law and Oscillation of springFind k from Hooke’s Law and then use the oscillation equation Autumn, a young 20 kg girl, is playing on a trampoline. The trampoline sinks down 9 cm when she stands in the middle. What is the spring constant? If the trampoline then begins to bounce, what would the frequency of the bounces be?

  25. The PLAN: Using Hooke’s Law and Oscillation of spring Autumn, a young 20 kg girl, is playing on a trampoline. The trampoline sinks down 9 cm when she stands in the middle. What is the spring constant? If the trampoline then begins to bounce, what would the frequency of the bounces be? 1st Find Force of Gravity on mass 2nd Find k from Hooke’s Law 3rd use the oscillation equation to find T4th convert to Frequency Fg= m ag List : m = 20 kg Δx = 9 cm = 0.09 m f = ?? Fsp= k Δx

  26. Autumn, a young 20 kg girl, is playing on a trampoline. The trampoline sinks down 9 cm when she stands in the middle. What is the spring constant? Using Hooke’s Law & Oscillation of spring 1st Find Force of Gravity on mass List : m = 20 kg Δx = 9 cm = 0.09 m f = ?? Fg= m ag Fg= 20kg(-9.8m/s/s) Fg= - 196 N Recall From the FBD on the Lab FS = + 196 N SO. . .

  27. Example of Combination of Hooke’s Law and Oscillation of spring Autumn, a young 20 kg girl, is playing on a trampoline. The trampoline sinks down 9 cm when she stands in the middle. What is the spring constant? 2nd Find k from Hooke’s Law List : m = 20 kg Δx = 9 cm = 0.09 m Fs= 196 N f= ?? Fsp= k Δx 196 N =k(0.09m) 2180 N/m = k

  28. Example of Combination of Hooke’s Law and Oscillation of spring Autumn, a young 20 kg girl, is playing on a trampoline. The trampoline sinks down 9 cm when she stands in the middle. What is the spring constant? If the trampoline then begins to bounce, what would the frequency of the bounces be? 3rd use the oscillation equation to find T List : m = 20 kg Δx = 9 cm = 0.09 m Fs= 196 N k = 2180 N/m T = f = ?? 20 kg 2180 N/m (0.958 s) .00917 s2 .602 sec

  29. Example of Combination of Hooke’s Law and Oscillation of spring Autumn, a young 20 kg girl, is playing on a trampoline. The trampoline sinks down 9 cm when she stands in the middle. What is the spring constant? If the trampoline then begins to bounce, what would the frequency of the bounces be? 4th convert to frequency List : m = 20 kg Δx = 9 cm = 0.09 m Fs= 196 N k = 2180 N/m T = 0.602 sec f = ?? .602 s 1.66 Hz

  30. Spring Problems 4 part Spring problemUse Fg to find the k value and then use same string with same k to find 2nd mass. If two “Grumpy Old Men” went ice fishing and were comparing their fish with the extension of the same spring, solve the following spring problem: “Grumpy Sam” caught the first fish and magically realized the fish had a mass of 23 kg. When this fish was suspended on the spring, like the one we suspended masses on in lab, the spring stretched so it was 3 cm longer than it was without the fish. What is the spring constant for the spring? “Grumpy Joe” then caught a fish that caused the same spring to extend 5 cm from the length of the empty spring,. What was the mass of “Grumpy Joe’s” fish?

  31. The Plan to solve: If two “Grumpy Old Men” went ice fishing and were comparing their fish with the extension of the same spring, solve the following spring problem: “Grumpy Sam” caught the first fish and magically realized the fish had a mass of 23 kg. When this fish was suspended on the spring, like the one we suspended masses on in lab, the spring stretched so it was 3 cm longer than it was without the fish. What is the spring constant for the spring? Example of 4 part Spring problem 1stUse Fg to find the Force on the spring 2nd Use Hooke to find the k value 3rd Same spring with same k to find 2nd Force4th Convert weight to mass. List : m = 23 kg Fg= ?? Δx = 3 cm = 0.03 m Fsp = ??

  32. If two “Grumpy Old Men” went ice fishing and were comparing their fish with the extension of the same spring, solve the following spring problem: “Grumpy Sam” caught the first fish and magically realized the fish had a mass of 23 kg. When this fish was suspended on the spring, like the one we suspended masses on in lab, the spring stretched so it was 3 cm longer than it was without the fish. What is the spring constant for the spring? Examples of 4 part Spring problem List : m = 23 kg Fg= Δx = 3 cm = 0.03 m Fsp = 1stUse Fg to find the Force on the spring Fg= m ag - 225 N = - Fs Fg= 23kg(-9.8m/s/s) Fg= - 225 N + 225 N = + Fs

  33. If two “Grumpy Old Men” went ice fishing and were comparing their fish with the extension of the same spring, solve the following spring problem: “Grumpy Sam” caught the first fish and magically realized the fish had a mass of 23 kg. When this fish was suspended on the spring, like the one we suspended masses on in lab, the spring stretched so it was 3 cm longer than it was without the fish. What is the spring constant for the spring? Examples of 4 part Spring problem List : m = 23 kg Fg= - 225 N Δx = 3 cm = 0.03 m Fsp = 225 N 2nd use Hooke to find the k value Fsp= k Δx 225 N =k(0.03m) 7500 N/m =k

  34. “Grumpy Joe’s” Fish NEW FORCE NEW MASSSAME SPRING!! “Grumpy Joe” then caught a fish that caused the same spring to extend 5 cm from the length of the empty spring,. What was the mass of “Grumpy Joe’s” fish? Examples of 4 part Spring problem List : m = ??? kg Fg= ???? N Δx = 5 cm = 0.05 m Fsp = ?? N k = 7500 N/m 3rd same spring with same k to find other Force Fsp= k Δx Fsp= 7500N/m(0.05m) Fsp= 375 N

  35. “Grumpy Joe’s” Fish NEW FORCE NEW MASSSAME SPRING!! “Grumpy Joe” then caught a fish that caused the same spring to extend 5 cm from the length of the empty spring,. What was the mass of “Grumpy Joe’s” fish? Examples of 4 part Spring problem List : m = ??? kg Fg= -375 N Δx = 5 cm = 0.05 m Fsp = 375 N k = 7500 N/m 4th convert weight to mass Fg= m ag - 375 N = - Fs -375 N= m(-9.8m/s/s) m= 38.3 kg + 375 N = + Fs

  36. Equation SheetSlides for Springs and Pendulums

  37. Period and Frequency-notes • Hertz is unit that means 1/sec • Abbreviated ------- Hz • Mega Hertz –FM radio • Kilo Hertz – AM radio Page 3 Space #4 Period # repetitions # cycles # revolutions Hz Sec-1 1/sec f Frequency

  38. Period and Frequency • Hertz is unit that means 1/sec • Abbreviated ------- Hz • Mega Hertz –FM radio • Kilo Hertz – AM radio Page 3 Space #5 Period Hz Sec-1 1/sec f Use when you know either T or f Frequency

  39. Oscillations for Pendulums only-Notes Page 3 Space #6 Length of the pendulum and gravity determine how fast the pendulum oscillates back and forth. Period All 3 equations are the same, just re-arranged m/s/s m/s2 Scalar-positive!! Hz Sec -1 1/sec

  40. Page 4 #1 Page 4 #2

  41. Springs only page 4 Space #3

  42. Period and Frequency • Hertz is unit that means 1/sec ( Hz)

  43. Hooke’s Law for Springs only

  44. Springs only

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