m k F = "kx T = 2# L T = 2# Notes on Ch. 11 Equations: F = "kx The force (F, measured in Newtons) produced by a spring is equal to the L g T = 2#

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1 Name: Physics Chapter 11 Study Guide Useful Information: F = "kx T = 2# L T = 2# m v = f$ PE g k e = 1 2 kx A Basic Understanding: Chapter 11 Odd Numbered Core Problems Chapter 11 Review Problems:! 3, 5, 9, 12, 13, 19, 21, 32, 35, 41, 43. Pushing to be Better: Chapter 11 Your Try Problems Chapter 11 Even Numbered Core Problems Chapter 11 Review Problems: 2, 4, 8, 10, 14, 15, 16, 18, 20, 23, 24, 25, 26, 27, 30, 31, 34, 36, 37, 38, 39, 40, 44, 45, 46, 48, 49. Standardized Test Prep Digging Deeper: Chapter 11 Review Problems: 50, 51. Individual Inquiry Notes on Ch. 11 Equations: F = "kx The force (F, measured in Newtons) produced by a spring is equal to the spring constant (k, measured in Newtons/meter) times the amount the spring is stretched (x, measured in meters). Note that x is ONLY the amount that the spring is stretched. If the spring has an original length of 35cm, and you stretch it to a total length of 45cm, you only use the 10cm of stretch for your value of x. T = 2# L g The period (T, measured in seconds) is equal to two pi times the square root of length (L, measured in meters) divided by the acceleration due to gravity (g, meters per second squared.) One period is the time to go through a complete cycle. Up to down is only have a cycle. One period would be up to down, and then down to up. VERY IMPORTANT: in this equation, L is the distance from the pivot point to the center of mass of the object. Please also note that this equation does not depend on the mass of the pendulum. T = 2# m k The period of a mass on a spring depends on the square root of the mass divided by the spring constant. (See notes on previous equations above for information about T, m and k. Physics Ch.11 Study Guide page 1 of 2

2 v = f" The velocity of any wave anywhere is the product of its frequency times its wavelength. v is velocity, measured in meters per second. f is frequency, measured in Hertz, which are abbreviated Hz. But 1 Hz is equal to one divided by one second. So Hz = 1/s. " This symbol is a Greek letter lambda. It s a Greek L. In this case lambda stands for wavelength and is measured in meters. One wave goes through a complete cycle. One full wave looks like this: Bonus question: why does this graph have the wavelength ending just a little past 6? What is the exact value for where it crosses? PE e = 1 2 kx 2 The elastic potential energy (Joules) of a spring is equal to 1/2 times the spring constant (N/m) times the distance stretched (m) squared. Physics Ch.11 Study Guide page 2 of 2

3 Name: Chapter 11 Worked Examples Physics 1) A pendulum is made by attaching a string to a uniform cylinder of metal that has a length of 8.4 cm. How long should the string be in order to give the pendulum a period of 1.32 seconds? Your Try: A physics student wishes to make a pendulum that has a period of exactly two seconds. They solve the equation and come up with a length of 99.4 cm. They make a string that is exactly 99.4 cm and attach it to a metal ball that has a diameter of 5.0 cm. What will the period of their pendulum be? Physics Ch. 11 Worked Examples page 1 of 2

4 2) A spring has a spring constant of 52 N/m and an unstretched length of 0.15 m. A mass of 500 g is hung from the end of the spring. a) what is the length of the spring when the mass hangs at rest? b) what is the period of vibration for the system? Your Try: A spring has a spring constant of 37 N/m and an unstretched length of 0.23 m. When a mass is hung from the end of the spring, the period of vibration is 0.48 seconds. a) What is the mass of the mass? b) what is the length of the spring when the mass hangs at rest? Physics Ch. 11 Worked Examples page 2 of 2

5 Physics Chapter 11 Your Try Problems (Based on various worked examples.) 3) Videos 11b-e (ADVANCED): Springs used for Hooke s Law should have some space between the coils when they are just hanging with nothing on them. This is so that there is truly zero force at zero stretch. Suppose you use a spring where the coils are touching to start out with. You take hang a 100 g mass from the spring, and measure the stretch to be 15cm. You then hang a 200 g mass from the spring, and measure the stretch to be 35cm. a) What is the spring constant for the spring? b) How much tension is the spring under when there is nothing attached to it? 4) Video 11h: A rough estimate of the waves in the supplemental video Making Standing Waves says there are four complete wavelengths in a distance of 20 meters. With a frequency of 0.6 Hz. Calculate the speed of the water waves in this tank. 5) Video 11k: A spring with nothing attached to it has a length of m. When a 300 g mass is hung from one end, the new length is m. The mass is then pulled down by hand an additional 10.0cm and released. a) Give the KE, GPE and SPE of the system when it is being held at the bottom. b) Give the KE, GPE and SPE of the system when it reaches the top of its motion. c) Give the KE, GPE and SPE of the system when it passes through equilibrium. d) Give the maximum speed of the mass.

6 Answers to Chapter 11 Your Try Problems Worked Example 1: A physics student wishes to make a pendulum... Period = s Worked Example 2: A spring has a spring constant of 37 N/m... a) m = 216 grams b) length of spring = m 3) Videos 11b-e (ADVANCED): Springs used for Hooke s Law should... a) k = N/m b) Tension = N 4) Video 11h: A rough estimate of the waves in the supplemental video... v = 3 m/s 5) Video 11k: A spring with nothing attached to it has a length of m... a) KE = 0J, GPE = 0J, SPE = 0.65J b) KE = 0J, GPE = 0.59J, SPE = 0.06J c) KE = 0.08J, GPE = 0.29 J, SPE = 0.28 d) v(max) = 0.72 m/s

7 Name: Physics Chapter 11 Core Problems 1) The wavelength of this wave is: a) 3 b) 6 c) 2 d) -2 to 2 e) 4 2) The amplitude of this wave is: a) 3 b) 6 c) 2 d) -2 to 2 e) 4 3) A 1.00 m long string (not shown) is attached to the end of the hook on a 1kg mass that is shown in the diagram below to make a pendulum. What is the period of this pendulum? Hook, negligible mass 7.5cm 1kg 11.5cm Physics Ch. 11 Core Problems page 1 of 2

8 4) A spring has an unstretched length of 13.3 cm, and a spring constant of 34 N/m. When a mass is attached to the end of the spring, the spring stretches to a total length of 24.5 cm. The mass is then pulled down slightly and released. a) What is the mass of the mass attached to the spring? b) What is the period of vibration for this system? I Refer to the diagram to the left, which represents a mass suspended on a spring. The mass oscillates between levels I and III. Level II is halfway between I and III. 5) The acceleration of the mass is a maximum at: a) Level I b) Level II c) Level III d) Levels I and III e) Always m/s 2 (all levels the same). II 6) At level III: KE PE(grav) PE(elastic) a) Minimum Minimum Maximum b) Intermediate Intermediate Maximum c) Minimum Maximum Minimum d) Intermediate Maximum Minimum e) Maximum Intermediate Minimum III 7) A string on a musical instrument has a length of 0.75 m. Waves on the string travel with a speed of 660 m/s. What is the fundamental frequency of the string? Physics Ch. 11 Core Problems page 2 of 2

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