Explanation For this problem, in the circular movement the force of the spring is pulling to the center, using the Newton’s second law we can solve for the angular velocity , we just need and expression for the spring constant using the period of 0.35 s. Given: The period of 0.35 s when the mas hanged from the spring. The spring stretched by the 15% of its length. Formula used: In a circular movement, the force is pointing to the pivot. The only present force is the spring’s. Using the Newton’s second law: ∑ F = k · x = m · a Where k is the spring constant, x is the length stretched of the spring, m is the mass; and a is the acceleration, which for circular movement can be calculated as: a = v 2 r Where v is the lineal speed of the mass and r is the radius of circle. Substituting the secondequation in the first one: k · x = m · v 2 r The velocity v can be expressed as: v = w · r Where w is the angular velocity when the mass is in circular movement. Therefore: k · x = m · ( w · r ) 2 r k · x = m · w 2 · r We need to solve for w : . The radius is: r = L + x Where L is the length of the spring without been stretched or compressed. We need an expression of the spring constant. Using the period of oscillation of the mass when it hanged from the spring: T = 2 π W Where W is the angular velocity and it is calculated as: W = k m Therefore: 2 π T = k m Solving for k : k = m ( 2 π T ) 2 Substituting in the equation for the angular velocity in circular movement: w 2 = m ( 2 π T ) 2 · x m

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

4th Edition

ISBN: 9780133953145

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Chapter 15, Problem 50EAP

To determine

The frequency in rpm for the spring’s length stretches by its 15%

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Chapter 15, Problem 49EAP

Chapter 15, Problem 51EAP

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Chapter 15 Solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

Ch. 15 - Prob. 1CQ Ch. 15 - A pendulum on Planet X, where the value of g is...Ch. 15 - FIGURE Q15.3 shows a position-versus-time graph...Ch. 15 - FIGURE Q15.4 shows a position-versus-time graph...Ch. 15 - 5. Equation 15.25 states that . What does this...Ch. 15 - A block oscillating on a spring has an amplitude...Ch. 15 - A block oscillating on a spring has a maximum...Ch. 15 - 8. The solid disk and circular hoop in FIGURE...Ch. 15 - FIGURE Q15.9 shows the potential-energy diagram...Ch. 15 - Suppose the damping constant b of an oscillator...

Ch. 15 - Prob. 11CQ Ch. 15 - 12. What is the difference between the driving...Ch. 15 - An air-track glider attached to a spring...Ch. 15 - An air-track is attached to a spring. The glider...Ch. 15 - Prob. 3EAP Ch. 15 - An object in SHM oscillates with a period of 4.0 s...Ch. 15 - What are the (a) amplitude, (b) frequency, and (c)...Ch. 15 - What are the (a) amplitude, (b) frequency, and (c)...Ch. 15 - FIGURE EX15.7 is the Position-versus-time graph of...Ch. 15 - FIGURE EX15.8 is the velocity-versus-time graph of...Ch. 15 - An object in simple harmonic motion has an...Ch. 15 - An object in simple harmonic motion has amplitude...Ch. 15 - An object in simple harmonic motion has amplitude...Ch. 15 - An object in simple harmonic motion has amplitude...Ch. 15 - An air-track glider attached to a spring...Ch. 15 - 14. A block attached to a spring with unknown...Ch. 15 - 15. A 200 g air-track glider is attached to a...Ch. 15 - A 200 g mass attached to a horizontal spring...Ch. 15 - Prob. 17EAP Ch. 15 - A 1.0 kg block is attached to a spring with spring...Ch. 15 - Prob. 19EAP Ch. 15 - Prob. 20EAP Ch. 15 - A spring is hanging from the ceiling. Attaching a...Ch. 15 - 22. A spring with spring constant 15 N/m hangs...Ch. 15 - 23. A spring is hung from the ceiling. When a...Ch. 15 - Prob. 24EAP Ch. 15 - A 200 g ball is tied to a string. It is pulled to...Ch. 15 - Prob. 26EAP Ch. 15 - Prob. 27EAP Ch. 15 - Prob. 28EAP Ch. 15 - Prob. 29EAP Ch. 15 - A 100 g mass on a 1.0-m-long string is pulled 8.0...Ch. 15 - A uniform steel bar swings from a pivot at one end...Ch. 15 - Prob. 32EAP Ch. 15 - Prob. 33EAP Ch. 15 - Prob. 34EAP Ch. 15 - Vision is blurred if the head is vibrated at 29 Hz...Ch. 15 - Prob. 36EAP Ch. 15 - Prob. 37EAP Ch. 15 - a. When the displacement of a mass on a spring is...Ch. 15 - For a particle in simple harmonic motion, show...Ch. 15 - A 100g block attached to a spring with spring...Ch. 15 - A 0.300 kg oscillator has a speed of 95.4cm/s when...Ch. 15 - An ultrasonic transducer, of the type used in...Ch. 15 - Astronauts in space cannot weigh themselves by...Ch. 15 - 44. Your lab instructor has asked you to measure a...Ch. 15 - A 5.0 kg block hangs from a spring with spring...Ch. 15 - Prob. 46EAP Ch. 15 - A block hangs in equilibrium from a vertical...Ch. 15 - Prob. 48EAP Ch. 15 - 49. Scientists are measuring the properties of a...Ch. 15 - Prob. 50EAP Ch. 15 - A compact car has a mass of 1200 kg. Assume that...Ch. 15 - Prob. 52EAP Ch. 15 - Prob. 53EAP Ch. 15 - Prob. 54EAP Ch. 15 - Prob. 55EAP Ch. 15 - Prob. 56EAP Ch. 15 - Prob. 57EAP Ch. 15 - A uniform rod of mass M and length L swings as a...Ch. 15 - Prob. 59EAP Ch. 15 - 60. A 500 g air-track glider attached to a spring...Ch. 15 - Prob. 61EAP Ch. 15 - Prob. 62EAP Ch. 15 - A molecular bond can be modeled as a spring...Ch. 15 - Prob. 64EAP Ch. 15 - Prob. 65EAP Ch. 15 - Prob. 66EAP Ch. 15 - The 15 g head of a bobble-head doll oscillates in...Ch. 15 - An oscillator with a mass of 500 g and a period of...Ch. 15 - Prob. 69EAP Ch. 15 - Prob. 70EAP Ch. 15 - Prob. 71EAP Ch. 15 - Prob. 72EAP Ch. 15 - Prob. 73EAP Ch. 15 - A block ona frictionless FIGURE P15.74 to two...Ch. 15 - Prob. 75EAP Ch. 15 - Prob. 76EAP Ch. 15 - A solid sphere of mass M and radius R is suspended...Ch. 15 - A uniform rod of length L oscillates as a pendulum...Ch. 15 - Prob. 79EAP Ch. 15 - Prob. 80EAP Ch. 15 - FIGURE CP15.81 shows a 200 g uniform rod pio4ed at...

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