Concept explainers
A simple harmonic oscillator consists of a 0.50 kg block attached to a spring. The block slides back and forth along a straight line on a frictionless surface with equilibrium point .x = 0. At t = 0 the block is at x = 0 and moving in the positive x direction. A graph of the magnitude of the net force
Figure 15-55 Problem 81.
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Fundamentals of Physics Extended
Additional Science Textbook Solutions
Organic Chemistry
Human Physiology: An Integrated Approach (8th Edition)
Genetic Analysis: An Integrated Approach (3rd Edition)
Biology: Life on Earth with Physiology (11th Edition)
Microbiology: An Introduction
Campbell Biology: Concepts & Connections (9th Edition)
- Use the data in Table P16.59 for a block of mass m = 0.250 kg and assume friction is negligible. a. Write an expression for the force FH exerted by the spring on the block. b. Sketch FH versus t.arrow_forwardA mass is placed on a frictionless, horizontal table. A spring (k=100N/m) , which can be stretched or compressed, is placed on the table. A 5.00-kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=4.0 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion. (b) Find the position, velocity, and acceleration of the mass at time t=3.00 s.arrow_forwardCalculate the maximum values of the amplitudes of the response functions shown in Figures 3-22 and 3-24. Obtain numerical values for β = 0.2ω0 when a = 2 m/s2, ω0 = 1 rad/s, and t0 = 0.arrow_forward
- A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.arrow_forwardSome people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.arrow_forwardA block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown in Figure P7.15. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is k = 0.350. Figure P7.15arrow_forward
- Two springs are connected each other and suspended vertically. To the bottom one, a body of mass .2 kg is fastened. Find the elasticity coefficient of one of the Two springs is the other spring has a constant of 30n/m and total elongation is 10 cmarrow_forwardFor Exercises 81–-82, consider a 1-kg object oscillating at the end of a horizontal spring. The horizontal position x(f) of the object is given by x(1) sin (wt) + xpcos(wi) WWW -3-2-1 0 1 2 3 where v, is the initial velocity, x, is the initial position, and w is the number of back-and-forth cycles that the object makes per unit time t. 81. At time t = 0 sec, the object is moved 3 ft to the left of the equilibrium position and then given a velocity of 4 ft/sec to the right (vo = 4 ft/sec). Vo sin(wt) + xocos (wi) to represent the a. If the object completes 1 cycle in 1 sec (w = 1), write a model of the form x(t) horizontal motion of the spring. b. Use the reduction formula to write the function in part (a) in the form x(t) = ksin(t + a). Round a to 2 decimal places. c. What is the maximum displacement of the object from its equilibrium position? 82. At time t = 0 sec, the object is moved 2 ft to the right of the equilibrium position and then given a velocity of 3 ft/sec to the left (vo…arrow_forward2) (a)The springs of a mountain bike are compressed vertically by 5 mm when a cyclist of mass 60 kg sits on it. When the cyclist rides the bike over a bump on a track, the frame of the bike and the cyclist oscillate up and down. Using the formula F = - ks, calculate the value of k, the constant for the springs of the bike. (b)The total mass of the frame of the bike and the cyclist is 80 kg. Calculate the period of oscillation of the cyclist. (c)Calculate the number of oscillations of the cyclist per second.arrow_forward
- (B) llllllll Students set up an experiment by attaching an ideal vertical spring to a support and hanging a block of known mass from the spring. The students pull the block down and release it from rest. The students then measure the period of the block's oscillation. This procedure is repeated for several trials using the same spring but with blocks of different known masses. The students are instructed to create a linear graph using the mass m of each block and the period T of the block's motion. The slope of the graph will be used to calculate the force constant k of the spring. Which of the following best indicates how the students should create their linear graph and how k can be calculated from the slope of the graph? E k Graph T on the vertical axis and m on the horizontal axis; set k = 2π slope Graph T² on the vertical axis and m on the horizontal axis; set k Graph T on the vertical axis and m² on the horizontal axis; set k Graph T² on the vertical axis and m on the horizontal…arrow_forwardA hummingbird of mass 0.16 oz lands on the end of a small horizontal branch, whichsubsequently oscillates up and down with a period of one second. Assuming that the twig is amassless spring. Estimate its force constant.arrow_forwardYou pull on a string with a horizontal force of magnitude F = 40 N that is attached to a block of mass m, = 7.5 kg, then to the axle of a solid cylinder of mass m. = 4.8 kg and radius r = 0.4 m, then to a spring of spring constant k = 140 N/m. This is all done on an inclined plane where there is friction ( 4s = 0.68 and , = 0.31 ), and the incline angle is e = 25 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the Cylinder, Spring, and Block on Ramp spring stretches. 000000000- b yb First, what is the speed of the block and cylinder after you have pulled the block and cylinder 86 cm down the plane?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning