Concept explainers
A cart with mass m=4.2 kg is moving on a frictionless surface. One end of the cart is attached to a spring, the other end of which is attached to a rigid wall. There is no other force exerted on the cart besides the spring force, and the cart follows simple harmonic motion. When the spring is at its equilibruim position, the carat is moving at the speed of 2.1 m/s and the spring can stretch or be compressed as far as 15 cm from the equilibruim position during this simple harmonic motion.
What is the amplitude of a carts simple harmonic motion?
What is the spring constant of the spring?
What is the period of this simple harmonic motion?
What is the maximum acceleration of the cart?
What is the speed of the cart when it is 10 cm away from the equilibrium position of the spring?
Given
m=4.2 Kg
Vm=2.1 m/s
Am=0.15m
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 1 images
- You 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_forwardA spring with spring constant 23 N/m is compressed a distance of 8.0 cm by a ball with a mass of 219.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 8.0 cm and is also released, leaving the spring at point A. Assume the ball rolls, but ignore other effects of friction. (Assume that the ball is a solid ball.) (a) What is the speed of the ball at point B?(b) What is the speed of the block at point B?arrow_forwardThe moment of inertia of a physical pendulum of 3 kg oscillating at small angles around an axis at a distance h = 0.8 m from the center of mass is given as I = 1.2 kg m ^ 2. What should be the length of a simple pendulum with a mass of 0.8 kg oscillating in the same period as the small oscillations of the pendulum? bIf the swing amplitude is 0.5 rad, what is the maximum value of the angular acceleration? (a-10rad/S b-20rad/s c-1/10rad/s d-20rad/S). ( figure for first question)arrow_forward
- All spiders are very sensitive to vibrations. An orb spider will sit at the center of its large, circular web and monitor radial threads for vibrations created when an insect lands. Assume that these threads are made of silk with a linear density of 1.0 × 10-5 kg/m under a tension of 0.40 N, both typical numbers. If an insect lands in the web 30 cm from the spider, how long will it take forthe spider to find out?arrow_forwardA spring is hung from the ceiling. A 0.588-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.101 m before momentarily coming to rest, after which it moves back upward. (a) VWhat is the spring constant of the spring? (b) Find the angular frequency of the block's vibrations. (a) Number i 57.09 Units N/m (b) Number i 97.0989 Units rad/sarrow_forwardSuppose that a simple pendulum consists of a small 60.0 g bob at the end of a cord of negligible mass. If the angle u between the cord and the vertical is given by u = (0.0800 rad) cos[(4.43 rad/s)t + f], what are (a) the pendulum’s length and (b) its maximum kinetic energy?arrow_forward
- Hello, here is my question Consider an object that undergoes simple harmonic motion without frictionbetween x = -A and x = +A. (a) Explain whether the object spends less time, more time, or the same amount of time between x = –A/2 and x = +A/2 as it does for |x| > A/2. (b) Determine the two values of x in terms of A where the kinetic energy of the object is equal to the potential energy of the object. Express the spring constant as k and the mass as m. Thank you!arrow_forwardProblem 9: An ideal pendulum of length L=1.1 m supports a mass of m =0.5 kg. Initially the pendulum is lifted such that it makes an angle of 0 = 26 degrees with respect to the vertical. m 10arrow_forwardThe wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration KG=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 8=0°. The spring's length at the state 2 is L2=4 m. (1) If the mass center G is set as the origin (datum), the gravitational potential energy at the state 1 is_____ (two decimal places) 1116441 L₂ State 2 State 1arrow_forward
- A 60 coil spring has a spring constant of 403 N/m. It is cut into 4 shorter springs, each of which has 15 coils. One end of a 15 coil spring is attached to a wall. An object of mass 36 kg is attached to the other end of the spring, and the system is set into horizontal oscillation. What is the angular frequency of the motion?arrow_forwardA 50 cm long spring with spring constant 302 N/m has a mass 1.4 kg attached to it, and it can ocillate on a horizontal table without any friction. When the spring is pulled so that its length is 59 cm, what is the magnitude of the restoring force exerted by the spring?arrow_forwardA spring oriented vertically is attached to a hard horizontal surface as in the figure below. The spring has a force constant of 1.32 kN/m. How much is the spring compressed when a object of mass m = 2.15 kg is placed on top of the spring and the system is at rest?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON