Concept explainers
A child’s toy consists of a small wedge that has an acute angle θ (Fig. P6.28). The sloping side of the wedge is frictionless, and an object of mass m on it remains at constant height if the wedge is spun at a certain constant speed. The wedge is spun by rotating, as an axis, a vertical rod that is firmly attached to the wedge at the bottom end. Show that, when the object sits at rest at a point at distance L up along the wedge, the speed of the object must be v = (gL sin θ)1/2.
Figure P6.28
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
Additional Science Textbook Solutions
Cosmic Perspective Fundamentals
University Physics Volume 3
Loose Leaf For Explorations: Introduction To Astronomy
University Physics Volume 1
MODERN PHYSICS (LOOSELEAF)
The Physical Universe
- A stone of mass 800.0 g is fastened to a string of length 75.0 cm which would break when the tension in it exceeds 50.0 N. The stone is whirled in a vertical plane with axis of rotation being 150 cm above the ground. The angular speed is gently increased until the string breaks. At which point along the circular path is the break likely to occur?arrow_forwardThe motion of spinning a hula hoop around one's hips can be modeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is less than R, the radius of the hoop. Suppose Maria spins a hula hoop with a mass of 0.72 kg and a radius of 0.65 m around her waist. The rotation axis is perpendicular to the plane of the hoop, but approximately 0.43 m from the center of the hoop. (a) What is the rotational inertia of the hoop in this case?(b) If the hula hoop is rotating with an angular speed of 13.1 rad/s, what is its rotational kinetic energy?arrow_forwardInitially, a small 4.0-kg rock is whirling at the end of a very thin string in a circular path of radius 1.25 m on a horizontal frictionless surface, as shown in the figure. The initial tangential speed of the rock was 8.0 m/s. The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to 0.25 m. What is the instantaneous speed of the mass at the moment the string reaches a length of 0.25 m?arrow_forward
- The motion of spinning a hula hoop around one's hips can be modeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is less than R, the radius of the hoop. Suppose Maria spins a hula hoop with a mass of 0.74 kg and a radius of 0.67 m around her waist. The rotation axis is perpendicular to the plane of the hoop, but approximately 0.45 m from the center of the hoop. (a) What is the rotational inertia of the hoop in this case? kg · m2 (b) If the hula hoop is rotating with an angular speed of 13.3 rad/s, what is its rotational kinetic energy? Jarrow_forwardThe motion of spinning a hula hoop around one's hips can be modeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is less than R, the radius of the hoop. Suppose Maria spins a hula hoop with a mass of 0.74 kg and a radius of 0.67 m around her waist. The rotation axis is perpendicular to the plane of the hoop, but approximately 0.45 m from the center of the hoop. (a) What is the rotational inertia of the hoop in this case? 0.45 X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg. m² (b) If the hula hoop is rotating with an angular speed of 13.3 rad/s, what is its rotational kinetic energy? 0.74 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. Jarrow_forwardOne end of a cord is fixed and a small 0.500-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.00 m, as shown in Figure P7.19. When angle = 20.0, the speed of the object is 8.00 m/s. At this instant, find the tension in the string, the tangential and radial components of acceleration and the total acceleration Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? Explain.arrow_forward
- A light, rigid rod is 68.5 cm long. Its top end is pivoted on a frictionless horizontal axle. The rod hangs straight down at rest with a small, massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full circle. What minimum speed at the bottom is required to make the ball go over the top of the circle?arrow_forwardA child’s toy consists of a small wedge that has an acute angle θ (as shown). The sloping side of the wedge is frictionless, and an object of mass m on it remains at constant height if the wedge is spun at a certain constant speed. The wedge is spun by rotating, as an axis, a vertical rod that is firmly attached to the wedge at the bottom end. Show that, when the object sits at rest at a point at distance L up along the wedge, the speed of the object must beυ = (gL sin θ)1/2.arrow_forwardIn a charming 19th-century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 3.50 m in diameter. The elevator is raised and lowered by turning the disk, and the cable does not slip on the rim of the disk but turns with it. (a) At how many rpm must the disk turn to raise the elevator at 25.0 cm/s? (b) To start the elevator moving, it must be accelerated at 19g. What must be the angular acceleration of the disk, in rad/s2?arrow_forward
- A block of mass m is placed on a rough surface that rotates at 15 rpm. If the body has a distance of 146 cm from the vertical rotation axis, how large must the friction coefficient be so that the body remains at rest?arrow_forwardA light string can support a stationary hanging load of 25.0 kg before breaking. An object of mass 3.00 kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r =0.8 m, and the other end of the string is held fixed as shown in the figure. What range of speeds can the object have before the string breaks?arrow_forwardOne method of pitching a softball is called the "windmill" delivery method, in which the pitcher's arm rotates through approximately 360° in a vertical plane before the 198-gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 91.0 mi/h. Assume that the angular acceleration is uniform throughout the pitching motion, and take the distance between the softball and the shoulder joint to be 70.0 cm. (a) Determine the angular speed of the arm in rev/s at the instant of release. rev/s (b) Find the magnitude of the value of the angular acceleration a in rev/s² and the radial and tangential acceleration of the ball just before it is released. α = rev/s² m/s² m/s² ar = at = (c) Determine the magnitude of the force exerted on the ball by the pitcher's hand (both radial and tangential components) just before it is released. Fr Ft = 1 N Narrow_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