L • VP2. A child's toy consists of a small wedge that has an acute angle u as shown above. 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 V9L sin 0 V =
L • VP2. A child's toy consists of a small wedge that has an acute angle u as shown above. 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 V9L sin 0 V =
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**VP2.** A child’s toy consists of a small wedge that has an acute angle \( \theta \) as shown above. The sloping side of the wedge is frictionless, and an object of mass \( m \) on it remains at a 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
\[ v = \sqrt{gL \sin \theta}. \]
**Diagram Explanation:**
The diagram illustrates a right-angled wedge with an object of mass \( m \) placed on its sloping side. The slope has an angle \( \theta \) with respect to the horizontal base. The object is at a distance \( L \) from the base along the slope. The wedge is attached to a vertical rod, which acts as the axis of rotation, located at the wedge's lower base. The concept involves analyzing the conditions for the object to maintain a stable position when the wedge is rotating.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9682b814-e7b6-40bb-8ab1-65efb8b73f6f%2F40426b0e-2383-4d6f-8af9-45ba603f33f8%2F280fokk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**VP2.** A child’s toy consists of a small wedge that has an acute angle \( \theta \) as shown above. The sloping side of the wedge is frictionless, and an object of mass \( m \) on it remains at a 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
\[ v = \sqrt{gL \sin \theta}. \]
**Diagram Explanation:**
The diagram illustrates a right-angled wedge with an object of mass \( m \) placed on its sloping side. The slope has an angle \( \theta \) with respect to the horizontal base. The object is at a distance \( L \) from the base along the slope. The wedge is attached to a vertical rod, which acts as the axis of rotation, located at the wedge's lower base. The concept involves analyzing the conditions for the object to maintain a stable position when the wedge is rotating.
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