A common demonstration, illustrated in Figure P10.72, consists of a ball resting at one end of a uniform board of length l, hinged at the other end, and elevated at an angle θ. A light cup is attached to the board at rc so that it will catch the ball when the support stick is suddenly removed. (a) Show that the ball will lag behind the falling board when θ is less than 35.3°. (b) If the board is 1.00 m long and is supported at this limiting angle, show that the cup must be 18.4 cm from the moving end.

A common demonstration, illustrated in Figure P10.72, consists of a ball resting at one end of a uniform board of length l, hinged at the other end, and elevated at an angle θ. A light cup is attached to the board at rc so that it will catch the ball when the support stick is suddenly removed. (a) Show that the ball will lag behind the falling board when θ is less than 35.3°. (b) If the board is 1.00 m long and is supported at this limiting angle, show that the cup must be 18.4 cm from the moving end.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 76P

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A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = ℓ. A painter of mass m stands on the ladder a distance d from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately. Figure P10.73 Problems 73 and 74.
A uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot located a distance = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 55.0 kg steps onto the left end of the beam and begins walking to the right as in Figure P10.28. The goal is to find the womans position when the beam begins to tip. (a) What is the appropriate analysis model for the beam before it begins to tip? (b) Sketch a force diagram for the beam, labeling the gravitational and normal forces acting on the beam and placing the woman a distance x to the right of the first pivot, which is the origin. (c) Where is the woman when the normal force n1 is the greatest? (d) What is n1 when the beam is about to tip? (e) Use Equation 10.27 to find the value of n2 when the beam is about to tip. (f) Using the result of part (d) and Equation 10.28, with torques computed around the second pivot, find the womans position x when the beam is about to tip. (g) Check the answer to part (e) by computing torques around the first pivot point. Figure P10.28
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