A broom balances at a point x from its upper end. When a weight of mass m is attached at its upper end, the point of balance shifts to x a. Find an expression for the weight of the broom b. What is the weight of the broom if m = 0.23 kg, x = 1.100 m and x 0.940 m? Hint: Recall that in the expression for the position of the center of mass, the integral represents a sum over all parts of the object in question. If another part is added then the sum is replaced by the same sum plus an extra term consisting of and integral over the added volume. If the extra part is discrete that can be modeled as a point mass, then the extra term will consist of the mass of the object multiplied by its position F dm becomes: Ie M orig orig mextra (M ons extra orig or, for an extra part that can be treated as a point mass F'dmrextra Mextra (M onis +mestra orig

A broom balances at a point x from its upper end. When a weight of mass m is attached at its upper end, the point of balance shifts to x a. Find an expression for the weight of the broom b. What is the weight of the broom if m = 0.23 kg, x = 1.100 m and x 0.940 m? Hint: Recall that in the expression for the position of the center of mass, the integral represents a sum over all parts of the object in question. If another part is added then the sum is replaced by the same sum plus an extra term consisting of and integral over the added volume. If the extra part is discrete that can be modeled as a point mass, then the extra term will consist of the mass of the object multiplied by its position F dm becomes: Ie M orig orig mextra (M ons extra orig or, for an extra part that can be treated as a point mass F'dmrextra Mextra (M onis +mestra orig

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 36P: A crane of mass m1 = 3 000 kg supports a load of mass m2 = 10 000 kg as shown in Figure P10.36. The...

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Find the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23
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.
The fishing pole in Figure P10.22 makes an angle of 20.0 with the horizontal. What is the torque exerted by the fish about an axis perpendicular to the page and passing through the anglers hand if the fish pulls on the fishing line with a force F=100N at an angle 37.0 below the horizontal? The force is applied at a point 2.00 m from the anglers hands. Figure P10.22
A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = = 4.00 m. A painter of mass m = 70.0 kg stands on the ladder d = 3.00 m 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.
What three factors affect the torque created by a force relative to a specific pivot point?
A wooden door 2.1 m high and 0.90 m wide is hung by two hinges 1.8 m apart. The lower hinge is 15 cm above the bottom of the door. The center of mass of the door is at its geometric center, and the weight of the door is 260 N, which is supported equally by both hinges. Find the horizontal force exerted by each hinge on the door.
When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of the bolt. How much torque are you exerting in newton-meters (relative to the center of the bolt)?
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
A rod 7.0 m long is pivoted at a point 2.0 m from the left end. A downward force of 50 N acts at the left end, and a downward force of 200 N acts at the right end. At what distance to the right of the pivot can a third force of 300 N acting upward be placed to produce rotational equilibrium? Note: Neglect the weight of the rod. (a) 1.0 m (b) 2.0 m (c) 3.0 m (d) 4.0 m (e) 3.5 m
Under what conditions can a rotating body be in equilibrium? Give an example.
(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850 m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges? There is only one pair of hinges.
Answer yes or no to the following questions. (a) Is it possible to calculate the torque acting on a rigid object without specifying an axis of rotation? (b) Is the torque independent of the location of the axis of rotation?