A sandwich board advertising sign is constructed as shown in Figure 9.33. The sign’s mass is 8.00 kg. (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force is exerted by each side on the hinge?

A sandwich board advertising sign is constructed as shown in Figure 9.33. The sign’s mass is 8.00 kg. (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force is exerted by each side on the hinge?

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Static Equilibrium And Elasticity

Section: Chapter Questions

Problem 7P

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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.
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 stepladder of negligible weight is constructed as shown in Figure P12.40, 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. Figure P12.40 Problems 40 and 41.
What three factors affect the torque created by a force relative to a specific pivot point?
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
Under what conditions can a rotating body be in equilibrium? Give an example.
In the What If? section of Example 12.2, let d represent the distance in meters between the person and the hinge at the left end of the beam. (a) Show that the cable tension is given by T = 93.9d + 125, with T in newtons. (b) Show that the direction angle of the hinge force is described by tan=(323d+41)tan53.0 (c) Show that the magnitude of the hinge force is given by R=8.82103d29.65104d+4.96105 (d) Describe how the changes in T, , and R as d increases differ from one another.
The diagram below shows a beam of length 20.0 m and mass 40.0 kg resting on two supports placed at 5.0 m from each end. A person ofmass 50.0 kg stands on the beam between the supports. The upward forces at the supports are shown. (a) Determine the magnitude of N1 + N2. (b) Determine the magnitude of the torque exerted by the beam about N2. Hint: Center of mass would be helpful here. (c) The person moves toward the X end of the beam to the position where the beam just begins to tip and reaction force N1 becomes zero as thebeam starts to leave the left support. Determine the distance of the girl from the end X when the beam is about to tip.
Abeam with a length of 3.50 m and a weight of 200 N is attached on one end to a vertical wall with a hinge. The other end of the beam is connected to cable that makes an angle of 60.0° with the wall as shown in the figure below. A box with a weight of 50.0 N sits on the beam, two-thirds of its length away from the wall. What is the magnitude of the force exerted on the beam by the hinge?
An individual leans forwards to pick up a box of 100 N. The weight of his upper body has a magnitude of 450 N. The back is pivoting around the base of the vertebral column. Consider the back of the individual as a rigid bar that is controlled by a muscle with an angle of 12° (See picture, d = trunk-head distance = 1 m).a) Calculate the magnitude of muscle force required to lift the box.b) Calculate the magnitude of the force at the base of the vertebral column. Hints: For (a) solve the equilibrium of moments, i.e. what force is required in the muscle to balance out the moments acting around the base of the spine.For (b), solve the equilibrium of forces acting on the spine, including the muscle force you’ve just calculated, in x and y separately. There are two extra forces not shown in the diagram: x and y contact forces acting at the base of the spine. These are whatever is needed to keep the total forces acting on the spine = 0 (so the spine isn’t accelerating off in some…
A homeowner is trying to move a stubborn rock from his yard. By using a a metal rod as a lever arm and a fulcrum (or pivot point) the homeowner will have a better chance of moving the rock. The homeowner places the fulcrum a distance ?=0.288 mfrom the rock, which has a mass of 465 kg, and fits one end of the rod under the rock's center of weight. If the homeowner can apply a maximum force of 671 N at the other end of the rod, what is the minimum total length ? of the rod required to move the rock? Assume that the rod is massless and nearly horizontal so that the weight of the rock and homeowner's force are both essentially vertical. The acceleration due to gravity is ?=9.81 m/s2.
A stationary 3.0-m board of mass 7.0 kg is hinged at one end. A force F is applied vertically at the other end, and the board makes a 30° angle with the horizontal. A 65-kg block r on the board 80 cm from the hinge as shown in the figure below. 80 cm (a) Find the magnitude of the force F. (b) Find the force exerted by the hinge. (c) Find the magnitude of the force F as well as the force exerted by the hinge (FH), if F is exerted, instead, at right angles to the board. F. eBook O Type here to search 近