3. Rigid-Body in Equilibrium: A Truck on a Drawbridge.drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truckdriver radios for help, sets the handbrake, and waits. Meanwhile, a boatapproaches, so the drawbridge is raised by means of a cable attached to the end opposite the hinge (seeA loaded cement mixer drives onto an oldfigure below). The drawbridge is 40.0 m long and has a mass of 12,000 kg; its center of gravity is at itsmidpoint. The cement mixer, with driver, has mass 30,000 kg. When the drawbridge has been raised to anangle of 30° above the horizontal, the cable makes an angle of 70° with the surface of the bridge.T70°k10.0m40.0 m30(i)Sketch the free-body diagram (FBD) of the drawbridge with complete forcelabels.(ii)(ii)Determine the moment arm () of each force. Show complete solution. Put the results in a table.Determine the sign of the torque, based on the direction of rotation of the beam that is causedby each torque. Indicate these on your FBD. Indicate the signs of the torques in the table ofresults.What is the tension (T) in the cable when the drawbridge is held in this position?What are the horizontal and vertical components of the force the hinge (Fpx and Fpy) exerts onthe drawbridge?(iv)(v)

Given:Length of the bridge, L = 40 mmass of the bridge, mb = 12000 kgdistance of truck from origin,…

A loaded cement mixer drives onto an old Rigid-Body in Equilibrium: A Truck on a Drawbridge. drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat

A loaded cement mixer drives onto an old Rigid-Body in Equilibrium: A Truck on a Drawbridge. drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter9: Statics And Torque

Section: Chapter Questions

Problem 18PE: In Figure 9.21, the cg of the pole held by the pole vaulter is 2.00 m from the left hand, and the...

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Two children of mass 20.0 kg and 30.0 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 3.00 m, at what distance from the pivot point is the small child sitting in order to maintain the balance?
In order to get his car out of the mud, a man ties one end of a rope to the front bumper and the other end to a tee 15 m away as shown below. He then pulls on the center of the rope with a force of 400 N, which causes its center to be displaced 0.30 m, as shown. What is the force of the rope on the car?
Suppose the weight of the drawbridge in Figure 9.34 is supported entirely by its hinges and the opposite shore, so that its cables are slack. (a) What fraction of the weight is supported by the opposite shore if the point of support is directly beneath the cable attachments? (b) What is the direction and magnitude of the force the hinges exert on the bridge under these circumstances? The mass of the bridge is 2500 kg.
(a) What minimum coefficient of friction is needed between the legs and the ground to keep the sign in Figure 9.35 in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?
Explain the need for tall towers on a suspension bridge to ensure stable equilibrium.
In Figure 9.21, the cg of the pole held by the pole vaulter is 2.00 m from the left hand, and the hands are 0.700 m apart. Calculate the force exerted by (a) his right hand and (b) his left hand. (c) If each hand supports half the weight of the pole in Figure 9.19, show that the second condition for equilibrium (net =0 ) is satisfied for a pivot other than the one located at the center of gravity of the pole. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium described above. Figure 9.21 A pole vaulter is holding a pole horizontally with both hands. The center of gravity is to the left side of the vaulter.
A uniform ladder of length L.and mass m1 rests against a frictionless wall. The ladder makes an angle 0 with the horizontal, (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when a firelighter of mass m2, has climbed a distance x along the ladder from the bottom, (b) If the ladder is just on the verge of slipping when the firefighter is a distance d along the ladder from the bottom, what is the coefficient of static friction between ladder and ground?
A 15.0-in uniform ladder weighing 500 N rests against frictionless wall. The ladder makes a 60.0 angle ESI with the horizontal, (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 800-N firelighter has climbed 4.00 m along the ladder from the bottom, (b) If the ladder is just on the verge of slipping when the firefighter is 9.00 m from the bottom, what is the coefficient of static friction between ladder and ground?
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) What is the mechanical advantage of a wheelbarrow, such as the one in Figure 9.24, if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of 5.50 cm, while the hands have a perpendicular lever arm of 1.02 m? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is 55.0 kg? (c) What force does the wheel exert on the ground? Figure 9.24 (a) In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot IS the wheel's axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. (b) In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel's load) is less than the input force (from the hand nearest the load), because the Input is exerted closer to the pivot than is the output
A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at .500 m from the end of the plank with force F2. If the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F1 and F2?
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.