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

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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Concept explainers

Center of Gravity of a system

The centre of gravity is a property that is based on the geometry of a rigid body or any particle. It is described as an equilibrium point or a hypothetical location where the total weight of the body is concentrated.

Question

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 truck
driver radios for help, sets the handbrake, and waits. Meanwhile, a boat
approaches, so the drawbridge is raised by means of a cable attached to the end opposite the hinge (see
A loaded cement mixer drives onto an old
figure below). The drawbridge is 40.0 m long and has a mass of 12,000 kg; its center of gravity is at its
midpoint. The cement mixer, with driver, has mass 30,000 kg. When the drawbridge has been raised to an
angle of 30° above the horizontal, the cable makes an angle of 70° with the surface of the bridge.
T
70°
k10.0m
40.0 m
30
(i)
Sketch the free-body diagram (FBD) of the drawbridge with complete force
labels.
(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 caused
by each torque. Indicate these on your FBD. Indicate the signs of the torques in the table of
results.
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 on
the drawbridge?
(iv)
(v)

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