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a) A trap-door 120 cm by 120 cm is kept horizontal by a string attached to the mid-point of the side opposite to that containing the hinge. The other end of the string is tied to a point 90 cm vertically above the hinge. If the trap-door weight is 50 N, calculate the tension in the string and the reaction at the hinge.
(b) A wine glass has a circular base 70 mm in diameter. When empty the centre of mass of the glass is 130 mm above the table. At what angle to the table would the base be when it tips over?
c) A 6.0 m long cantilevered balcony of mass 3.6 tonnes juts out as shown in the figure. The balcony is supported by a pivot at P 2.0 m from the wall. The centre of mass of the balcony is 0.5 m beyond the support P
1. What is the vertical force at the point D needed to prevent the balcony tipping?
2. Calculate the force the support P has to withstand
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Subject: Engineering | Topic: Statics | ID: 155296
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$ 1.0 |
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1. A square of side 2R has a circular hole of radius R/2 removed from one quarter as shown (Fig101a). The centre of the hole is located at (R/2, R/2) from the centre.
Locate the centre of mass with respect to the centre of the square.
2. An irregular shaped casting of mass M = 2.2 kg can’t be balanced to locate its centre of mass.
However, part of it is a uniform rod as shown (Fig1001b). The centre of mass can be found by supporting the rod at various positions distance x from the end of the rod and balancing it with a mass m at the end. Results are as in the table
(a) Plot a graph of moment G = m.x (vertical axis) against x (horizontal axis)
(b) Work out how m.x, M and X the distance of the centre of mass from the end of the rod are related
(c) Use your graph to locate X the position of the centre of mass ...MORE
Subject: Engineering | Topic: Statics | ID: 155299
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Guy wire AB is use to help support the utility pole AC.
a. Assuming the force supported by the utility pole is directed along the line AC. determine the force in wire AB and pole AC if P=1,000 lb.
b. If the guy wire is made of steel which has a maximum allowable axial stress of 40.000 psi, determine the minimum diameter of the cable that should be used (assume the cable is circular in cross-section).
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Subject: Engineering | Topic: Statics | ID: 155310
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One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. One force has a magnitude of 2.20 N and is applied perpendicular to the length of the stick at the free end. The other force has a magnitude of 5.70 N and acts at a 25.0° angle with respect to the length of the stick.
Where along the stick is the 5.70 N force applied?
Express this distance with respect to the end that is pinned (i.e find d). ...MORE
Subject: Engineering | Topic: Statics | ID: 155564
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The drawing shows a person (weight W = 598 N, L1 = 0.855 m, L2 = 0.423 m) doing push-ups.
Find the normal force exerted by the floor on each hand and each foot, assuming that the person holds this position. ...MORE
Subject: Engineering | Topic: Statics | ID: 155566
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A hiker, who weighs 1080 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3080 N, and rests on two concrete supports, one at each end. He stops one-fifth of the way along the bridge.
What is the magnitude of the force that a concrete support exerts on the bridge at each end? ...MORE
Subject: Engineering | Topic: Statics | ID: 155568
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A massless, rigid board is placed across two bathroom scales that are separated by a distance of 2.00 m.
A person lies on the board. The scale under his head reads 430 N, and the scale under his feet reads 340 N.
(a) Find the weight of the person.
(b) Determine the distance between the person's head and his center of gravity. ...MORE
Subject: Engineering | Topic: Statics | ID: 155570
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Determine the internal normal force, shear force, and moment at point C. ...MORE
Subject: Engineering | Topic: Statics | ID: 156166
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Determine the internal normal force, shear force, and moment at point C in the cantilever beam. Draw the shear and moment diagrams for the cantilever beam.
(Hint: There is a moment at A due to the fixed connection). ...MORE
Subject: Engineering | Topic: Statics | ID: 156168
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Draw the shear and moment diagrams for the beam shown below. ...MORE
Subject: Engineering | Topic: Statics | ID: 156170
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Draw the shear and moment diagrams for the beam shown below. ...MORE
Subject: Engineering | Topic: Statics | ID: 156172
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$ 2.0 |
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A 300 lbf weight is suspended from two strings as shown.
The strings will only transfer tension along their length.
Calculate tension in each string ...MORE
Subject: Engineering | Topic: Statics | ID: 157730
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F = 5000 lbf .
Calculate reactions at C and D for the weightless number ...MORE
Subject: Engineering | Topic: Statics | ID: 157732
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Draw the shear and moment diagrams for the beam at A,B,C and D.
L = 30 ft, w1 = 50 p/f, w2 =10 p/f
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Subject: Engineering | Topic: Statics | ID: 157734
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The hollow shaft shown is made of a steel that is assumed to be elastoplastic with tau Y = 145 MPa and G = 77.2 MPa. The inner radius r1 = 12.5 mm and outer radius r2 = 30 mm.
The magnitude T of the torque is slowly increased until the plastic zone first reaches the inner surface of the shaft‐the torque is then removed.
Determine the magnitude and location of the maximum residual shearing stress in the rod. ...MORE
Subject: Engineering | Topic: Statics | ID: 157747
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The free way sign for which the yield strength is "Y" is subject to horizontal wind force P as shown below.
Using the maximum shearing stress criterion, determine the maximum force P that the sign can carry.
For simplicity, ignore the shear force at the bottom. ...MORE
Subject: Engineering | Topic: Statics | ID: 157749
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For the stress state shown, find the principal stresses.
If "Y” is 300 MPa, will it fail according to maximum-distortion-energy criterion and maximum-shearing-stress criterion? ...MORE
Subject: Engineering | Topic: Statics | ID: 157751
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A pile(rod) with a circular cross-section of radius r is being driven into a tight fitting hole as shown in the figure.
Do you expect shear stress at point A, B, and C?
If so, what it the relation between the shear-stress distribution and the load P?
Please write an appropriate equation for the relation.
Hint: Free-body diagram
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Subject: Engineering | Topic: Statics | ID: 157753
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$ 2.0 |
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The system shown consists of cables AB and AC, horizontal cable CE, and vertical bar CD.
If the cables and bar have the failure strengths shown, determine the largest load P that can be supported by the system.
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Subject: Engineering | Topic: Statics | ID: 157999
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The cable-pulley systems shown are used to support a weight W.
Determine the cable tension T in terms of W. ...MORE
Subject: Engineering | Topic: Statics | ID: 158014
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$ 1.0 |
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