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Exam 12: Equilibrium and Elasticity

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Question 31

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A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm.Assuming g is constant, what is the location of the center of mass x_com, and the location of the center of gravity x_cog, of the two masses?

A) x_com = 1.5 cm, x_cog = 3.4 cm
B) x_com = 3.4 cm, x_cog = 1.5 cm
C) x_com = 1.5 cm, x_cog = 1.5 cm
D) x_com = 3.4 cm, x_cog = 3.4 cm
E) x_com = 1.5 cm, x_cog = 0 cm

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Question 32

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A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 * 10⁹ N/m².When it is subjected to a pressure of 3.0 * 10⁵ Pa its volume is:

A) 7.31 cm³
B) 7.99931 cm³
C) 8.00069 cm³
D) 8.69 cm³
E) none of these

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Question 33

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A ladder leans against a wall.If the ladder is not to slip, which one of the following must be true?

A 400-N uniform vertical boom is attached to the ceiling by a hinge, as shown.An 800-N weight W and a horizontal guy wire are attached to the lower end of the boom as indicated.The pulley is massless and frictionless.The tension force T of the horizontal guy wire has magnitude:

A net torque applied to a rigid object always tends to produce:

A shearing force of 50 N is applied to an aluminum rod with a length of 10 m, a cross-sectional area of 1.0 *10 ^{- 5} m, and shear modulus of 2.5 *10¹⁰ N/m². As a result the rod is sheared through a distance of:

An 80-N uniform plank leans against a frictionless wall as shown.The torque (about point P) applied to the plank by the wall is:

A uniform plank is 6.0 m long and weighs 80 N.It is balanced on a sawhorse at its center.An additional 160 N weight is now placed on the left end of the plank.To keep the plank balanced, it must be moved what distance to the right?

For a body to be equilibrium under the combined action of several forces:

A 5.0 m weightless strut, hinged to a wall, is used to support an 800-N block as shown.The horizontal and vertical components of the force of the hinge on the strut are:

A picture P of weight W is hung by two strings as shown.The magnitude of the tension force of each string is T.The total upward pull of the strings on the picture is:

A 960-N block is suspended as shown.The beam AB is weightless and is hinged to the wall at A.The tension force of the cable BC has magnitude:

To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at:

A certain wire stretches 0.90 cm when outward forces with magnitude F are applied to each end.The same forces are applied to a wire of the same material but with three times the diameter and three times the length.The second wire stretches:

A 4.0 m steel beam with a cross sectional area of 1.0 *10^-2 m² and a Young's modulus of 2.0* 10¹¹ N/m² is wedged horizontally between two vertical walls.In order to wedge the beam, it is compressed by 0.020 mm.If the coefficient of static friction between the beam and the walls is 0.35, the maximum mass (including its own) it can bear without slipping is:

The uniform rod shown below is held in place by the rope and wall.Suppose you know the weight of the rod and all dimensions.Then you can solve a single equation for the force exerted by the rope, provided you write expressions for the torques about the point:

Young's modulus can be used to calculate the strain for a stress that is: