Question 1

A heavy block is supported by three lines as shown.Which of the following statements is true in its entirety?

Accepted Answer

A) T1 > T2 and T2 > T3  
B) T2 > T1 and T1 > T3  
C) T2 > T3 and T3 > T1  
D) T3 > T1 and T1 > T2  
E) T1 > T3 and T2 > T3  
A) T1 > T2 and T2 > T3  
B) T2 > T1 and T1 > T3  
C) T2 > T3 and T3 > T1  
D) T3 > T1 and T1 > T2  
E) T1 > T3 and T2 > T3  C

Question 2

The bulk modulus of water is 2.0 $\times$ 109 N/m2.By how much must the pressure be increased to reduce the volume of 1.0 kg of water from 1.00 to 0.998 L?

Accepted Answer

A) 2.0 $\times$ 106 N/m2  
B) 4.0 $\times$ 106 N/m2  
C) 20 $\times$ 106 N/m2  
D) 40 $\times$ 106 N/m2  
E) 8.0 $\times$ 106 N/m2  
A) 2.0 $\times$ 106 N/m2  
B) 4.0 $\times$ 106 N/m2  
C) 20 $\times$ 106 N/m2  
D) 40 $\times$ 106 N/m2  
E) 8.0 $\times$ 106 N/m2  B

Question 3

A design project requires you to construct a crane to lift a maximum of 5000 kg and with a maximum upward acceleration of 2 m/s2,and with a safety factor of 5.If the cable is 20m long,by how much does the cable stretch when the crane is operating at the design limits?

Accepted Answer

A) 2.80 cm 
B) 1.05 cm 
C) 6.21 cm 
D) 0.84 cm 
E) 5.22 cm 
A) 2.80 cm 
B) 1.05 cm 
C) 6.21 cm 
D) 0.84 cm 
E) 5.22 cm B

Question 4

A 10-m long plank (of negligible mass)is supported at each end by vertical cables.A person of unknown weight sits on the plank between the cables.The tension in the left cable is 300 N,and in the right cable it is 200 N.How far is the person sitting from the left cable?

Accepted Answer

A) 2.0 m 
B) 3.0 m 
C) 4.0 m 
D) 6.0 m 
E) 7.0 m 
A) 2.0 m 
B) 3.0 m 
C) 4.0 m 
D) 6.0 m 
E) 7.0 m

Question 5

Use the figure to the right to answer the next problem.
A ball of mass m and radius r is placed next to a step of height ½ r.  
-What is the magnitude of the force the contact point c exerts on the ball when the applied force F just lifts the ball off the floor?

Accepted Answer

A) mg 
B) 1.5 mg 
C) 1.73 mg 
D) 2 mg 
E) 2.14 mg 
A) mg 
B) 1.5 mg 
C) 1.73 mg 
D) 2 mg 
E) 2.14 mg

Question 6

For a rigid body to remain in equilibrium it is necessary and sufficient that

Accepted Answer

A)  $\Sigma$  = 0 
B) $\Sigma$   $\alpha$ = 0 
C) $\Sigma$   = 0; $\Sigma$   = 0 
D) $\Sigma$   = 0 
E) $\Sigma$ mr2 = 0 
A)  $\Sigma$  = 0 
B) $\Sigma$   $\alpha$ = 0 
C) $\Sigma$   = 0; $\Sigma$   = 0 
D) $\Sigma$   = 0 
E) $\Sigma$ mr2 = 0

Question 7

The center of gravity and the center of mass coincide if

Accepted Answer

A) the body is in rotational equilibrium. 
B) the body is in translational equilibrium. 
C) the acceleration due to gravity is constant over the body. 
D) the body is in both translational and rotational equilibrium. 
E) any forces accelerating the body are constant. 
A) the body is in rotational equilibrium. 
B) the body is in translational equilibrium. 
C) the acceleration due to gravity is constant over the body. 
D) the body is in both translational and rotational equilibrium. 
E) any forces accelerating the body are constant.

Question 8

Use the following to answer the question:  
-The horizontal boom supporting the sign is of uniform construction and weighs 50 N.If the sign weighs 150 N,the angle between the force exerted by the hinge on the boom and the boom is

Accepted Answer

A) ~85º 
B) ~67º 
C) ~47º 
D) ~37º 
E) None of these is correct. 
A) ~85º 
B) ~67º 
C) ~47º 
D) ~37º 
E) None of these is correct.

Question 9

The sign shown in the figure weighs 200 N.The boom is of uniform construction.If the force exerted by the hinge on the boom is 300 N and acts at an angle of 20º above the horizontal,the tension in the tie cable is

Accepted Answer

A) ~205 N 
B) ~145 N 
C) ~413 N 
D) ~625 N 
E) None of these is correct. 
A) ~205 N 
B) ~145 N 
C) ~413 N 
D) ~625 N 
E) None of these is correct.

Question 10

Which of the following could not have units of N/m2?

Accepted Answer

A) Young's modulus 
B) shear modulus 
C) bulk modulus 
D) stress 
E) strain 
A) Young's modulus 
B) shear modulus 
C) bulk modulus 
D) stress 
E) strain

Question 11

Use the picture on the right to answer the next question. A steel wire and an aluminum wire of the same length L and diameter d are joined to form a wire of length 2L.The wire is fastened to the ceiling and a mass m is attached to the other end.  
-The amount of expansion in the aluminum portion is ____ the steel portion.

Accepted Answer

A) less than 
B) equal to 
C) greater than 
D) depends on how tight m is attached to the steel 
E) unable to tell 
A) less than 
B) equal to 
C) greater than 
D) depends on how tight m is attached to the steel 
E) unable to tell

Question 12

Use the following to answer the question:  
-The horizontal boom supporting the sign is of uniform construction and weighs 50 N.If the sign weighs 150 N,the force exerted by the hinge on the boom is

Accepted Answer

A) ~350 N 
B) ~304 N 
C) ~25 N 
D) ~550 N 
E) None of these is correct. 
A) ~350 N 
B) ~304 N 
C) ~25 N 
D) ~550 N 
E) None of these is correct.

Question 13

If the weight of the uniform boom shown in the figure is 2.00 kN,the tension in the horizontal guy wire supporting the boom and the 5.60-kN weight is

Accepted Answer

A) 13.2 kN 
B) 9.90 kN 
C) 9.20 kN 
D) 6.90 kN 
E) 3.00 kN 
A) 13.2 kN 
B) 9.90 kN 
C) 9.20 kN 
D) 6.90 kN 
E) 3.00 kN

Question 14

A ladder is extended to a length of 8 m.It rests against a smooth frictionless vertical wall at an angle of 55 degrees to the horizontal.The ladder has a mass of 30 kg,and its center of mass is three-eighths of the way up the ladder from the floor.Calculate the magnitude of the resultant of the horizontal and vertical forces at the bottom of the ladder and the floor.

Accepted Answer

A) 371 N 
B) 294 N 
C) 77.0 N 
D) 304 N 
E) 284 N 
A) 371 N 
B) 294 N 
C) 77.0 N 
D) 304 N 
E) 284 N

Question 15

Two wires,A and B,have the same initial length,but the radius of A is four times that of B,and the Young's modulus of A is a third that of B.If the same weight is attached to both wires,what is the ratio of the extension of A divided by the extension of B?

Accepted Answer

A) 0.19 
B) 48 
C) 5.3 
D) 1.3 
E) 0.75 
A) 0.19 
B) 48 
C) 5.3 
D) 1.3 
E) 0.75

Question 16

A box rests on a horizontal surface with one edge against a small ridge as shown.If the force   is 840 N and the bottom right edge of the box is just slightly off the ground,what is the weight of the box? (Hint: With the right edge slightly off the ground,the forces applied by the floor and the ridge must be at the bottom left corner of the box,and the angle can be taken to be negligibly small.)

Accepted Answer

A) 420 N 
B) 590 N 
C) 840 N 
D) 1.7 $\times$ 103 N 
E) 2.4 $\times$ 103 N 
A) 420 N 
B) 590 N 
C) 840 N 
D) 1.7 $\times$ 103 N 
E) 2.4 $\times$ 103 N

Question 17

Under which of the following conditions can a ladder standing on a frictionless horizontal floor and leaning against a rough vertical wall be in equilibrium?

Accepted Answer

A) The normal force exerted by the floor on the ladder equals the normal force the wall exerts on the ladder. 
B) The weight of the ladder is equal in magnitude to the frictional force the wall exerts on the ladder. 
C) A ladder in this situation cannot be in equilibrium. 
D) The normal force exerted by the floor on the ladder equals the weight of the ladder. 
E) The normal force exerted by the floor on the ladder equals the frictional force the wall exerts on the ladder. 
A) The normal force exerted by the floor on the ladder equals the normal force the wall exerts on the ladder. 
B) The weight of the ladder is equal in magnitude to the frictional force the wall exerts on the ladder. 
C) A ladder in this situation cannot be in equilibrium. 
D) The normal force exerted by the floor on the ladder equals the weight of the ladder. 
E) The normal force exerted by the floor on the ladder equals the frictional force the wall exerts on the ladder.

Question 18

A ball of radius r and mass m is hung using a light string of length L from a frictionless vertical wall.The normal force on the ball due to the wall is

Accepted Answer

A) mgr/L 
B)    
C)    
D) mgL/r 
E) None of these is correct. 
A) mgr/L 
B)    
C)    
D) mgL/r 
E) None of these is correct.

Question 19

Two unequal,antiparallel forces

Accepted Answer

A) can be replaced by a single force. 
B) can be replaced by a couple whose torque equals the torque about the center of mass of the original forces. 
C) can be replaced by equal,parallel forces. 
D) can be replaced by a single force plus a couple whose torque equals the torque about the center of mass of the original forces. 
E) can be replaced by none of these. 
A) can be replaced by a single force. 
B) can be replaced by a couple whose torque equals the torque about the center of mass of the original forces. 
C) can be replaced by equal,parallel forces. 
D) can be replaced by a single force plus a couple whose torque equals the torque about the center of mass of the original forces. 
E) can be replaced by none of these.

Question 20

When a certain truck stands on a level roadway,its front wheels support 1.11 kN,and its rear wheels support 18.9 kN.If the front and rear axles are 3.66 m apart,the horizontal distance between the rear axle and the center of gravity of the truck is approximately

Accepted Answer

A) 0.305 m 
B) 0.610 m 
C) 0.244 m 
D) 0.229 m 
E) 0.203 m 
A) 0.305 m 
B) 0.610 m 
C) 0.244 m 
D) 0.229 m 
E) 0.203 m

Exam 12: Static Equilibrium and Elasticity

A heavy block is supported by three lines as shown.Which of the following statements is true in its entirety?

The bulk modulus of water is 2.0 ×\times× 109 N/m2.By how much must the pressure be increased to reduce the volume of 1.0 kg of water from 1.00 to 0.998 L?

A design project requires you to construct a crane to lift a maximum of 5000 kg and with a maximum upward acceleration of 2 m/s2,and with a safety factor of 5.If the cable is 20m long,by how much does the cable stretch when the crane is operating at the design limits?

A 10-m long plank (of negligible mass)is supported at each end by vertical cables.A person of unknown weight sits on the plank between the cables.The tension in the left cable is 300 N,and in the right cable it is 200 N.How far is the person sitting from the left cable?

Use the figure to the right to answer the next problem. A ball of mass m and radius r is placed next to a step of height ½ r. -What is the magnitude of the force the contact point c exerts on the ball when the applied force F just lifts the ball off the floor?

For a rigid body to remain in equilibrium it is necessary and sufficient that

The center of gravity and the center of mass coincide if

Use the following to answer the question: -The horizontal boom supporting the sign is of uniform construction and weighs 50 N.If the sign weighs 150 N,the angle between the force exerted by the hinge on the boom and the boom is

The sign shown in the figure weighs 200 N.The boom is of uniform construction.If the force exerted by the hinge on the boom is 300 N and acts at an angle of 20º above the horizontal,the tension in the tie cable is

Which of the following could not have units of N/m2?

Use the following to answer the question: -The horizontal boom supporting the sign is of uniform construction and weighs 50 N.If the sign weighs 150 N,the force exerted by the hinge on the boom is

If the weight of the uniform boom shown in the figure is 2.00 kN,the tension in the horizontal guy wire supporting the boom and the 5.60-kN weight is

Two wires,A and B,have the same initial length,but the radius of A is four times that of B,and the Young's modulus of A is a third that of B.If the same weight is attached to both wires,what is the ratio of the extension of A divided by the extension of B?

Under which of the following conditions can a ladder standing on a frictionless horizontal floor and leaning against a rough vertical wall be in equilibrium?

A ball of radius r and mass m is hung using a light string of length L from a frictionless vertical wall.The normal force on the ball due to the wall is

Two unequal,antiparallel forces

When a certain truck stands on a level roadway,its front wheels support 1.11 kN,and its rear wheels support 18.9 kN.If the front and rear axles are 3.66 m apart,the horizontal distance between the rear axle and the center of gravity of the truck is approximately

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The bulk modulus of water is 2.0 $\times$ 10⁹ N/m².By how much must the pressure be increased to reduce the volume of 1.0 kg of water from 1.00 to 0.998 L?

A design project requires you to construct a crane to lift a maximum of 5000 kg and with a maximum upward acceleration of 2 m/s²,and with a safety factor of 5.If the cable is 20m long,by how much does the cable stretch when the crane is operating at the design limits?

Which of the following could not have units of N/m²?