Question 1

A horizontal uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.

Accepted Answer

A)   74 cm
B)   70 cm
C)   65 cm
D)   86 cm
E)   62 cm B

Question 2

A mobile is made of identical objects of mass m suspended so that the lowest row has one object, the row above two objects, and the row above three objects. All the strings are at 45° angles. What is the average tension in the strings connecting the highest row to the ceiling?

Accepted Answer

A)  
B)  
C)   mg
D)  
E)   B

Question 3

A 20-m long steel wire (cross-section 1.0 cm2, Young's modulus 2.0 × 1011 N/m2), is subjected to a load of 25 000 N. How much will the wire stretch under the load?

Accepted Answer

A)   0.25 cm
B)   2.5 cm
C)   12.5 cm
D)   25 cm
E)   1.25 cm B

Question 4

Which one of the following cannot be a definition of an elastic modulus?

Accepted Answer

A)  
B)  
C)  
D)  
E)

Question 5

An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by

Accepted Answer

A)   .
B)   .
C)   .
D)   mg.
E)   .

Question 6

One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium?

Accepted Answer

A)   .
B)   .
C)   .
D)   .
E)   .

Question 7

The free body diagram below represents a 1 500 kg car sitting on a 3 000 kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below:

Accepted Answer

A)  1L should be 0. 
E)   Because the perpendicular distance to   from the right end of the bridge is 0, F2L should be 0." class="answers-bank-image d-inline" rel="preload" > never produces a torque on the bridge no matter where the axis of rotation is placed.
B)  1L should be 0. 
E)   Because the perpendicular distance to   from the right end of the bridge is 0, F2L should be 0." class="answers-bank-image d-inline" rel="preload" > never produces a torque on the bridge no matter where the axis of rotation is placed.
C)  1L should be 0. 
E)   Because the perpendicular distance to   from the right end of the bridge is 0, F2L should be 0." class="answers-bank-image d-inline" rel="preload" > cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge.
D)   Because the perpendicular distance to1L should be 0. 
E)   Because the perpendicular distance to   from the right end of the bridge is 0, F2L should be 0." class="answers-bank-image d-inline" rel="preload" > from the left end of the bridge is 0, F1L should be 0.
E)   Because the perpendicular distance to1L should be 0. 
E)   Because the perpendicular distance to   from the right end of the bridge is 0, F2L should be 0." class="answers-bank-image d-inline" rel="preload" > from the right end of the bridge is 0, F2L should be 0.

Question 8

The diagrams below show forces of magnitude F applied to an equilateral triangular block of uniform thickness. In which diagram(s) is(are) the block in equilibrium?

Accepted Answer

A)   A
B)   B
C)   C
D)   D
E)   A and B

Question 9

A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor?

Accepted Answer

A)   43 lb
B)   34 lb
C)   38 lb
D)   47 lb
E)   24 lb

Question 10

How large a force is necessary to stretch a 2.0-mm diameter copper wire (Y = 11 × 1010 N/m2) by 1.0%?

Accepted Answer

A)   2.1 kN
B)   3.5 kN
C)   6.9 kN
D)   11 kN
E)   5.4 kN

Question 11

A 25-ft long crane supported at its lower end by a pin is elevated by a horizontal cable as shown in the figure. A 250-lb load is suspended from the outer end of the crane. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. What is the tension in the horizontal cable?

Accepted Answer

A)   610 lb
B)   540 lb
C)   640 lb
D)   570 lb
E)   2 000 lb

Question 12

The 1 560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the upper hinge?

Accepted Answer

A)   6 950 N, left
B)   6 950 N, right
C)   7 640 N, left
D)   7 640 N, right
E)   15 300 N, left

Question 13

A horizontal uniform 1.20-N meter stick is held up by two vertical strings, one at the 20-cm mark and the other at the 60-cm mark. What is the tension in the string at the 60-cm mark?

Accepted Answer

A)   0.30 N
B)   0.45 N
C)   0.60 N
D)   0.90 N
E)   1.0 N

Question 14

The center of gravity of an object is at the same position as the center of mass when

Accepted Answer

A)   is the same at both ends of the object.
B)   the object is located in a region where is uniform over the entire object.
C)   the object is as large as the body that exerts the gravitational force on it.
D)   any of the conditions above is satisfied.
E)   either (a)  or (b)  above is satisfied.

Question 15

A uniform 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable?

Accepted Answer

A)   54 lb
B)   69 lb
C)   47 lb
D)   61 lb
E)   75 lb

Question 16

Sebastian has drawn a free-body diagram for a ladder of mass m leaning against a frictionless wall. His diagram is shown below. What is his error?

Accepted Answer

A)   is in the wrong direction.
B)   should be directed upwards, not down.
C)   should be perpendicular to the wall, not parallel to it.
D)   should be down into the floor for to have the given direction.
E)   is correct, but there should also be a force perpendicular to the wall.

Question 17

Angie says that an object is in equilibrium if the net torques about the center of mass is zero. Robbie says that an object is in equilibrium if the sum of external forces is zero. Which one, if either, is correct?

Accepted Answer

A)   Both are correct: an object is in equilibrium if either condition holds.
B)   Neither is correct: both conditions must hold simultaneously.
C)   Neither is correct: the net external force and the net external torque about any axis must be zero.
D)   Neither is correct: an object is in equilibrium only if its velocity is zero in all coordinate systems.
E)   Both are correct: if the sum of the external forces is zero, the net torque about any axis is automatically zero, and vice versa.

Question 18

A non-uniform meter stick is found to balance on a knife edge at the 60-cm mark. Where is the center of gravity of the meter stick?

Accepted Answer

A)   at the 40-cm mark
B)   at the 45-cm mark
C)   at the 50-cm mark
D)   at the 55-cm mark
E)   at a position not given

Question 19

The 1 560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the lower hinge?

Accepted Answer

A)   6 950 N, left
B)   6 950 N, right
C)   7 640 N, left
D)   7 640 N, right
E)   15 300 N, left

Question 20

Exhibit 12-1
A square of side  is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 12-1. The displacement of the x coordinate of the center of mass (from C to C') is

Accepted Answer

A)   .
B)   .
C)   .
D)   .
E)   .

Exam 12: Static Equilibrium and Elasticity

A horizontal uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.

A mobile is made of identical objects of mass m suspended so that the lowest row has one object, the row above two objects, and the row above three objects. All the strings are at 45° angles. What is the average tension in the strings connecting the highest row to the ceiling?

A 20-m long steel wire (cross-section 1.0 cm², Young's modulus 2.0 × 10¹¹ N/m²) , is subjected to a load of 25 000 N. How much will the wire stretch under the load?

Which one of the following cannot be a definition of an elastic modulus?

An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by

One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium?

The free body diagram below represents a 1 500 kg car sitting on a 3 000 kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below:

The diagrams below show forces of magnitude F applied to an equilateral triangular block of uniform thickness. In which diagram(s) is(are) the block in equilibrium?

A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor?

How large a force is necessary to stretch a 2.0-mm diameter copper wire (Y = 11 × 10¹⁰ N/m²) by 1.0%?

The 1 560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the upper hinge?

A horizontal uniform 1.20-N meter stick is held up by two vertical strings, one at the 20-cm mark and the other at the 60-cm mark. What is the tension in the string at the 60-cm mark?

The center of gravity of an object is at the same position as the center of mass when

A uniform 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable?

Sebastian has drawn a free-body diagram for a ladder of mass m leaning against a frictionless wall. His diagram is shown below. What is his error?

Angie says that an object is in equilibrium if the net torques about the center of mass is zero. Robbie says that an object is in equilibrium if the sum of external forces is zero. Which one, if either, is correct?

A non-uniform meter stick is found to balance on a knife edge at the 60-cm mark. Where is the center of gravity of the meter stick?

The 1 560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the lower hinge?

Exam 12: Static Equilibrium and Elasticity

A horizontal uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.

A mobile is made of identical objects of mass m suspended so that the lowest row has one object, the row above two objects, and the row above three objects. All the strings are at 45° angles. What is the average tension in the strings connecting the highest row to the ceiling?

A 20-m long steel wire (cross-section 1.0 cm2, Young's modulus 2.0 × 1011 N/m2) , is subjected to a load of 25 000 N. How much will the wire stretch under the load?

Which one of the following cannot be a definition of an elastic modulus?

An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by

One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium?

The free body diagram below represents a 1 500 kg car sitting on a 3 000 kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below:

The diagrams below show forces of magnitude F applied to an equilateral triangular block of uniform thickness. In which diagram(s) is(are) the block in equilibrium?

A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor?

How large a force is necessary to stretch a 2.0-mm diameter copper wire (Y = 11 × 1010 N/m2) by 1.0%?

The 1 560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the upper hinge?

A horizontal uniform 1.20-N meter stick is held up by two vertical strings, one at the 20-cm mark and the other at the 60-cm mark. What is the tension in the string at the 60-cm mark?

The center of gravity of an object is at the same position as the center of mass when

A uniform 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable?

Sebastian has drawn a free-body diagram for a ladder of mass m leaning against a frictionless wall. His diagram is shown below. What is his error?

Angie says that an object is in equilibrium if the net torques about the center of mass is zero. Robbie says that an object is in equilibrium if the sum of external forces is zero. Which one, if either, is correct?

A non-uniform meter stick is found to balance on a knife edge at the 60-cm mark. Where is the center of gravity of the meter stick?

The 1 560 kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the lower hinge?

A 20-m long steel wire (cross-section 1.0 cm², Young's modulus 2.0 × 10¹¹ N/m²) , is subjected to a load of 25 000 N. How much will the wire stretch under the load?

How large a force is necessary to stretch a 2.0-mm diameter copper wire (Y = 11 × 10¹⁰ N/m²) by 1.0%?