Question 1

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?
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

Accepted Answer

The answer of A non-uniform meter stick is found to...

Question 2

The 1560 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)6950 N, left
B)6950 N, right
C)7640 N, left
D)7640 N, right
E)15,300 N, left

Accepted Answer

The force exerted by the door on the upper hinge is to the right, due to the torque created by the weight of the door acting at its center of mass. The force can be calculated by considering the torques about the lower hinge to find the force at the upper hinge that keeps the door in equilibrium.

Question 3

Stress is proportional to strain means that
A)stress = constant × strain.
B)stress = (constant 1) × strain + constant 2.
C)stress =  .
D)stress =  .
E)stress × strain = constant.

Accepted Answer

The statement "stress is proportional to strain" means that stress and strain are directly proportional to each other, and the relationship between the two can be expressed as a constant of proportionality. This relationship can be represented mathematically as stress = constant × strain, which is option A.

Question 4

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

Accepted Answer

The answer of A horizontal uniform 1.20-N meter stick is...

Question 5

The 1560-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)6950 N, left
B)6950 N, right
C)7640 N, left
D)7640 N, right
E)15,300 N, left

Accepted Answer

The answer of The 1560-kg solid steel door to a...

Question 6

For safety in climbing, a mountaineer uses a 50-m long nylon rope that is 1.0 cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6 m. Find the Young's modulus for the rope material.

Accepted Answer

The answer of For safety in climbing, a mountaineer uses...

Question 7

An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by 
A)  .
B)  .
C)  .
D)mg.
E)  .

Accepted Answer

The tension in each wire balances the weight of the object, which is mg. Therefore, the tension in each wire is equal to mg/2, which is choice D.

Question 8

The four tires of an automobile are inflated to a gauge pressure of 2.0 × 10⁵ N/m² (29 PSI). Each of the four tires has an area of 0.024 m² that is in contact with the ground. Determine the weight of the auto.

Accepted Answer

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Question 9

John is carrying a shovelful of snow. The center of mass of the 3.00 kg of snow he is holding is 15.0 cm from the end of the shovel. He is pushing down on the opposite end of the shovel with one hand and holding it up 30.0 cm from that end with his other hand. Ignore the mass of the shovel. Sarah says that his hand pushing down on the shovel must be exerting a greater force than the hand pushing up. James says it is just the reverse. Which one, if either, is correct?
A)Sarah, because the hand pushing down must exert a greater force to match the torque exerted by the snow.
B)James, because, depending on the location of the axis of rotation, the hand pushing down can counteract the torque exerted by the snow.
C)James, because the hand pushing up must exert a force that equals the sum of the force of the hand pushing down and the weight of the snow.
D)James, because both (b) and (c) above are correct.
E)Neither, because the hands exert forces of equal magnitudes.

Accepted Answer

The answer of John is carrying a shovelful of snow....

Question 10

Find the minimum diameter of a steel wire 18 m long that will stretch no more than 9 mm when a load of 380 kg is hung on the lower end. (Y steel = 2.0 × 10¹¹ N/m²)

Accepted Answer

The answer of Find the minimum diameter of a steel...

Question 11

The free-body diagram below represents a 1500-kg car sitting on a 3000-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: ​  ​  ​
A)  never produces a torque on the bridge no matter where the axis of rotation is placed.
B)  never produces a torque on the bridge no matter where the axis of rotation is placed.
C)  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 to  from the left end of the bridge is 0, F1L should be 0.
E)Because the perpendicular distance to  from the right end of the bridge is 0, F2L should be 0.

Accepted Answer

The error in the torque equation is that because the perpendicular distance to F1 from the left end of the bridge is 0, F1L should be 0. Therefore, option D is correct and the other options are either irrelevant or incorrect.

Question 12

If 1.0 m³ of concrete weighs 5 × 10⁴ N, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? (The compression strength of concrete is 1.7 × 10⁷N/m².)

Accepted Answer

The answer of If 1.0 m³ of concrete weighs 5...

Question 13

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) 
B) 
C)mg
D) 
E)

Accepted Answer

Let the tension in the strings be T. Consider the top-most object. It is suspended by two strings, each at 45° angles. Therefore, the tension in each string is T/√2. Now consider the second top-most row of objects. The tension in the string connected to the top-most object is T/√2 (since it is at 45°). The tension in each of the other two strings is also T/√2 (since each is at 45° and they are symmetric). Therefore, the total upward force on the second top-most row is 2(T/√2) + 2(T/√2) = 4T/√2. Since there are three objects in this row, the average upward force on each object is (4T/√2)/3 = 4T/(3√2). Similarly, considering the bottom two rows, we can find the average upward force on an object in each row to be (2T/√2)/1 = 2T/√2 and (3T/√2)/2 = 3T/(2√2), respectively. 
Now consider the top row of objects again. The total upward force on this row is (2T/√2) + (4T/(3√2)) = (8T/(3√2)). Since there is only one object in this row, the upward force on it must be (8T/(3√2))/1 = 8T/(3√2). Therefore, the tension in the string connected to this object must be equal to its upward force, which is 8T/(3√2). This is the average tension in the strings connecting the highest row to the ceiling. Simplifying, we get 8T/(3√2) = T, so T = 3√2/8. Therefore, the answer is B.

Question 14

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? ​  ​
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.

Accepted Answer

The answer of Sebastian has drawn a free-body diagram for...

Quiz 14: Static Equilibrium, Elasticity, and Fracture

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 1560 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?

Stress is proportional to strain means that

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 1560-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?

For safety in climbing, a mountaineer uses a 50-m long nylon rope that is 1.0 cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6 m. Find the Young's modulus for the rope material.

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

The four tires of an automobile are inflated to a gauge pressure of 2.0 × 105 N/m2 (29 PSI). Each of the four tires has an area of 0.024 m2 that is in contact with the ground. Determine the weight of the auto.

Find the minimum diameter of a steel wire 18 m long that will stretch no more than 9 mm when a load of 380 kg is hung on the lower end. (Y steel = 2.0 × 1011 N/m2)

The free-body diagram below represents a 1500-kg car sitting on a 3000-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: ​ ​ ​

If 1.0 m3 of concrete weighs 5 × 104 N, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? (The compression strength of concrete is 1.7 × 107 N/m2.)

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?

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? ​ ​

The four tires of an automobile are inflated to a gauge pressure of 2.0 × 10⁵ N/m² (29 PSI). Each of the four tires has an area of 0.024 m² that is in contact with the ground. Determine the weight of the auto.

Find the minimum diameter of a steel wire 18 m long that will stretch no more than 9 mm when a load of 380 kg is hung on the lower end. (Y steel = 2.0 × 10¹¹ N/m²)

The free-body diagram below represents a 1500-kg car sitting on a 3000-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:

If 1.0 m³ of concrete weighs 5 × 10⁴ N, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? (The compression strength of concrete is 1.7 × 10⁷N/m².)

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?