Question 1

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest percent?
A) the 1.00-m wire
B) the 3.00-m wire
C) the 2.00-m wire
D) They will all stretch by the same percent.

Accepted Answer

D

Question 2

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest distance?
A) the 2.00-m wire
B) the 3.00-m wire
C) the 1.00-m wire
D) They will all stretch by the same distance.

Accepted Answer

The amount a wire stretches under a given load is directly proportional to its length. Therefore, the 3.00-m wire will stretch the most.

Question 3

If the sum of the external forces on an object is zero, then the sum of the external torques on it
must also be zero.

Accepted Answer

The sum of external forces being zero ensures the object's center of mass does not accelerate, but it does not guarantee that the sum of external torques is zero. External torques can still exist and cause rotational motion if they are not balanced, even if the net external force is zero.

Question 4

Two blocks are made of the same material, but one has twice the volume of the other block. Which block will have the greater shear modulus?
A) It will be the same for both of them.
B) the larger one
C) the smaller one

Accepted Answer

The shear modulus is a material property and does not depend on the volume of the material.

Question 5

Two solid spheres are made from the same material, but one has twice the diameter of the other. Which sphere will have the greater bulk modulus?
A) the larger one
B) the smaller one
C) It will be the same for both spheres.

Accepted Answer

Bulk modulus is a material property that describes how compressible the material is, and it does not depend on the size or shape of the object made from that material. Therefore, both spheres will have the same bulk modulus since they are made from the same material.

Question 6

The graph in the figure shows the tensile stress as a function of the tensile strain in a certain wire. What does the slope of this graph give us for this wire?

A) the pressure in the wire
B) the tensile stress in the wire
C) Young's modulus for the material of the wire
D) the tension in the wire
E) the percent change in the length of the wire

Accepted Answer

The answer of The graph in the figure shows the...

Question 7

Tensile strain is
A) the stress per unit area.
B) the applied force per unit area.
C) the ratio of stress to elastic modulus.
D) the ratio of the change in length to the original length.

Accepted Answer

Tensile strain is defined as the ratio of the change in length to the original length, which measures how much an object is stretched or elongated under tensile stress.

Question 8

Tensile stress is
A) applied force per cross-sectional area.
B) the strain per unit length.
C) the same as force.
D) the ratio of the change in length.

Accepted Answer

Tensile stress is defined as the applied force per unit cross-sectional area. This is a measure of how much force is exerted per unit area of the material.

Question 9

If the sum of the external torques on an object is zero, then the sum of the external forces on it
must also be zero.

Accepted Answer

The sum of the external torques being zero ensures angular momentum is conserved, but this does not necessarily mean the sum of the external forces is zero, as linear and angular dynamics are governed by different conditions. Zero net torque means no change in rotational motion, while zero net force means no change in linear motion; these can occur independently.

Question 10

Which of the following are SI units of Young's modulus? (There could be more than one correct choice.) 
A) $\mathrm { kg } \cdot \mathrm { m } ^ { 2 } / \mathrm { s } ^ { 2 }$
B) $\mathrm { N } / \mathrm { m } \cdot \mathrm { s } ^ { 2 }$
C) $\mathrm { kg } \cdot \mathrm { m } / \mathrm { s } ^ { 2 }$
D) $\mathrm { kg } / \mathrm { m } \cdot \mathrm { s } ^ { 2 }$
E) $\mathrm { kg } / \mathrm { m } ^ { 2 }$

Accepted Answer

The answer of Which of the following are SI units...

Question 11

A croquet mallet balances when suspended from its center of mass, as shown in the left part of the figure. If you cut the mallet into two pieces at its center of mass, as shown in the right part of the figure, how do the masses of the two pieces compare? (There could be more than one correct choice.)

A) The piece with the head of the mallet has the greater mass.
B) The masses are equal.
C) The piece with the head of the mallet has the smaller mass.
D) It is impossible to tell.

Accepted Answer

The answer of A croquet mallet balances when suspended from...

Question 12

Which one of the following would be expected to have the smallest bulk modulus?
A) helium vapor
B) solid iron
C) liquid water
D) liquid mercury
E) solid uranium

Accepted Answer

The bulk modulus is a measure of a material's resistance to uniform compression. Gases like helium vapor have the smallest bulk modulus because their particles are far apart, making them much easier to compress than solids or liquids. Solid iron, liquid water, liquid mercury, and solid uranium all have significantly higher bulk moduli due to the closer proximity of their particles, which makes them more resistant to compression.

Question 13

Which one of the following is an accurate statement?
A) Tensile stress is measured in newtons.
B) The ratio of tensile stress to tensile strain is called Young's modulus.
C) Tensile strain is measured in meters.
D) "Stress" has a meaning very close to "stretch."
E) "Strain" has a meaning very close to "force."

Accepted Answer

Tensile stress divided by tensile strain gives Young's modulus, which is a measure of the stiffness of a material.

Question 14

When a car is weighed, it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale, and then records a second reading as the rear wheels go over
The scale. The weight of the car is equal to
A) the weight under the rear wheels.
B) the difference of the two weights.
C) the weight under the front wheels.
D) the average of the two weights.
E) the sum of the two weights.

Accepted Answer

The weight of the car is the total weight distributed across all wheels, so it is the sum of the weight recorded under the front wheels and the weight recorded under the rear wheels.

Question 15

Two wires are made out of the same metal, but one wire is twice as long as the other wire. Which wire will have the greatest elastic modulus?
A) the longer wire
B) the shorter wire
C) It will be the same for both wires.

Accepted Answer

The elastic modulus of a material is an inherent property that does not depend on the length or size of the material. Both wires, being made of the same metal, will have the same elastic modulus regardless of their lengths.

Question 16

A piece of iron sinks to the bottom of a lake where the pressure is 21 times what it is at the surface of the lake. Which statement best describes what happens to the volume of that piece of iron?
A) Its volume increases slightly.
B) Its volume decreases slightly.
C) Its volume becomes 1/21 what it was at the surface.
D) Its volume becomes 21 times greater than at the surface.
E) There has been no change in the volume of the iron.

Accepted Answer

Iron is a solid with a very high bulk modulus, meaning it is very resistant to compression. However, under extremely high pressures, like 21 times atmospheric pressure at the bottom of a lake, its volume will decrease slightly, not significantly, due to its incompressible nature.

Question 17

A large 75-kg lighting fixture can be hung from wires of identical size and shape made of aluminum, brass, or copper. The values of Young's modulus for these metals are $0.70 \times 10 ^ { 11 } \mathrm {~Pa}$ (aluminum), $0.91 \times 10 ^ { 11 } \text { (brass), and } 1.1 \times 10 ^ { 11 } \text { (copper) }$
Which wire would stretch the least distance?
A) copper
B) aluminum
C) brass
D) They will all stretch the same distance.

Accepted Answer

The wire that would stretch the least distance is the one made of the material with the highest Young's modulus, as this modulus measures the stiffness of a material. Copper has the highest Young's modulus ($1.1 \times 10^{11} \text{ Pa}$) among the given materials, meaning it is the stiffest and thus will stretch the least under the same load.

Question 18

If an object remains at rest, then the sum of both the external torques and the external forces on the
object must be zero.

Accepted Answer

For an object to remain at rest, both the net external force and the net external torque acting on it must be zero, according to Newton's first law of motion and the rotational equivalent of Newton's first law. This ensures there is no linear or rotational acceleration.

Question 19

A piece of iron sinks to the bottom of a lake where the pressure is 21 times what it is at the surface. Which statement best describes what happens to the density of that piece of iron?
A) There has been no change in the density of the iron.
B) Its density becomes 1/21 what it was at the surface.
C) Its density decreases slightly.
D) Its density increases slightly.
E) Its density becomes 21 times greater than what it was at the surface.

Accepted Answer

The answer of A piece of iron sinks to the...

Question 20

If the sum of both the external torques and the external forces on an object is zero, then the object
must be at rest.

Accepted Answer

An object can be in uniform motion (constant velocity) as well, as both conditions satisfy the first condition of equilibrium (net force is zero) and the second condition of equilibrium (net torque is zero), allowing for constant velocity motion, not just rest.

Quiz 9: Static Equilibrium; Elasticity and Fracture

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest percent?

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest distance?

If the sum of the external forces on an object is zero, then the sum of the external torques on it must also be zero.

Two blocks are made of the same material, but one has twice the volume of the other block. Which block will have the greater shear modulus?

Two solid spheres are made from the same material, but one has twice the diameter of the other. Which sphere will have the greater bulk modulus?

The graph in the figure shows the tensile stress as a function of the tensile strain in a certain wire. What does the slope of this graph give us for this wire?

Tensile strain is

Tensile stress is

If the sum of the external torques on an object is zero, then the sum of the external forces on it must also be zero.

Which of the following are SI units of Young's modulus? (There could be more than one correct choice.)

Which one of the following would be expected to have the smallest bulk modulus?

Which one of the following is an accurate statement?

When a car is weighed, it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale, and then records a second reading as the rear wheels go over The scale. The weight of the car is equal to

Two wires are made out of the same metal, but one wire is twice as long as the other wire. Which wire will have the greatest elastic modulus?

A piece of iron sinks to the bottom of a lake where the pressure is 21 times what it is at the surface of the lake. Which statement best describes what happens to the volume of that piece of iron?

If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero.

A piece of iron sinks to the bottom of a lake where the pressure is 21 times what it is at the surface. Which statement best describes what happens to the density of that piece of iron?

If the sum of both the external torques and the external forces on an object is zero, then the object must be at rest.