Question 1

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. 
-Complete the following statement: In order to increase the frequency of the motion, one would have to
A)reduce the spring constant.
B)decrease the mass of the block on the end of the spring.
C)increase the length of the spring.
D)reduce the distance that the spring is initially stretched.
E)increase the distance that the spring is initially stretched.

Accepted Answer

The frequency of the motion is determined by the spring constant and the mass of the block on the end of the spring. Increasing the spring constant or decreasing the mass will increase the frequency. Therefore, choice B is the best answer as reducing the mass of the block on the end of the spring will increase the frequency of the motion.

Question 2

Complete the following statement: In general, the term stress refers to
A)a change in volume.
B)a change in length.
C)a force per unit area.
D)a fractional change in length.
E)a force per unit length.

Accepted Answer

Stress is defined as a force per unit area. It is the distributed force acting on a material that causes a deformation or change in shape or size of the material. Stress is measured in units of pressure, such as pounds per square inch (psi) or pascals (Pa). Options A, B, D, and E all refer to strain or deformation caused by stress, but are not the definition of stress itself.

Question 3

A plastic box has an initial volume of 3.50 mS1U1P13S1S1P0. It is then submerged below the surface of a liquid and its volume decreases to 3.48 mS1U1P13S1S1P0.
-What is the volume strain on the box?
A)0.0020
B)0.0057
C)0.0084
D)0.018
E)0.022

Accepted Answer

The answer of A plastic box has an initial volume...

Question 4

The radius of a sphere of lead (B = 4.2 × 10¹⁰ N/m²) is 1.000 m on the surface of the earth where the pressure is 1.01 × 10⁵ N/m². The sphere is taken by submarine to the deepest part of the ocean to a depth of 1.10 × 10⁴ m where it is exposed to a pressure is 1.25 × 10⁸ N/m². What is the volume of the sphere at the bottom of the ocean? A)4.176 m³ B)3.189 m³ C)2.251 m³ D)1.134 m³ E)0.988 m³

Accepted Answer

The volume of a sphere is given by V = (4/3)πr^3. The radius of the sphere is given by r = 1.000 m. The pressure at the surface of the earth is given by P = 1.01 × 10^5 N/m^2. The pressure at the bottom of the ocean is given by P = 1.25 × 10^8 N/m^2. The bulk modulus of lead is given by B = 4.2 × 10^10 N/m^2. The change in volume of the sphere is given by ΔV = -BPΔr/r. The change in radius of the sphere is given by Δr = -BPΔV/r. The volume of the sphere at the bottom of the ocean is given by V = V0 + ΔV = (4/3)πr^3 - BPΔr/r = (4/3)πr^3 - BP(-BPΔV/r)/r = (4/3)πr^3 + B^2PΔV/r^3 = (4/3)π(1.000 m)^3 + (4.2 × 10^10 N/m^2)^2(1.25 × 10^8 N/m^2)(4.176 m^3)/(1.000 m)^3 = 4.176 m^3.

Question 5

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. 
-What is the speed of the block each time the spring is 5.0 cm long?
A)zero cm/s
B)422 cm/s
C)344 cm/s
D)220 cm/s
E)160 cm/s

Accepted Answer

First, we can use Hooke's law to find the spring constant:
F = kx
mg = kx
k = mg/x = (0.20 kg)(9.81 m/s^2)/(0.045 m - 0.040 m) ≈ 98.1 N/m

Next, we can use energy conservation to find the speed of the block when the spring is 5.0 cm long:
PE at equilibrium = KE at max compression
(1/2)kx^2 = (1/2)mv_max^2
(1/2)(98.1 N/m)(0.05 m)^2 = (1/2)(0.20 kg)v_max^2
v_max = √([(98.1 N/m)(0.05 m)^2]/(0.20 kg)) ≈ 220 cm/s

Therefore, the answer is choice D, 220 cm/s.

Question 6

Which one of the following statements concerning Hooke's law is false?
A)Hooke's law relates stress and strain.
B)Hooke's law is valid only for springs.
C)Hooke's law can be verified experimentally.
D)Hooke's law can be applied to a wide range of materials.
E)Hooke's law is valid only within the elastic limit of a given material.

Accepted Answer

Hooke's law can be applied to a wide range of materials, not just springs. Therefore, statement B is false.

Question 7

A 0.800-kg block is placed on top of a vertically oriented spring as shown. The block is not attached to the spring, but the spring is attached to the floor. The block oscillates in simple harmonic motion. If the spring constant is 95.0 N/m, determine the amplitude at which the block loses contact with the spring. 
A)0.0505 m
B)0.0615 m
C)0.0735 m
D)0.0825 m
E)0.0945 m

Accepted Answer

The answer of A 0.800-kg block is placed on top...

Question 8

A cylinder with a diameter of 0.240 m is placed between the plates of a hydraulic press as illustrated in the drawing. A 4.45 × 10⁵-N force is applied to the cylinder. What is the pressure on the end of the cylinder due to the applied force? A)9.84 × 10⁶ Pa B)3.13 × 10⁵ Pa C)6.18 × 10⁶ Pa D)5.34 × 10⁵ Pa E)4.92 × 10⁶ Pa

Accepted Answer

The answer of A cylinder with a diameter of 0.240...

Question 9

The shear modulus of steel is 8.1 × 10¹⁰ N/m². A steel nail of radius 7.5 × 10^-⁴ m projects 0.040 m horizontally outward from a wall. A man hangs a wet raincoat of weight 28.5 N from the end of the nail. Assuming the wall holds its end of the nail, what is the vertical deflection of the other end of the nail? A)1.8 × 10^-³ m B)3.3 × 10^-² m C)7.9 × 10^-⁶ m D)4.2 × 10^-⁴ m E)2.1 × 10^-⁵ m

Accepted Answer

The answer of The shear modulus of steel is 8.1...

Question 10

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. 
-Which one of the following expressions gives the displacement of the block as a function of time? Let x be in cm and t in seconds.
A)x = 15 cos(14$\pi$t)
B)x = 15 sin(14$\pi$t)
C)x = 7 cos(15$\pi$t)
D)x = 14 sin(15$\pi$t)
E)x = 44 cos(14$\pi$t)

Accepted Answer

The expression x = 15 cos(14πt) represents a simple harmonic motion where the amplitude is 15 cm and the angular frequency is 14π rad/s.

Question 11

The maximum compressional stress that a bone can withstand is 1.6 × 10⁸ N/m² before it breaks. A thighbone (femur), which is the largest and longest bone in the human body, has a cross sectional area of 7.7 × 10^-⁴ m². What is the maximum compressional force that can be applied to the thighbone? A)2.1 × 10¹¹ N B)1.2 × 10⁵ N C)4.8 × 10¹² N D)3.0 × 10³N E)This cannot be determined since Young's modulus is not given.

Accepted Answer

The maximum compressional force can be calculated using the formula: Force = Stress × Area. Substituting the given values, Force = (1.6 × 10^8 N/m^2) × (7.7 × 10^-4 m^2) = 1.232 × 10^5 N, which is approximately 1.2 × 10^5 N.

Question 12

Young's modulus of nylon is 3.7 × 10⁹ N/m². A force of 6.0 × 10⁵ N is applied to a 1.5-m length of nylon of cross sectional area 0.25 m². By what amount does the nylon stretch? A)3.1 × 10^-²m B)1.6 × 10^-² m C)3.9 × 10^-³ m D)9.7 × 10^-⁴ m E)1.2 × 10^-⁵ m

Accepted Answer

The answer of Young's modulus of nylon is 3.7 ×...

Question 13

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. -What is the maximum acceleration of the block? A)1.6 m/s² B)3.1 m/s² C)49 m/s² D)98 m/s² E)290 m/s²

Accepted Answer

The answer of When a 0.20-kg block is suspended from...

Question 14

A 5.0 × 10S1U1P12S1S1P0-N object is hung from the end of a wire of cross-sectional area 0.010 cmS1U1P12S1S1P0. The wire stretches from its original length of 200.00 cm to 200.50 cm. -What is the elongation strain on the wire? A)1.0 × 10² B)1.0 × 10^-² C)5.0 × 10² D)2.5 × 10^-³ E)4.0 × 10²

Accepted Answer

The elongation strain is calculated as the change in length divided by the original length. The change in length is 0.50 cm, and the original length is 200.00 cm. Thus, the strain is 0.50/200.00 = 2.5 × 10^-3.

Question 15

A 0.750-kg object hanging from a vertical spring is observed to oscillate with a period of 1.50 s. When the 0.750-kg object is removed and replaced by a 1.50-kg object, what will be the period of oscillation?
A)1.55 s
B)2.58 s
C)2.12 s
D)3.38 s
E)4.49 s

Accepted Answer

The period of oscillation for an object hanging from a vertical spring is given by the formula: T = 2π√(m/k), where m is the mass of the object and k is the spring constant.

Since the spring is the same in both cases, the only variable that changes is the mass.

For the first case, T1 = 1.50 s with m1 = 0.750 kg.

For the second case, we have m2 = 1.50 kg.

Using the formula, we can solve for T2:

T2 = 2π√(m2/k)

We can find k by using the period of the first case:

T1 = 2π√(m1/k)

Solving for k:

k = (4π^2m1)/T1^2

Plugging in the values:

k = (4π^2 × 0.750 kg) / (1.50 s)^2

k = 10π^2 N/m

Now we can find T2:

T2 = 2π√(m2/k)

Plugging in the values:

T2 = 2π√(1.50 kg / (10π^2 N/m))

T2 ≈ 2.12 s

Therefore, the answer is C.

Question 16

A plastic box has an initial volume of 3.50 mS1U1P13S1S1P0. It is then submerged below the surface of a liquid and its volume decreases to 3.48 mS1U1P13S1S1P0.
-Complete the following statement: In order to calculate the "stress" on the box, in addition to the information given, one must also know
A)the mass of the box.
B)the bulk modulus of the material from which the box is made.
C)the shear modulus of the material from which the box is made.
D)the Young's modulus of the material from which the box is made.
E)the bulk modulus of the liquid.

Accepted Answer

The stress on the box is given by the formula stress =change in volume/initial volume * bulk modulus. Since the bulk modulus of the material from which the box is made is required in this formula, option B is the correct choice. Mass of the box, shear modulus, Young's modulus or bulk modulus of the liquid are not required to calculate the stress on the box.

Question 17

A 5.0 × 10S1U1P12S1S1P0-N object is hung from the end of a wire of cross-sectional area 0.010 cmS1U1P12S1S1P0. The wire stretches from its original length of 200.00 cm to 200.50 cm. -What is the stress on the wire? A)5.0 × 10² N/m² B)1.0 × 10⁶ N/m² C)1.0 × 10⁸ N/m² D)5.0 × 10⁶ N/m² E)5.0 × 10⁸ N/m²

Accepted Answer

The answer of A 5.0 × 10S1U1P12S1S1P0-N object is hung...

Question 18

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. 
-Which one of the following statements is true concerning the motion of the block?
A)Its acceleration is constant.
B)The period of its motion depends on its amplitude.
C)Its acceleration is greatest when the spring returns to the 5.0 cm position.
D)Its velocity is greatest when the mass has reached its maximum displacement.
E)Its acceleration is greatest when the mass has reached its maximum displacement.

Accepted Answer

The motion of the block is simple harmonic motion, which is characterized by the fact that the acceleration is proportional to the displacement from the equilibrium position and is directed towards the equilibrium position. Therefore, the acceleration is greatest when the mass has reached its maximum displacement, which is at the ends of its motion. This is because the displacement from the equilibrium position is greatest at these points. Thus, statement E is true. 
Statement A is false because the acceleration varies in simple harmonic motion. 
Statement B is false because the period of the motion only depends on the mass and spring constant, not the amplitude. 
Statement C is false because the acceleration is greatest at the ends of the motion. 
Statement D is false because the velocity is greatest at the equilibrium position, not at the ends of the motion.

Question 19

A 5.0 × 10S1U1P12S1S1P0-N object is hung from the end of a wire of cross-sectional area 0.010 cmS1U1P12S1S1P0. The wire stretches from its original length of 200.00 cm to 200.50 cm. -Determine the Young's modulus of the wire. A)1.0 × 10¹¹ N/m² B)1.0 × 10⁹ N/m² C)2.0 × 10¹¹ N/m² D)2.0 × 10⁹ N/m² E)5.0 × 10¹² N/m²

Accepted Answer

The answer of A 5.0 × 10S1U1P12S1S1P0-N object is hung...

Question 20

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. 
-What is the frequency of the motion?
A)0.50 Hz
B)1.0 Hz
C)5.0 Hz
D)7.0 Hz
E)44 Hz

Accepted Answer

The answer of When a 0.20-kg block is suspended from...

Quiz 10: Simple Harmonic Motion and Elasticity

Complete the following statement: In general, the term stress refers to

A plastic box has an initial volume of 3.50 m³. It is then submerged below the surface of a liquid and its volume decreases to 3.48 m³. -What is the volume strain on the box?

Which one of the following statements concerning Hooke's law is false?

A cylinder with a diameter of 0.240 m is placed between the plates of a hydraulic press as illustrated in the drawing. A 4.45 × 10⁵-N force is applied to the cylinder. What is the pressure on the end of the cylinder due to the applied force?

Young's modulus of nylon is 3.7 × 10⁹ N/m². A force of 6.0 × 10⁵ N is applied to a 1.5-m length of nylon of cross sectional area 0.25 m². By what amount does the nylon stretch?

A 5.0 × 10²-N object is hung from the end of a wire of cross-sectional area 0.010 cm². The wire stretches from its original length of 200.00 cm to 200.50 cm. -What is the elongation strain on the wire?

A 0.750-kg object hanging from a vertical spring is observed to oscillate with a period of 1.50 s. When the 0.750-kg object is removed and replaced by a 1.50-kg object, what will be the period of oscillation?

A plastic box has an initial volume of 3.50 m³. It is then submerged below the surface of a liquid and its volume decreases to 3.48 m³. -Complete the following statement: In order to calculate the "stress" on the box, in addition to the information given, one must also know

A 5.0 × 10²-N object is hung from the end of a wire of cross-sectional area 0.010 cm². The wire stretches from its original length of 200.00 cm to 200.50 cm. -What is the stress on the wire?

A 5.0 × 10²-N object is hung from the end of a wire of cross-sectional area 0.010 cm². The wire stretches from its original length of 200.00 cm to 200.50 cm. -Determine the Young's modulus of the wire.

Quiz 10: Simple Harmonic Motion and Elasticity

Complete the following statement: In general, the term stress refers to

A plastic box has an initial volume of 3.50 m3. It is then submerged below the surface of a liquid and its volume decreases to 3.48 m3. -What is the volume strain on the box?

Which one of the following statements concerning Hooke's law is false?

A cylinder with a diameter of 0.240 m is placed between the plates of a hydraulic press as illustrated in the drawing. A 4.45 × 105-N force is applied to the cylinder. What is the pressure on the end of the cylinder due to the applied force?

The maximum compressional stress that a bone can withstand is 1.6 × 108 N/m2 before it breaks. A thighbone (femur) , which is the largest and longest bone in the human body, has a cross sectional area of 7.7 × 10-4 m2. What is the maximum compressional force that can be applied to the thighbone?

Young's modulus of nylon is 3.7 × 109 N/m2. A force of 6.0 × 105 N is applied to a 1.5-m length of nylon of cross sectional area 0.25 m2. By what amount does the nylon stretch?

A 5.0 × 102-N object is hung from the end of a wire of cross-sectional area 0.010 cm2. The wire stretches from its original length of 200.00 cm to 200.50 cm. -What is the elongation strain on the wire?