Question 1

10-1
A relaxed spring protrudes from an opening 0.0500 meters as shown in Figure A.
A 1.00-kg block is found to just force the spring completely into the opening as shown in Figure B. 
-Determine the spring constant k.
A)20.0 N/m
B)196 N/m
C)392 N/m
D)3920 N/m
E)7840 N/m

Accepted Answer

The answer of 10-1
A relaxed spring protrudes from an opening...

Question 2

In a certain clock, a pendulum of length L₁ has a period T₁ = 0.95 s.The length of the pendulum is adjusted to a new value L₂ such that T₂ = 1.0 s.What is the ratio L₂/L₁? A)0.90 B)0.95 C)1.0 D)1.1 E)1.3

Accepted Answer

The period of a pendulum is directly proportional to the square root of its length. Therefore, (L₂/L₁)^2 = T₁/T₂ = 0.95/1.0 = 0.95. Solving for the ratio yields L₂/L₁ = sqrt(0.95) = 1.024. Rounding to one decimal place gives 1.0, which is the closest choice.

Question 3

A simple harmonic oscillator with a period of 2.0 s is subject to damping so that it loses one percent of its amplitude per cycle.About how much energy does this oscillator lose per cycle?
A)0.5 %
B)1.0 %
C)2.0 %
D)3.0 %
E)4.0 %

Accepted Answer

The answer of A simple harmonic oscillator with a period...

Question 4

A spring with a spring constant k = 1600 N/m is at rest on the bottom of an inclined plane.A 7.0-kg block slides down the plane and makes contact with the spring at point A as shown.After contact, the spring is compressed to point B, 0.20 m from point A, where the speed of the block is zero m/s.What was the speed of the block just before contact with the spring? 
A)3.2 m/s
B)12 m/s
C)2.4 m/s
D)9.1 m/s
E)4.2 m/s

Accepted Answer

The answer of A spring with a spring constant k...

Question 5

A pendulum is transported from sea-level, where the acceleration due to gravity g is 9.80 m/s², to the bottom of Death Valley.At this location, the period of the pendulum is decreased by 3.00%.What is the value of g in Death Valley? A)9.22 m/s² B)9.51 m/s² C)9.80 m/s² D)10.1 m/s² E)10.4 m/s²

Accepted Answer

The answer of A pendulum is transported from sea-level, where...

Question 6

A cable stretches by an amount d as it supports a crate of mass M.The cable is cut in half.What is the mass of the load that can be supported by either half of the cable if the cable stretches by an amount d?
A)M/4
B)M/2
C)M
D)2M
E)4M

Accepted Answer

The answer of A cable stretches by an amount d...

Question 7

A cable stretches by an amount d when it supports a crate of mass M.The cable is then cut into three equal pieces.If the same crate is supported by any one of these pieces, by how much will the cable stretch?
A)d
B)d/3
C)d/6
D)3d
E)9d

Accepted Answer

Assuming the cable has uniform properties throughout, cutting it into equal pieces would not change the amount of stretch. Each piece would still stretch by d when supporting the crate. Therefore, the amount of stretch when the crate is supported by any one of the three pieces would be d/3.

Question 8

Complete the following sentence: Resonance occurs in harmonic motion when
A)the system is overdamped.
B)the system is critically damped.
C)the energy in the system is a minimum.
D)the driving frequency is the same as the natural frequency of the system.
E)the energy in the system is proportional to the square of the motion's amplitude.

Accepted Answer

Resonance occurs in harmonic motion when the driving frequency is the same as the natural frequency of the system. This is because the external force enhances the motion of the system by adding energy at the natural frequency, leading to large amplitude oscillations. Choosing options A, B, and C are incorrect, as they do not relate to resonance in harmonic motion. Option E is also incorrect, as the energy in the system is not necessarily proportional to the square of the motion's amplitude.

Question 9

What are the SI units of the shear modulus? A)N/m² B)N/m C)N . m D)N/m³ E)N . m²

Accepted Answer

The answer of What are the SI units of the...

Question 10

A cable stretches by an amount d when it supports a crate of mass M.The cable is replaced by another cable of the same material having the same length and twice the diameter.If the same crate is supported by the thicker cable, by how much will the cable stretch?
A)d/4
B)d/2
C)d
D)2d
E)4d

Accepted Answer

The answer of A cable stretches by an amount d...

Question 11

A cable stretches by an amount d when it supports a crate of mass M.The cable is replaced by another cable of the same material having the same length and twice the diameter.What is the mass of the load that can be supported by the thicker cable if it stretches by an amount d?
A)M/4
B)M/2
C)M
D)2M
E)4M

Accepted Answer

The answer of A cable stretches by an amount d...

Question 12

10-1
A relaxed spring protrudes from an opening 0.0500 meters as shown in Figure A.
A 1.00-kg block is found to just force the spring completely into the opening as shown in Figure B. 
-How much potential energy is stored in the spring in Figure B?
A)0.245 J
B)0.490 J
C)4.90 J
D)9.80 J
E)zero J

Accepted Answer

The answer of 10-1
A relaxed spring protrudes from an opening...

Question 13

An iron ball hangs from a 21.5-m steel cable and is used in the demolition of a building at a location where the acceleration due to gravity is 9.78 m/s².The ball is swung outward from its equilibrium position for a distance of 4.20 m.Assuming the system behaves as a simple pendulum, find the maximum speed of the ball during its swing. A)4.45 m/s B)2.83 m/s C)17.8 m/s D)1.71 m/s E)9.78 m/s

Accepted Answer

The period of a simple pendulum is given by:
T = 2π√(L/g)
where L is the length of the cable and g is the acceleration due to gravity. Plugging in the given values, we get:
T = 2π√(21.5/9.78) ≈ 6.370 seconds
The maximum speed of the ball occurs at the equilibrium position (i.e., the bottom of the swing). At this point, all of the potential energy has been converted to kinetic energy:
PE = KE
mgh = 1/2mv^2
where m is the mass of the ball, h is the initial height of the ball (i.e., the length of the cable), and v is the maximum speed of the ball. Solving for v, we get:
v = √(2gh)
where g is the acceleration due to gravity. Plugging in the given values, we get:
v = √(2×9.78×21.5) ≈ 9.758 meters per second
However, this is the velocity at the bottom of the swing, and the ball is swung out from its equilibrium position by a distance of 4.20 m. Using conservation of energy, we can find the velocity at this point:
PE + KE = PE + KE
mgh + 0 = mghcosθ + 1/2mv^2
where θ is the angle between the cable and the vertical (i.e., the initial angle of swing). Since the angle is not given, we can assume that it is small enough such that cosθ ≈ 1. Solving for v, we get:
v = √(2gh)
where h is the length of the cable plus the additional distance swung out (i.e., 21.5 + 4.20 = 25.7 m). Plugging in the values, we get:
v = √(2×9.78×25.7) ≈ 2.828 meters per second
Therefore, the maximum speed of the ball during its swing is approximately 2.83 m/s, which corresponds to answer choice B.

Question 14

Complete the following statement: Young's modulus cannot be applied to
A)a stretched wire.
B)a compressed rod.
C)a bending beam.
D)a compressed liquid.
E)a stretched rubber band.

Accepted Answer

Young's modulus is only applicable to solid materials that exhibit linear elasticity. Liquids do not exhibit this type of behavior, so Young's modulus cannot be applied to them.

Question 15

Which one of the following terms is used to describe a system in which the degree of damping is just enough to stop the system from oscillating?
A)critically damped
B)underdamped
C)slightly damped
D)overdamped
E)resonance

Accepted Answer

A system is critically damped when the degree of damping is such that it prevents oscillations from occurring. This is an ideal condition for many engineering and control applications, as it allows for quick and precise responses without overshooting or ringing. Underdamped systems oscillate about their equilibrium position, overdamped systems take longer to reach equilibrium and may not return to the equilibrium position if disturbed, and resonance occurs when a system is forced to vibrate at its natural frequency, resulting in large oscillations.

Question 16

What is the period of a pendulum consisting of a 6-kg object oscillating on a 4-m string?
A)0.25 s
B)0.50 s
C)1.0 s
D)2.0 s
E)4.0 s

Accepted Answer

The answer of What is the period of a pendulum...

Question 17

A simple pendulum consists of a ball of mass m suspended from the ceiling using a string of length L.The ball is displaced from its equilibrium position by a small angle $\theta$.What is the magnitude of the restoring force that moves the ball toward its equilibrium position and produces simple harmonic motion?
A)kx
B)mg
C)mg(cos $\theta$)
D)mg(sin$\theta$)
E)mgL(sin $\theta$)

Accepted Answer

The restoring force that moves the ball toward its equilibrium position is provided by the component of the weight of the ball along the direction of displacement. This component is mg sin θ, where θ is the angle of displacement. Therefore, the magnitude of the restoring force is mg sin θ.

Question 18

The spring constant for the spring in a special cannon is 1800 N/m.In cocking the cannon, the spring is compressed 0.55 m.What is the initial speed of a 7.0-kg cannonball at rest on the free end of the spring when it is released?
A)77 m/s
B)140 m/s
C)12 m/s
D)8.8 m/s
E)16 m/s

Accepted Answer

We can use the conservation of energy to solve this problem. The initial potential energy of the spring is equal to the final kinetic energy of the cannonball.
$$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$$
where $m$ is the mass of the cannonball, $v$ is its speed, $k$ is the spring constant, and $x$ is the compression of the spring.
Plugging in the given values, we get:
$$\frac{1}{2}(7.0	ext{ kg})v^2 = \frac{1}{2}(1800	ext{ N/m})(0.55	ext{ m})^2$$
Simplifying and solving for $v$, we get:
$$v = \sqrt{\frac{(1800	ext{ N/m})(0.55	ext{ m})^2}{7.0	ext{ kg}}} \approx 140	ext{ m/s}$$
Therefore, the answer is B.

Question 19

A simple pendulum on earth has a period of 6.0 s.What is the approximate period of this pendulum on the moon where the acceleration due to gravity is roughly 1/6 that of earth?
A)1.0 s
B)2.4 s
C)6.0 s
D)15 s
E)36 s

Accepted Answer

The answer of A simple pendulum on earth has a...

Question 20

A thin, circular hoop with a radius of 0.32 m is hanging on a nail.Adam notices that the hoop is oscillating back and forth through small angles like a physical pendulum.The moment of inertia of the hoop for the rotational axis passing through the nail is I = 2mr².What is the period of the hoop? A)1.3 s B)0.94 s C)0.59 s D)1.1 s E)1.6 s

Accepted Answer

The answer of A thin, circular hoop with a radius...

Quiz 10: Simple Harmonic Motion and Elasticity

10-1 A relaxed spring protrudes from an opening 0.0500 meters as shown in Figure A. A 1.00-kg block is found to just force the spring completely into the opening as shown in Figure B. -Determine the spring constant k.

In a certain clock, a pendulum of length L1 has a period T1 = 0.95 s.The length of the pendulum is adjusted to a new value L2 such that T2 = 1.0 s.What is the ratio L2/L1?

A simple harmonic oscillator with a period of 2.0 s is subject to damping so that it loses one percent of its amplitude per cycle.About how much energy does this oscillator lose per cycle?

A pendulum is transported from sea-level, where the acceleration due to gravity g is 9.80 m/s2, to the bottom of Death Valley.At this location, the period of the pendulum is decreased by 3.00%.What is the value of g in Death Valley?

A cable stretches by an amount d as it supports a crate of mass M.The cable is cut in half.What is the mass of the load that can be supported by either half of the cable if the cable stretches by an amount d?

A cable stretches by an amount d when it supports a crate of mass M.The cable is then cut into three equal pieces.If the same crate is supported by any one of these pieces, by how much will the cable stretch?

Complete the following sentence: Resonance occurs in harmonic motion when

What are the SI units of the shear modulus?

A cable stretches by an amount d when it supports a crate of mass M.The cable is replaced by another cable of the same material having the same length and twice the diameter.If the same crate is supported by the thicker cable, by how much will the cable stretch?

A cable stretches by an amount d when it supports a crate of mass M.The cable is replaced by another cable of the same material having the same length and twice the diameter.What is the mass of the load that can be supported by the thicker cable if it stretches by an amount d?

10-1 A relaxed spring protrudes from an opening 0.0500 meters as shown in Figure A. A 1.00-kg block is found to just force the spring completely into the opening as shown in Figure B. -How much potential energy is stored in the spring in Figure B?

Complete the following statement: Young's modulus cannot be applied to

Which one of the following terms is used to describe a system in which the degree of damping is just enough to stop the system from oscillating?

What is the period of a pendulum consisting of a 6-kg object oscillating on a 4-m string?

The spring constant for the spring in a special cannon is 1800 N/m.In cocking the cannon, the spring is compressed 0.55 m.What is the initial speed of a 7.0-kg cannonball at rest on the free end of the spring when it is released?

A simple pendulum on earth has a period of 6.0 s.What is the approximate period of this pendulum on the moon where the acceleration due to gravity is roughly 1/6 that of earth?

A thin, circular hoop with a radius of 0.32 m is hanging on a nail.Adam notices that the hoop is oscillating back and forth through small angles like a physical pendulum.The moment of inertia of the hoop for the rotational axis passing through the nail is I = 2mr2.What is the period of the hoop?

In a certain clock, a pendulum of length L₁ has a period T₁ = 0.95 s.The length of the pendulum is adjusted to a new value L₂ such that T₂ = 1.0 s.What is the ratio L₂/L₁?

A pendulum is transported from sea-level, where the acceleration due to gravity g is 9.80 m/s², to the bottom of Death Valley.At this location, the period of the pendulum is decreased by 3.00%.What is the value of g in Death Valley?

A thin, circular hoop with a radius of 0.32 m is hanging on a nail.Adam notices that the hoop is oscillating back and forth through small angles like a physical pendulum.The moment of inertia of the hoop for the rotational axis passing through the nail is I = 2mr².What is the period of the hoop?