Question 1

A 75 g block is placed into oscillation of amplitude 22 cm as it hangs from a vertical spring.If it observed to have a maximum speed of 14 m/s as it travels through the equilibrium position,what is the spring constant?
A) 300 N/m
B) 22 N/m
C) 4.8 N/m
D) 1200 N/m

Accepted Answer

The correct answer is A because the spring constant is given by k = mω^2, where m is the mass of the block and ω is the angular frequency of the oscillation. The angular frequency is given by ω = 2πf, where f is the frequency of the oscillation. The frequency is given by f = 1/T, where T is the period of the oscillation. The period is given by T = 2π√(m/k). Substituting these equations into the equation for the spring constant, we get k = 4π^2m/T^2. Substituting the given values into this equation, we get k = 4π^2(0.075 kg)/(0.22 m)^2 = 300 N/m.

Question 2

A pendulum when on Earth has a period of 1.00 s.When transported to the moon,where the gravitational acceleration is 1/6 that on Earth,the period of the pendulum would be:
A) 4.1 s.
B) 1.00 s
C) 2.4 s

Accepted Answer

The period of a pendulum is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. When the pendulum is transported to the moon, the acceleration due to gravity is 1/6 that on Earth, so the period of the pendulum will be T = 2π√(L/(g/6)) = 2π√(6L/g) = 2π√(6) * T_Earth = 4.1 s.

Question 3

A block is placed in oscillation on a frictionless horizontal surface attached to a spring that is also attached to a wall.If,when stretched away from equilibrium by 15 cm and released,it oscillates with a period of 0.25s,and if the mass of the block is 15 kg,what force was required to stretch the spring by the initial 15 cm?
A) 230 N
B) 450 N
C) 710 N
D) 360 N
E) 1400 N

Accepted Answer

The answer of A block is placed in oscillation on...

Question 4

A grandfather clock keeps time using a pendulum whose length is finely adjustable.If you have a grandfather clock that is running fast,should you shorten or lengthen the pendulum?
A) Shorten it
B) Lengthen it
C) You should reduce its mass
D) You should add mass to it

Accepted Answer

Lengthening the pendulum will increase its period of oscillation, which means it will take longer for the pendulum to swing back and forth. This will slow down the clock's timekeeping, compensating for its fast running. Shortening the pendulum would have the opposite effect of increasing the clock's speed. Changing the mass of the pendulum wouldn't have as significant of an effect on its timekeeping as changing its length.

Question 5

A pendulum with a bob of mass 150 g has the same period as a thin rod (not massless)of the same mass and length 17 cm when the rod is pivoted about its end.What is the length of the pendulum?
A) 12 cm
B) 15 cm
C) 22 cm
D) 27 cm

Accepted Answer

The answer of A pendulum with a bob of mass...

Question 6

A disk is suspended by a nail such that it pivots in a vertical plane about a point on the edge of the disk.If the disk's radius is 25 cm,what is the period of oscillation?
A) 0.71 s
B) Need the mass of the disk to calculate the period.
C) 1.2 s
D) 1.51 s

Accepted Answer

The answer of A disk is suspended by a nail...

Question 7

A pendulum that on Earth has period 0.52 s is taken to the surface of a large asteroid,where it is measured to have period 1.7 s.What is the value of the gravitational acceleration on the surface of that asteroid? A) 5.78 m/s² B) 0.48 m/s² C) 3.0 m/s² D) 0.92 m/s²

Accepted Answer

The answer of A pendulum that on Earth has period...

Question 8

In simple harmonic motion the position of the oscillator:
A) Is behind its acceleration by a quarter cycle,or $\pi$/2 radians
B) Leads its acceleration by a quarter cycle,or $\pi$/2 radians
C) Leads its velocity by a quarter cycle,or $\pi$/2 radians
D) Is behind its velocity by a quarter cycle,or $\pi$/2 radians

Accepted Answer

In simple harmonic motion, displacement and velocity are out of phase by a quarter cycle or π/2 radians, while displacement and acceleration are out of phase by half a cycle or π radians. Therefore, the position of the oscillator is behind its velocity by a quarter cycle or π/2 radians. So, option D is the correct answer.

Question 9

In simple harmonic motion the position of the oscillator:
A) Leads its acceleration by a half cycle,or $\pi$ radians
B) Leads its velocity by a half cycle,or $\pi$ radians
C) Is in phase with its acceleration
D) Is in phase with its velocity

Accepted Answer

In simple harmonic motion, the acceleration is proportional to the negative of the displacement, meaning they are out of phase by $\pi$ radians or a half cycle.

Question 10

A disk is suspended by a nail such that the pivots in a vertical plane about a point on the edge of the disk.If the period of oscillation of the disk is 1.25 s ,what is the disk's radius?
A) 26 cm
B) 78 cm
C) Cannot answer without knowing the disk's mass
D) 51 cm

Accepted Answer

The period of oscillation for a physical pendulum is given by $ T = 2\pi \sqrt{\frac{I}{mgd}} $, where $ I $ is the moment of inertia, $ m $ is the mass, $ g $ is the acceleration due to gravity, and $ d $ is the distance from the pivot to the center of mass. For a disk pivoting about its edge, $ I = \frac{3}{2}mr^2 $ and $ d = r $. Solving for $ r $ using the given period $ T = 1.25 $ s, we find $ r \approx 0.26 $ m or 26 cm. The mass cancels out, so it is not needed.

Question 11

When the position of a simple harmonic oscillator is equal to A/2,where A is the amplitude,the kinetic energy is: A) (3/4)kA² B) (1/4)kA² C) (3/8)kA² D) (1/8)kA² E) (1/2)kA²

Accepted Answer

The answer of When the position of a simple harmonic...

Question 12

A 125 g pendulum bob hung on a string of length 35 cm has the same period as when the bob is hung from a spring and caused to oscillate.What is the spring's elastic constant?
A) 1.9 N/m
B) 3.5 N/m
C) 5.2 N/m
D) 27 N/m

Accepted Answer

The period of a pendulum is given by T = 2π√(L/g), and the period of a spring-mass system is T = 2π√(m/k). Equating these and solving for k gives k = (mg)/L. Substituting m = 0.125 kg, g = 9.8 m/s², and L = 0.35 m, we find k ≈ 3.5 N/m.

Question 13

A block is placed in oscillation on a frictionless horizontal surface attached to a spring that requires 125 N for the block to be stretched 15 cm away from equilibrium.From this position it is released,and oscillates with a period of 0.25 s.What is the mass of the block?
A) 0.66 kg
B) 4.1 kg
C) 1.3 kg
D) 5.3 kg

Accepted Answer

We can use the formula for the period of oscillation of a spring-mass system:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the spring constant.

We are given that the period is 0.25 s, so we can rearrange the equation to solve for the mass:

m = (T²k)/(4π²)

To find k, we need to convert the given stretch distance into a force. The spring constant k is defined as the force required to stretch the spring by one unit of distance. So if the block needs a force of 125 N to be stretched 15 cm, we can divide 125 by 0.15 to get:

k = 833.3 N/m

Now we can plug in the values for T and k and solve for m:

m = (0.25² x 833.3)/(4π²) = 1.3 kg

Therefore, the mass of the block is 1.3 kg.

Quiz 10: Elasticity and Oscillations

A 75 g block is placed into oscillation of amplitude 22 cm as it hangs from a vertical spring.If it observed to have a maximum speed of 14 m/s as it travels through the equilibrium position,what is the spring constant?

A pendulum when on Earth has a period of 1.00 s.When transported to the moon,where the gravitational acceleration is 1/6 that on Earth,the period of the pendulum would be:

A grandfather clock keeps time using a pendulum whose length is finely adjustable.If you have a grandfather clock that is running fast,should you shorten or lengthen the pendulum?

A pendulum with a bob of mass 150 g has the same period as a thin rod (not massless) of the same mass and length 17 cm when the rod is pivoted about its end.What is the length of the pendulum?

A disk is suspended by a nail such that it pivots in a vertical plane about a point on the edge of the disk.If the disk's radius is 25 cm,what is the period of oscillation?

A pendulum that on Earth has period 0.52 s is taken to the surface of a large asteroid,where it is measured to have period 1.7 s.What is the value of the gravitational acceleration on the surface of that asteroid?

In simple harmonic motion the position of the oscillator:

In simple harmonic motion the position of the oscillator:

A disk is suspended by a nail such that the pivots in a vertical plane about a point on the edge of the disk.If the period of oscillation of the disk is 1.25 s ,what is the disk's radius?

When the position of a simple harmonic oscillator is equal to A/2,where A is the amplitude,the kinetic energy is:

A 125 g pendulum bob hung on a string of length 35 cm has the same period as when the bob is hung from a spring and caused to oscillate.What is the spring's elastic constant?

A block is placed in oscillation on a frictionless horizontal surface attached to a spring that requires 125 N for the block to be stretched 15 cm away from equilibrium.From this position it is released,and oscillates with a period of 0.25 s.What is the mass of the block?