A 95 kg solid sphere with a 15 cm radius is suspended by a vertical wire. A torque of 0.20 N · m is required to rotate the sphere through an angle of 0.85 rad and then maintain that orientation. What is the period of the oscillations that result when the sphere is then released?

A 95 kg solid sphere with a 15 cm radius is suspended by a vertical wire. A torque of 0.20 N · m is required to rotate the sphere through an angle of 0.85 rad and then maintain that orientation. What is the period of the oscillations that result when the sphere is then released?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.20P

See similar textbooks

Related questions

Q: The pendulum in the figure consists of a uniform disk with radius r = 15.0 cm and mass 880 g…

Q: Record Spring Constant Here: N/m Run 1 Amplitude = 2.00 cm Mass = .550 kg rad/s Run 2 Amplitude =…

A: This question can easily be solved by applying the basic concept of simple harmonic motion .

Q: A 0.40-kg mass hangs on a spring with a spring constant of 12 N/m. The system oscillates with a…

Q: A 21 g ball with a radius of 30 mm rolls back and forth in a hemispherical bowl of radius 6 cm.…

A: Given Mass of the ball = 21 g Radius of the ball = 30 mm Radius of the hemispherical ball = 6 cm To…

Q: A body of mass 0.4kg moves with S.H.M of amplitude of 0.8m and a period of 2 seconds. Determine (i)…

A: mass, m = 0.4 kg Amplitude, A = 0.8m period, T =2 s

Q: In the figure, a solid cylinder M attached to a horizontal spring k (k = 3.00 N/m) rolls without…

A: Given:- spring constant = 3.0 Nm spring stretched by the 0.250 m Find:- a)…

Q: .25kg harmonoc oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20…

A: We know that Conservation of energy of the spring E=KE+PEspringE=12mv2+12kx2

Q: A simple pendulum of length L= 2.69 m is released from rest from a position making an angle of 9°…

A: L = 2.69 m θi = 9oθf = 6oLet the mass = m g = 9.8 ms2

Q: A physics student uses a rod of an unknown length to demonstrate a physical pendulum. The period of…

A: Given: Physical Pendulum, Period of oscillation, T = 2.20 sMoment of Inertia, I = 0.15 ML2 Diagram:…

Q: The pendulum in the figure consists of a uniform disk with radius r = 14.0 cm and mass 860 g…

Q: A 9 kg block is attached to a spring with a spring constant of 5 N/m. While the block is sitting at…

A: Solution: The moment at which the student hits the block with the hammer, the kinetic energy of the…

Q: simple pendulum with mass m = 1.2 kg and length L = 2.48 m hangs from the ceiling. It is pulled back…

Q: The pendulum in the figure consists of a uniform disk with radius r = 13.0 cm and mass 750 g…

A: (a). the rotational inertia of the pendulum about the pivot point is

Q: A simple pendulum of length 20 cm and mass 5.0 g is suspended in a race car traveling with constant…

A: The formula for the acceleration in a uniform circular motion is: The formula for the frequency of…

Q: Engineers roll a ball with a mass of 2kg and radius of 0.25m down a ramp (without slipping). The…

A: Since you have asked for a handwritten solution, I have handwritten the solution and uploaded it.…

Q: In a pendulum, is it angular velocity or angular acceleration that is proportional to sin (theta)?

Q: A pendulum's angular position is given by 0 = 0.0300 cos(@t), where 0 is in radians and w = 8.48…

A: Given, angular position of a pendulum, θ= 0.0300 cosωt ω= 8.48 rads

Q: A simple pendulum is made of a 50 cm-string and a bob of mass m. At t = 0, the %3D pendulum is at…

Q: Any object moving with a specified angular velocity is known to be an object that moves in simple…

Q: child with mass of 10 kg gets into a toy car with mass of 65 kg on a playground, causing it to sink…

Q: The bob of a simple pendulum is pulled to the right by an angle 0_0 = 10° and then released from…

A: 2. Angular amplitude of pendulum, θo = 10° Period of oscillation, T = 1 second, So, angular…

Q: A composite pendulum consisting of a uniform disk with radius R and mass 6m is connected to a…

Q: A solid cylinder of mass M, radius R, and length L, rolls around a light, thin axle at its center.…

A: Length of cylinder = L Mass of Cylinder= M The radius of cylinder = R The springs are connected in…

Q: A pointlike body of mass m made of lead is fixed inside a homogeneous solid sphere of radius R and…

A: Given data The mass of the point-like body is m. The radius of the sphere is R The location distance…

Q: A spring is compressed by 0.0610 m and is used to launch an object horizontally with a speed of 2.80…

A: Given, Compression in the spring = 0.0610 m. The horizontal speed of the object = 2.80 m/s.…

Q: A 3.72 kg iron box is suspended from a spring with a spring constant of k=18 N/m. The mass is pulled…

A: The mass of the iron box is 3.72 kg, and spring constant of the spring is 18 N/m, and the distance…

Q: A 1.80 kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a…

A: Given: The mass of monkey is m=1.80 kg. The distance is d=0.250 m. The time period is T=0.94 s. The…

Q: A simple pendulum is made of a 2 m-string and a bob of mass m. At t = 0, the pendulum is at its…

A: Given : Length L = 2 m Initial velocity v= 0.2 m/s Mass = m kg We have to calculate the Maximum…

Q: Which of these forces could result in simple harmonic motion: AF (r) 2r. B.F (z) = -2x*. C.F (r) =…

Q: What is the maximum speed of the object? What is the amplitude of the object's position? What is…

A: a) The object’s velocity can be determined as, Here, ax, amax, vmax, T, δ, and t represent the…

Q: A 95 kg solid sphere with a 15 cm radius is suspended by a vertical wire. A torque of 0.20 Nm is…

Q: The pulley in the figure has radius R = 1.0m and moment of inertia I = 10kg.m2. The block of mass m…

Q: complicated shape is made to swing about a point that is 192 cm from the center of mass of the…

Q: a 800g body vibrates S.H.M with amplitude of 0.30 m. The restoring force is 60N and the displacement…

A: Given: mass of body, m = 800 g = 0.8 kg amplitude, A = 0.30 m restoring force, F = 60 N…

Q: A certain alarm clock ticks four times each second, with each tick representing half a period. The…

A: Given, Radius, r=0.25 m, and mass, m=0.50 g=0.0005 kg. Time period, T=0.5 s.

Q: A 1.5-m length pendulum is displaced by an initial angle = +6° and released from rest. If the…

A: Frequency of oscillations is proportional to acceleration due to gravity and inversely to length for…

Q: A point in a machine moves with simple harmonic motion. When this point is 0.8 metre from the mid…

A: distance from mid point = X1=0.8m velocity at that point = V1= 10m/s distance = X2= 1.5m velocity at…

Q: A 1.5 kg uniform meter stick pivoted at one end oscillates as a physical pendulum with a period of…

A: Length of meter stick L = 1m. Moment of inertia of stick about Center of mass = ML²/12

Q: A solid sphere, made of acrylic plastic with a density of 1.1 g/cm3,1.1 g/cm3, has a radius of 5.0…

A: Given data- Density of solid sphere d=1.1 g/cm3 Radius of sphere r=5.0 cm

Q: rotational inertia is 450 kg·m2 hangs from a wire whose torsion constant is 2300 N·m/rad. What is…

A: Given Rotational inertia I = 450 kg m2 Torsional constant k = 2300 N m /rad

Q: The pendulum in the figure consists of a uniform disk with radius r = 17.0 cm and mass 680 g…

A: Given data:Mass of the disk, M = 680 g = 0.680 kgRadius of the disk, r = 17.0 cm = 0.17 mLength of…

Q: the pendulum consists of a uniform disk with radius r = 10.0 cm and mass 500 g attached to a uniform…

Question

Please provide me solution how to solve this.

A 95 kg solid sphere with a 15 cm radius
is suspended by a vertical wire. A torque of
0.20 N · m is required to rotate the sphere
through an angle of 0.85 rad and then
maintain that orientation. What is the
period of the oscillations that result when
the sphere is then released?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.00105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. (a) What effective force constant should the springs have to make the object oscillate with a period of 2.00 s? (b) What energy is stored in the springs for a 2.00-m displacement from equilibrium?
If a car has a suspension system with a force constant of 5.00104 N/m , how much energy must the car’s shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?
Check Your Understanding Identify an object that undergoes uniform circular motion. Describe how you could trace the SHM of this object.
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 12.28.
Determine the angular frequency of oscillation of a thin, uniform, vertical rod of mass m and length L pivoted at the point O and connected to two springs (Fig. P16.78). The combined spring constant of the springs is k(k = k1 + k2), and the masses of the springs are negligible. Use the small-angle approximation (sin ). FIGURE P16.78
The temperature of the atmosphere oscillates from a maximum near noontime and a minimum near sunrise. Would you consider the atmosphere to be in stable or unstable equilibrium?
An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
. A mass of 0.75 kg is attached to a relaxed spring with k = 2.5 N/m. The mass rests on a horizontal, frictionless surface. If the mass is displaced by 0.33 m, what is the magnitude of the force exerted on the mass by spring? If the mass is then released to execute simple harmonic along the surface, with what frequency will it oscillate?
A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?
Assume that a pendulum used to drive a grandfather clock has a length L0=1.00 m and a mass M at temperature T=20.00 °C. It can be modeled as a physical pendulum as a rod oscillating around one end. By what percentage will the period change if the temperature increases by 10°C? Assume the length of the rod changes linearly with temperature, where L=L0(1+T) and the rod is made of (=18106C1) .
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?