Two uniform, solid cylinders of radius R and total mass M are connectedalong their common axis by a short, light rod and rest on a horizontaltabletop. A frictionless ring at the rod’s center is attached toa spring of force constant k; the spring’s other end is fixed. The cylindersare pulled to the left a distance x, stretching the spring, then releasedfrom rest. Due to friction between the tabletop and the cylinders, the cylindersroll without slipping as they oscillate. Show that the motion of thecenter of mass of the cylinders is simple harmonic, and find its period.

Two uniform, solid cylinders of radius R and total mass M are connectedalong their common axis by a short, light rod and rest on a horizontaltabletop. A frictionless ring at the rod’s center is attached toa spring of force constant k; the spring’s other end is fixed. The cylindersare pulled to the left a distance x, stretching the spring, then releasedfrom rest. Due to friction between the tabletop and the cylinders, the cylindersroll without slipping as they oscillate. Show that the motion of thecenter of mass of the cylinders is simple harmonic, and find its period.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter7: Dry Friction

Section: Chapter Questions

Problem 7.80P

See similar textbooks

Related questions

Q: Prelab Exercises for Angular Motion 1. Draw a free-body diagram for mass M, while in motion (Fig.…

A: To Draw : The free body diagram for and centrifugal force.Given :

Q: Given: A uniform slender rod is at rest upon a frictionless horizontal surface when a force (F) is…

Q: machine part has the shape of a solid uniform sphere of mass 220 gg and diameter 3.50 cmcm . It is…

Q: The system shown below is made up of two pulleys attached to the same shaft, with radii ri and re of…

Q: The sliding glass door rolls on the two small lower wheels A and B. Under normal conditions the…

Q: 4. A solid disc of mass 6.5 kg and radius 0.5 m rests on a 2.25 kg trolley. A light cord is wrapped…

A: Given Data: Mass of the Solid disk M=6.5 kg radius of the solid Disk r = 0.5 m Mass of the trolley…

Q: A centrifugal clutch has four shoes which slide radially in a spider keyed to the driving shaft and…

A: Centrifugal clutches generally consists of motor pulleys. Inside the rim of these pulleys, various…

Q: Q3: The ship has a turbine rotor fix with its axis along the longitudinal axis of the ship makes…

A: Pitching is defined as rotation along a transverse axis, which is comparable to an axis parallel to…

Q: The rod PQ of length L = V2 m and uniformly distributed mass of M = 10 kg, is released from rest at…

Q: HW2 A uniform disc of 80 mm radius has a mass of 2000 g. It is mounted centrally in bearings that…

Q: 4 -(Kinetics of Curvilinear Motion) Tow weights W, and W2 of 8KN and 5KN are attached at the ends of…

Question

Two uniform, solid cylinders of radius R and total mass M are connected
along their common axis by a short, light rod and rest on a horizontal
tabletop. A frictionless ring at the rod’s center is attached to
a spring of force constant k; the spring’s other end is fixed. The cylinders
are pulled to the left a distance x, stretching the spring, then released
from rest. Due to friction between the tabletop and the cylinders, the cylinders
roll without slipping as they oscillate. Show that the motion of the
center of mass of the cylinders is simple harmonic, and find its period.

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 8 images

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, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

3.32). As shown in Figure 3, a yo-yo toy is formed by wrapping a massless cord around adisk of radius R= 0.2 m and mass M=3 kg. The cord is vertical and its top end is fixed and the disk isinitially stationary. The cord remains vertical for the entire motion and does not slide on the disk.When the disk is released from rest, it falls down by a distance H=0.8 m, The moment of inertia ofthe disk around its center is I disk=1/2mdiskR^2a . Find the angular acceleration of the disk when it is lowered by a distance H.b . Find the angular velocity of the disk when it is lowered by a distance H.
4 -(Kinetics of Curvilinear Motion) Tow weights W, and W2 of 8KN and 5KN are attached at the ends of a flexible cable. The cable passes over a pulley of 100 cm diameter. The weight of the pulley is 600N with a radius of gyration of 50cm about its axis of rotation. Find the torque which must be applied to the pulley to raise the 8KN weight with an acceleration 1.5 m/s?. Neglect friction in the pulley bearing. 50 cm 600N T 8kN 5kN W,
Problems 3.64 and 3.65 Te stem shown is initially at rest when the bent bar starts to rotate about the vertical is AB with constant angular acceleration a son between the collar of mass m = intially d = 70 cm from the spin axis AB. 3 rad/s. The coefficient of static fric- 2 kg and the bent bar is u, = 0.35, and the collar is %3D %3D %3D Problem 3.64 Assuming the motion starts at 1 = 0, determine the time at which the allar starts to slip relative to the bent bar. Figure P3.64 and P3.65 of rotations undergone by the bent bar when the
Question 2: A point-mass M of mass m is tied to a string which winds around a cylinder like a bobbin. The string is pinned on the cylinder at some point, and P denotes the point at which the string leaves the bobbin and starting from which it is taut. The cylinder has radius a and rotates at a constant rate around the vertical axis of the fixed frame F (which is also the axis of symmetry of the bobbin). The motion takes place in the hori- zontal plane, which is assumed frictionless. See figure. (a) Find a relationship between l, a and expressing that the length of the string is constant (b) Compute the velocity and acceleration of point M with respect to F. (c) Apply LMB in F to the system consisting of the point mass M alone (don't forget to start with a free body diagram!). Deduce a differential equation for l as well as the value of the string's tension in terms of the other parameters. (d) (bonus) Solve the differential equation for l. eo Ω Mas P M FIGURE 1 - The spinning bobbin.…
Q4. As shown in the image below, a force of P= 310 N is applied to the 64-kg cart. The dimensions are a = 0.29 m, b = 0.21 m, and c = 0.28 m, and the angle 0 = 26. The mass center of the cart is at point G. Assume the wheels are weightless and free to roll (therefore, friction can be ignored). Take g = 9.81 m/s?. (1) Determine the total normal force at the wheels at A. A FBD and kinetic diagram must be included on your notes. Your answer must include 1 place after the decimal point, and the proper SI unit. P 0.4 m C В 0.08 m
5. A uniform solid cylinder with M 2R mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley M with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string. The string doesn't slip over the pulley surface, and the cylinder rolls without slipping on the tabletop. Find the magnitude of the acceleration of the block after the system is released from rest.
7. A cage of mass 2500 kg is raised and lowered by a winding drum of 1.5 m diameter. A brake drum is attached to the winding drum and the combined mass of the drums is 1000 kg and their radius of gyration is 1.2 m. The maximum speed of descent is 6 m/s and when descending at this speed, the brake must be capable of stopping the load in 6 m. Find 1. the tension of the rope during stopping at the above rate, 2. the friction torque necessary at the brake, neglecting the inertia of the rope, and 3. In a descent of 30 m, the load starts from rest and falls freely until its speed is 6 m/s. The brake is then applied and the speed is kept constant at 6 m/s until the load is 10 m from the bottom. The brake is then tightened so as to give uniform retardation, and the load is brought to rest at the bottom. Find the total time of descent. [Ans. 32 kN ; 29.78 kN-m ; 7.27 s]
A string is wrapped around a uniform disk of mass M = 2.1 kg and radius R = 0.12 m. (Recall that the moment of inertia of a uniform disk is (1/2) MR².) Attached to the disk are four low-mass rods of radius b = 0.16 m, each with a small mass m = 0.7 kg at the end. The device is initially at rest on a nearly frictionless surface. Then you pull the string with a constant force F = 30 N. At the instant when the center of the disk has moved a distance d = 0.041 m, a length w = 0.033 m of string has unwound off the disk. •m bi m m Part 1 M, R Part 2 d V= 0.708548386 Your answer is correct. Part 3 m (a) At this instant, what is the speed of the center of the apparatus? @01 = i 5.08017 Save for Later F Your answer is incorrect. (b) At this instant, what is the angular speed of the apparatus? 002 = i w+d Save for Later m/s eTextbook and Media F radians/s (c) You keep pulling with constant force 30 N for an additional 0.042 s. Now what is the angular speed of the apparatus? radians/s Attempts: 1…
A circular rigid disk of mass m kg and radius rm is stationary at the top of a fixed sphere of radius 2r m. The disk is disturbed slightly from rest and rolls with planar motion down the sphere without slipping. Determine the value of angle at which the disk leaves the sphere. Derive the tangential friction force F between the disk and sphere as a function of angle 0. sphere -2r. disk o'r
Please show all work and diagrams! Anything is helpful.
A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I= cMR2. As shown in the figure, the sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side, but now with no friction at all between the sphere and the ramp. What height does the sphere reach?
Mechanical Engineering Question