In the diagram below, the center of a disk of mass M is attached to a spring of spring constant k. The other end of the spring is connected to a fixed wall. When the spring is at its resting length, the center of mass of the disk is at x = 0. Then the disk is rolled a distance A from the equilibrium position and released, allowing it to roll back and forth under the influence of the spring. (a) Starting from Newton’s second law for rotation, show that the x-coordinate of disk’s center of mass obeys an equation of the form
Force , F = -K*x , where k IS SPRING CONSTANT
F = m*a
m*d2Xcm/dt^2 = -K*Xcm
d2Xcm/dt^2 = -K/m * Xcm
d2Xcm/dt^2 = - omega^2 * Xcm
where omega^2 = K/m.
In the diagram below, the center of a disk of mass M is attached to a...
A mass is connected to the center of a rotating disk via a spring. The mass is constrained by a smooth (frictionless) slot to only move in a purely radial direction X Lo The disk has radius Rand starts rotating from rest at a constant angular acceleration (counterclockwise). The starting position of the mass is as shown, where its distance away from the center of the disk is the same as the resting length of the spring. Gravity points into...
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
Free body diagram: 24 0.5r 0.5r No slip (a) An ec centric disk is rotating on the ground as shown in the figure above. The disk has radius r. The distance between the center of mass of the disk (denoted as C) to its geometric center (denoted as O) is 1 r. The angle of rotation of the disk is θ and the displacement at point O is x. The disk has mass m. The moment of inertia with respect...
7) A block of mass m, resting on a horizontal frictionless surface, is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6 J of work to compress the spring by 0.13 m. If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 15 m/s2. Find the value of (a) the mass of the block. As the block passes through its equilibrium position, a...
QUESTIONS A block of mass m, resting on a horizontal frictionless surface, is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6J of work to compress the spring by 13 cm; then it is released from rest. It experiences a maximum acceleration of 15 m/s2. Find the value of (a) the mass of the block. As the block passes through its equilibrium position, a lump of putty of mass mi -...
A block of mass m, resting on a horizontal frictionless surface, is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6 J of work to compress the spring by 13 cm; then it is released from rest. It experiences a maximum acceleration of 15 m/s2. Find the value of (a) the mass of the block. As the block passes through its equilibrium position, a lump of putty of mass mi -...
A block of mass m, resting on a horizontal frictionless surface, is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6 J of work to compress the spring by 13 cm; then it is released from rest. It experiences a maximum acceleration of 15 m/s2. Find the value of (a) the mass of the block. As the block passes through its equilibrium position, a lump of putty of mass mi -...
Figure 3 Uniform disk Uniform rod 3) Figure 3 illustrates a physical pendulum comprising a uniform disk having mass M and radius R and a rod having the length R and mass M. The disk is pivotally mounted with a friction-less horizontal axis of rotation that extends through the center of mass of the disk. The rod is fixedly attached to the edge of the disk and it extends vertically downward when the pendulum is in a state of static...
A block of mass m, resting on a horizontal frictionless surface, is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6J of work to compress the spring by 13 cm; then it is released from rest. It experiences a maximum acceleration of 15 m/s2. Find the value of (a) the mass of the block. As the block passes through its equilibrium position, a lump of putty of mass mı = 1.2...
Three 28-lb rotor disks are attached to a shaft which rotates at 720 rpm. Disk A is attached eccentrically so that its mass center is 0.25 in. from the axis of rotation, while disks Band Care attached so that their mass centers coincide with the axis of rotation. Where should 2-lb weights be bolted to disks Band Cto balance the system dynamically? 4 in in 6 in 4 in in. The placement of added masses is: On B On C...