A small ball is attached to one end of a spring that has an unstrained length of 0.212 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 2.88 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.0160 m. By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless?

The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration KG=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k-2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 0=0°. The spring's length at the state 2 is L2=4 m. _(kg-m²) (two decimal (9) The mass moment of inertial about the IC center is IIC=_ places) L₂ State 2 State 1

A cube, whose mass is 0.700 kg, is attached to a spring with a force constant of 110 N/m. The cube rests upon a frictionless, horizontal surface (shown in the figure below). A cube labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the cube is displaced by a distance A to the right of its equilibrium position. The cube is pulled to the right a distance A = 0.110 m from its equilibrium position (the vertical dashed line) and held motionless. The cube is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the cube?  N (b) At that very instant, what is the magnitude of the cube's acceleration (in m/s2)?  m/s2 (c) In what direction does the acceleration vector point at the instant of release?

An ornament of mass 40.6 g is attached to a vertical ideal spring with a force constant (spring constant) of 45.6 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?

The frame is made from uniform rod which has a mass p per unit length. A smooth recessed slot constrains the small rollers at A and B to travel horizontally. Force P is applied to the frame through a cable attached to an adjustable collar C. Determine the magnitudes and directions of the normal forces which act on the rollers if (a) h = 0.24L, (b) h = 0.50L, and (c) h = 0.91L. The forces will be positive if up, negative if down. Evaluate your results for p = 1.8 kg /m, L = 575 mm, and P = 48 N. What is the acceleration of the frame in each case? (a) Answers: (b) L (c) A h = 0.24L: h = 0.50L: h = 0.91L: L A = A A = B i i i P B N₁ B N, B N, i i N₁ª N,9 N₁9 i i m/s m/s m/s

A small ball is attached to one end of a spring that has an unstrained length of 0.185 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 4.80 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.0190 m. By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless? Number Units

Two masses, m1 and m2, are attached to a 1.95-m-long steel wire which runs over a light, frictionless pulley as shown. Assume the cross section of the wire is circular with a diameter of d = 4.00 mm, m1 = 3.30 kg, and m2 = 4.90 kg. The masses are released from rest and allowed to move freely. Compared with its length before the masses were attached, by how much has the wire stretched (in mm) while the masses are in\

An ornament of mass 36.9 g is attached to a vertical ideal spring with a force constant (spring constant) of 51.8 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?

A cube, whose mass is 0.720 kg, is attached to a spring with a force constant of 110 N/m. The cube rests upon a frictionless, horizontal surface (shown in the figure below). A cube labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the cube is displaced by a distance A to the right of its equilibrium position. The cube is pulled to the right a distance A = 0.140 m from its equilibrium position (the vertical dashed line) and held motionless. The cube is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the cube?  N (b) At that very instant, what is the magnitude of the cube's acceleration (in m/s2)?  m/s2 (c) In what direction does the acceleration vector point at the instant of release?  Away from the equilibrium position (i.e., to the right in the figure). Toward the equilibrium position (i.e., to…

The figure blow shows the kinetic energy of a simple pendulum versus its angle θ from the vertical.  Note the energy units are in milli-joules.  The vertical axis is set by Ks=4mJ and the mass of the pendulum bob is 0.200 kg.  Determine the length of the pendulum in meters.  Use g = 9.8 N/kg.