A solid cylinder has a 3.9 m long string wrapped around it. The free-end of the string is held and the solid cylinder is released thus unwinding the string as it falls. Find out how fast the solid cylinder will be going at the moment the string is completely unwound assuming no thermal energy is generated.

A small ball is attached to one end of a spring that has an unstrained length of 0.222 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 4.52 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.0102 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 i eTextbook and Media Units +

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

Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (the figure (Figure 1)). There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being tested on earth, but it is to be used on Mars, where the acceleration due to gravity is 3.71 m/s2. In the earth tests, when m is set to 13.0 kg and allowed to fall through 5.00 m, it gives 300.0 J of kinetic energy to the drum. If the system is operated on Mars, through what distance would the 13.0-kg mass have to fall to give the same amount of kinetic energy to the drum? How fast would the 13.0-kg mass be moving on Mars just as the drum gained 300.0 J of kinetic energy?