An object hanging from a vertical spring oscillates with a period of 0.35 s. Suppose the same object and spring are placed on a horizontal frictionless surface and the object is in a horizontal circle swung (uniform circular motion) with the open end of the spring as the pivot. How many rotations per minute is needed to stretch the spring by 15%?
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- 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 1Engineers 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?
- = A pendulum consists of a rod of mass 1.80 kg and length L 1.00 m with a solid sphere at one end with mass 0.320 kg and radius 24.0 cm (see the following figure). If the pendulum is released from rest at an angle of 0 = 29.0°, what is the angular velocity at the lowest point? Axis A Part 1 + To solve this problem it will be necessary to first find the moment of inertia of the pendulum. What is its moment of inertia? Part 2 + What is the initial gravitational potential energy of the pendulum? Define the gravitational potential energy to be zero when the pendulum is at its lowest point. Part 3 What is the angular velocity of the pendulum at its lowest point?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 UnitsPlease Asap
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