Work Done to Stop a Rolling Hoop
How much work must be done on the hoop to stop it?
What is the relationship between the kinetic energy of the hoop and the work needed to stop it?
Work Done on the Hoop to Stop It
The amount of work that must be done on the hoop to stop it is equal to the kinetic energy of the hoop. To calculate the work, we can use the equation KE = 0.5 x m x v2, where KE is the kinetic energy, m is the mass of the hoop, and v is its velocity.
When a 190 kg hoop is moving at a speed of 0.140 m/s, the kinetic energy of the hoop is 0.5 x 190 x (0.140)2 = 11.9 J. Therefore, 11.9 J of work must be done on the hoop to stop it.
To stop the hoop, an external force must act on it to reduce its kinetic energy. This force could come from friction with the surface or an opposing force such as wind resistance. Once the kinetic energy is reduced to zero, the hoop will come to a stop.
The work done is equal to the change in kinetic energy of the hoop, which is the difference between the initial kinetic energy and the final kinetic energy. Since the initial kinetic energy is 11.9 J and the final kinetic energy is 0, the amount of work done on the hoop is indeed 11.9 J.