Reflections on the Work Required to Stop a Rolling Hoop
How much work is required to stop the hoop?
(a) The mass of a hoop of radius 1.0 m is 6.0 kg. It rolls across a horizontal surface with a speed of 10.0 m/s. How much work is required to stop the hoop?
If the hoop starts up a surface at to the horizontal with a speed of 10.0 m/s, how far along the incline will it travel before stopping and rolling back down?
(b) If the hoop starts up a surface at to the horizontal with a speed of 10.0 m/s, how far along the incline will it travel before stopping and rolling back down?
Answer:
(A) 300 J of labour is needed to stop the hoop. The hoop has a kinetic energy of 300 J.
(B) The hoop will roll up the slope for 2.55 m before coming to a stop and rolling back down.
Reflecting on the work required to stop a rolling hoop, we can see that 300 J of labour is needed to bring the hoop to a halt. This is because the hoop possesses a kinetic energy of 300 J due to its mass and speed.
When the hoop starts up a surface at an angle to the horizontal with a speed of 10.0 m/s, it will travel a distance of 2.55 m along the incline before coming to a stop and rolling back down. This distance is determined by the transformation of the hoop's initial kinetic energy into potential energy as it ascends the slope.
The potential energy at the highest point of the incline is equal to the initial kinetic energy of the hoop, which is 300 J. By equating potential energy (mgh) to 300 J, we can solve for the height attained by the hoop, which is approximately 3.06 m. Using this height and the incline angle, we can calculate that the hoop will travel a distance of 2.55 m along the incline before reversing its course.
This reflection highlights the relationship between kinetic and potential energy in the motion of the hoop, illustrating the concept of energy transformation in physics. By understanding the work required to stop a rolling hoop and the distance it can travel on an incline, we gain insight into the principles of energy conservation and mechanical motion.