Final answer:
If the force of friction is constant throughout the motion, the bead will eventually come to a stop after a certain number of revolutions. The negative work done by friction is equal to the initial kinetic energy of the bead, and the distance over which the friction force acts is equal to the circumference of the circular motion. By equating the negative work done by friction to the initial kinetic energy and dividing the distance travelled by the circumference, we can determine the number of revolutions the bead can make before stopping.
Step-by-step explanation:
In this scenario, if the force of friction is constant throughout the motion, the bead will eventually come to a stop after a certain number of revolutions. This can be determined by considering the work done by friction. When the bead is pushed, it gains kinetic energy, which is gradually lost due to the work done by friction. The negative work done by friction is equal to the initial kinetic energy of the bead, and the distance over which the friction force acts is equal to the circumference of the circular motion.
- Find the initial kinetic energy of the bead using the formula KE = (1/2)mv^2, where m is the mass of the bead and v is its velocity.
- Calculate the work done by friction using the formula W = -Fd, where F is the force of friction and d is the distance travelled by the bead.
- Equate the negative work done by friction to the initial kinetic energy and solve for the distance travelled by the bead.
- Divide the distance travelled by the circumference of the circular motion to find the number of revolutions the bead can make before stopping.