Final answer:
The work done on the bike and girl by friction as she comes to a stop is -259.5305 joules, indicating that this amount of energy is removed from the system.
Step-by-step explanation:
To calculate the work done on the bike and the girl as she comes to a stop, we can use the work-energy principle. The work done by the friction force is equal to the change in kinetic energy of the girl and her bicycle. Since she comes to a stop, her final kinetic energy is 0, and the initial kinetic energy can be calculated using the equation KE = (1/2)mv2, where m is the mass and v is the velocity.
The initial kinetic energy is:
KEi = (1/2) * 20.1 kg * (5.1 m/s)2 = 259.5305 J
The final kinetic energy is 0 J since the girl stops completely:
KEf = 0 J
The work done by friction, which brings the bike and the girl to a stop, is equal to the negative change in kinetic energy:
Work = KEf - KEi = 0 J - 259.5305 J = -259.5305 J
Therefore, the work done on the bike and girl by friction is -259.5305 joules, which indicates that energy is removed from the system by friction.