Final answer:
The final speed of the rock at the bottom of the bowl is found using the principles of conservation of energy, accounting for the work done by friction. The loss in potential energy minus the work done by friction gives the kinetic energy, which allows us to solve for the final speed of the rock.
Step-by-step explanation:
The question is about the mechanics of energy conversion and work done by friction. To find the speed of the rock as it reaches point B at the bottom of the hemispherical bowl, we will use the conservation of energy principle and consider the work done by friction. Since the rock starts at rest, its initial kinetic energy is zero. As it slides down, it loses potential energy, which gets converted to kinetic energy. However, some energy is lost to work done by friction.
The loss in potential energy (PE) as the rock slides from point A to point B is calculated by PE = m • g • h, where m is the mass of the rock, g is acceleration due to gravity (9.8 m/s²), and h is the height which is equal to the radius R of the bowl, since the rock started from the top edge. Therefore, PE = 0.20 kg • 9.8 m/s² • 0.50 m.
The work done by friction is given as 0.22 J. The conservation of mechanical energy states that the initial mechanical energy minus the work done by friction equals the final kinetic energy (KE). Hence, initial PE - work done by friction = final KE.
Final KE can be expressed as ½ • m • v², where v is the final velocity of the rock at the bottom. We solve for v to find the speed of the rock at point B.