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A bead of mass m = 6.20 kg is released from point A and slides on the frictionless track shown in Figure P5.30. The height of A is ha = 5.90 m.
Figure P5.30
(a) Determine the bead's speed at points B and C.
(b) Determine the net work done by the force of gravity in moving the bead from A to C
| point B | m/s |
| point C | m/s |
Transcribed Image Text:### Physics of a Roller Coaster Track
This diagram illustrates a section of a roller coaster track with significant points marked as A, B, and C:
- **Point A**: This is the starting point, where a ball with mass \( m \) is placed at a height \( h_a \). The height of point A indicates the potential energy at the start of the track.
- **Point B**: The track descends and then ascends to point B, which is located 3.20 meters above the ground. As the ball moves to this point, it converts some of its initial potential energy to kinetic energy and then back to potential energy.
- **Point C**: The next valley in the track, with point C at a height of 2.00 meters above the ground. At this point, the ball would have less potential energy than at point B but more kinetic energy after descending.
The track design showcases energy transformation principles, where potential energy is highest at point A and varies as the ball travels along the path, changing to kinetic energy as it moves. This demonstrates the conservation of mechanical energy in a frictionless system.
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