Oscillations - questions you have for the topic
Application of gravitation to International Space Station
Questions regarding video:
- Why does a bucket not hold water in the International Space Station (ISS)?
- Why doesn't the water from the cloth leaves the cloth when wringed?
Common misconceptions regarding gravitation in a space station orbiting Earth:
- Gravity in ISS is near zero (ISS is about 400km above Earth's surface => g ~ 8.7 N/kg which is about 90% of the field strength on Earth's surface)
- Astronauts are "weightless" (Gravitational force on astronauts in ISS is about 90% that on Earth's surface. The appearance of weightless/floating is due to the fact that both the passengers and ISS are falling towards Earth, contact force between passengers and ISS is zero.)
Other interesting questions:
- If ISS/satellite/moon are falling towards Earth, why don't these objects hit Earth? (Centripetal acceleration alters the direction of these objects' velocities, turning them towards the Earth. Earth is round. As they accelerate towards the Earth, the Earth’s surface curves away at the same angular rate. The distances between them and Earth’s surface remain constant.)
- How do you create "artificial gravity"?
Students' questions on Gravitation
Performance of Understanding - Work, Energy, Power
Description of assignment is found here. Please hand up by 15/4/13 noon.
Links to videos in the assignment:
5/4/13 - 9/4/13
Question - Work, Energy, PowerA 5.0 kg mass is carefully attached to the end of an unstretched vertical spring. The mass is carefully lowered until it reaches its equilibrium position. At this position the spring stretches by 4.0 mm. Assume that the mass of the spring is negligible.
- Determine the spring constant of the spring.
- Calculate the gain in elastic potential energy of the spring.
- Calculate the loss in the gravitational potential energy of the mass.
- Account for the difference in the previous two energies calculated.
1. Starting from equilibrium point, obtained spring constant = 12000 N/m
2. Ee = 0.5*k*x^2 = 98 mJ (2s.f)
3. Eg = m*g*h = 200 mJ (2s.f) [Note that the energy in part 2 is half of part 3 before rounding]
4. This question usually posed the largest problem to student because
- lack of understanding on the interplay of forces to bring the mass "carefully" to equilibrium
- assumption that the loss in gravitational potential energy (GPE) must be converted to either kinetic energy (KE) or elastic potential energy (EPE) according to energy conservation. Any difference is usually attributed to energy lost by friction/drag/heat/etc.
- By "carefully" lowering the mass, the mass is being moved with no resultant force (thought experiment) over infinite time to its equilibrium position, ie, no increase in kinetic energy
- As the spring extend, the force on the mass due to the spring is increasing but smaller than the gravitational force until the equilibrium point
- The force exerted by the hand is required to achieve the above condition (see below). The absence of the force will mean that the mass will oscillate about the equilibrium point instead of coming to rest.
- Since the displacement of the mass is in opposite direction to the applied force by the hand, negative work is done by the hand
- Student must know that negative work done on a system (by the hand in this question) reduces the mechanical energy of the system
- The rectangular area bounded by the gravitational force is the change in GPE which is larger than the energy stored in the spring (red shaded triangle). When the force applied by the hand is absent, the difference in the energy becomes the KE of the mass, ie, oscillation.
- The negative work done by the force by the hand on the mass removes this excess energy so that the KE of the system remains at zero