(A) Identify how the gravitational potential energy changes as a shuttle takes off from the launch pad.
(b) Explain the consequences to the space craft and its occupants if the shuttle is undergoing re-entry, and the angle of re-entry is significantly greater (steeper) than optimal.
Increases
at first use mgh but as radius gets to be order of magnitude of earth radius you have to integrate using
F = integral of Gravitational constant*mshuttle*mearth/r^2 dr
which is constant * (1/rearth-1/rshuttleaboveearth)
If angle is steep, force of gravity becomes much bigger that mass times centripetal acceleration becuase V tangential is too small and body accelertates downward too fast.
(A) To identify how the gravitational potential energy changes as a shuttle takes off from the launch pad, we need to understand the concept of gravitational potential energy and the factors affecting it.
Gravitational potential energy refers to the energy an object possesses due to its position relative to a gravitational field. It is directly related to an object's height and mass. The formula for gravitational potential energy is given by:
PE = mgh
where PE is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance from the object to the reference point.
As the shuttle takes off from the launch pad, its height from the ground increases, resulting in a change in gravitational potential energy. Initially, the shuttle has a certain potential energy at the launch pad, but as it gains altitude, moving away from the Earth's surface, its gravitational potential energy increases. This is because the distance between the shuttle and the Earth's center (h) is increasing in the formula.
Therefore, as the shuttle takes off, its gravitational potential energy increases accordingly.
(b) If the angle of re-entry during a space shuttle's return is significantly greater (steeper) than optimal, it could have various consequences for both the spacecraft and its occupants.
1. Increased Heat: A steeper re-entry angle causes a higher rate of descent, increasing the atmospheric drag. This increased drag leads to higher temperatures due to the greater compression and friction experienced by the spacecraft. The excessive heat generated could potentially damage or even destroy the spacecraft.
2. Greater G-Forces: A steeper re-entry angle results in a higher rate of deceleration, subjecting the occupants to greater g-forces. This increased force can put significant stress on the crew, potentially leading to injuries or physical discomfort.
3. Limited Control: A steeper angle of re-entry makes it more challenging to control the spacecraft due to the increased forces acting upon it. Controlling the descent becomes more complicated, and the risk of destabilization or loss of control increases.
4. Increased Stress on Thermal Protection System: The thermal protection system (heat shield) of the spacecraft is designed to handle specific re-entry conditions within a specific range of angles. If the re-entry angle is steeper than optimal, the thermal protection system may be subjected to higher temperatures and stresses beyond its design limits, potentially compromising its efficiency and putting the occupants at risk.
In summary, a steeper re-entry angle than optimal can result in increased heat, higher g-forces, limited control, and additional stress on the thermal protection system, posing potential risks to both the spacecraft and its occupants.