Currently Surveying a Hypergiant Star - Impulse Engine - Engineering Assignment Help

Assignment Task :

Question 1.
Assume you are the chief engineer onboard a starship of mass m1, which is currently surveying a hypergiant star of mass m2 and radius r. The starship has an impulse engine capable of attaining a top speed of 10,000 km/s.

(b) The ship’s impulse engine is damaged by a solar flare and can now only attain a top speed of 200 km/s. The captain wants to jettison the cargo hold, which will reduce
the mass of the starship by 10%, but without giving the jettisoned mass an initial velocity. Referring to the equation you used in part (a), explain if this will help your
starship escape the gravitational field of the star?

(c) You advised the captain to instead jettison the cargo with an initial velocity away from the starship and towards the star. What is the minimal initial velocity of the jettisoned cargo, if this is to help the ship to escape the star’s gravitational field at the top speed of the damaged impulse engine? 

(d) What is the total mechanical energy (kinetic and potential) of the starship at this orbital height? Remember the mass of the ship is now reduced by 10% from m1. [Hint:
universal gravitational potential energy is negative]

 
(e) What is the acceleration due to gravity of the star that is experienced by the starship at this orbital height?

Question 2.
A stunt rider goes around a cylindrical wall as shown in figure 2. The combined mass of rider and motorbike is m, coefficient of kinetic friction between the wheels and the wall is μk.

(b) The stunt rider has recently put on weight, and he thinks he need to go slightly faster than the previous minimum speed in order to not fall from the vertical wall. Is he right? Explain why or why not.

(c) When performing the stunt at the minimum speed stated in part (a), what is the total kinetic energy for one of his wheels? Assume that the wheel is a solid disk with a
radius of 0.18 m.

(d) What is the angular momentum of the wheel?

(e) He switched to a wheel with 0.2 m radius now. Does the kinetic energy and the angular momentum change? If yes, what are the values? If not, explain why not.

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