Problem 1:
As a new manufacturing process, a large LX-10 charge will be used to shock harden finished metallic sprockets that should be so superior to other sprockets that this product alone should put that Cogswell Cogs (SSS inc's main competitor) right out of business. Cosmo wants to use Palladium for the cogs so that they will have superior rotational momentum in zero gravity.
a) Calculate the interface pressure at the LX-10 / Palladium interface?
Problem 2:
The kid who lives down the hall, Elroy, is working on a science fair project to stun Martian cockroaches into submission with blast overpressure. He wants to use a brass cylinder, launched from a gas gun, to impact a cylinder of Comp B explosive at 1.0 km/s. Elroy needs your help to figure out if this is enough of an impact to initiate the explosive. Elroy has already calculated that the result of the impact will be a pressure of 5.95 GPa and a particle velocity of 0.823 km/s.
a) How long in time must the pressure pulse be to allow for a detonation to occur?
b) What is the minimum distance that the shock must traverse to allow for a detonation to occur?
Problem 3:
Cosmo wants to be known as the making the best Sprockets in the universe. He has an idea that he can forge Molybdenum sprockets by extreme impact using a simultaneous double impact by two rocket sleds with 304SS impact dies. But to do this you need to guarantee that the internal stress of the material where the two shock waves collide achieves a minimum of 100 GPa.
Ideally the velocity of the rockets would be identical, but the surplus solid propellant rocket engines that Cosmo acquired are known to have a tolerance in thrust. For your first shot, the right going rocket sled is travels at 1.75 km/s (u1), impacting the Molybdenum forge material, creating a right going shock wave of 47.141 GPa, the particle velocity at the impact is 0.762 (to the right). Conversely, the left going rocket impacts the Molybdenum material going 1.35 km/s (u2) generating a shock pulse of 34.670 GPa with a particle velocity of 0.582 (to the left).
a) What will be the resulting pressure when the two shock waves collide WITHIN the Molybdenum material?
b) What is the magnitude and direction of the particle velocity AFTER the shock waves collide?
c) Will this technique satisfy the design requirement?
Problem 4:
To make sure that you don't break your really expensive drop forget machine, you must determine the shock pressure on the ANVIL of a large machine that forges copper couplers for the Multi-Generational space station. You know that when the high velocity (1.8 km/s) Platinum hammer impacts the copper blank a 60.198 GPa shock (with an initial particle velocity of 1.183 km/s) is generated in the copper. That shock will travel though the copper coupler and meet the Uranium anvil in a perfectly flat interface. Assume a long square shock pulse.
a) What is the pressure that is transmitted to the Uranium anvil from the copper forging?
b) What will the reflected pressure back into the copper forging be after encountering the anvil?
c) What is the shock velocity in the Uranium material after the shock has reached the anvil?
Problem 5:
One evening when you get home from a long 3 hour day at the office, you find your dog Astro playing with Rosie-Roomba the vacuuming robot. Astro did something to make Rosie go haywire causing Rosie to fire her hyper-sonic retro-rocket, propelling her into your new quartz light bed, shattering it into a million pieces (you should have bought the Temperpedic).
You wonder how hard the impact was to cause such damage. You decide to recreate the impact, and with the help of a VISAR velocity measurement system (that you made up from a laser pointer and a bunch of optics that you have lying around the apartment).
You guess that the impact created a long square shock that travels into the quartz material. The shock encounters a free surface across from the impact location, where you measure the particle velocity to be 1.0 km/s? You can ignore the actual 3D geometry of the sculpture and consider the problem to be one-dimensional.
a) Assuming no degradation as the shock transits the quartz, what is the pressure induced in the Quartz material by Rosie running into the end (ie...before it encounters the free surface)?
Extra Credit
As a favor to Cosmo, you volunteer to conduct an accident investigation where a rogue spacecraft has crashed into Cosmo's side electronics business. You need to determine how fast the spacecraft was going at impact to give to the ever present team of lawyers looking for someone to sue.
As luck would have it, the spacecraft impacted an instrumented Zirconium rod, allowing you to calculate the shock velocity down the rod. The spacecraft is made of 2024 Aluminum.
The zirconium rod had two time of arrival detectors (TOAD), separated by 10.0 cm letting you know when the shock pulse arrived after the impact. The first TOAD registers at 7.6 μs, and the second toad registers at 31.0 μs. You assume a one dimensional impact, and a long square shock pulse.
a) What was the impact velocity of the spacecraft at impact?