1) Barnes Wallis is famous for creating a 'bouncing bomb' able to destroy the great dams of the Ruhr in Germany. The bomb was cylindrical and bounced along on the water. It was spinning such that as it bounced it slowed down and came to a stop at the dam. The bomb then sank along the dam wall where an internal pneumatic pistol ignited the charge causing the bomb to explode hard against the dam surface. Wallis discovered that he needed the mass of the bomb to be just 4.3 tonnes consisting of 2.7 tonnes of explosives. The density of steel casing was about 7900 kg m-3 and the density of the explosive is about 800 kg m-3. Calculate the average radius of the bomb if the length was fixed at 1.6 meters. The force of impact (average force) of such a bomb on water after falling from a height of 75 m is enormous. First, find the speed of impact, assuming that air resistance is negligible. Then calculate the average force of impact of the bomb if it initially sinks to a depth of 3/4 of its diameter.
i. Use the volume of a cylinder to calculate the size required to encase the explosive. Assume the thickness of the casing is the same at the ends as it is around the outside of the cylinder. You should et two equations one for the size of the inside explosive and another for the outside casing. Some of the variables, however, will be shared between the two equations.
ii. Find the velocity of the bomb when it hits the water.
iii. If you know it goes from this velocity to zero velocity, in a distance equal to 3/4 of its diameter, then what is the deceleration of the bomb and what is the average force of impact?
2) In order to purify salt water and convert it into drinking water it is usually required to first boil the water and then re-condense the evaporated water back into its liquid state. There are now 7 billion people on our planet and in the US we use 1383 gallons per-person per-day, while at the same time pollution and over population is seeing water shortages throughout the world. The UN recently stated "Fierce competition for fresh water may well become a source of conflict and wars in the future." If solar power (with an efficiency of 10%) was to be used to purify water and the average solar insolation is approximately 250 watts per square meter, how much land would be required to provide water for the world? Assume that we want to rest of the world to have the adequate access to water that we enjoy in the western world. Average temperature of water at the surface of the ocean is 17o C, the density of water is 1000 kg m-3 , and 1 US Gallon = 0.00378541178 Cubic Meters.
This is a simple problem solving exercise. You shouldn't have any problems solving this. Just make sure that your units match up!
3) Given that the diameter of the moon is 3,480 km, and using a meter stick or tape measure plus a 25¢ coin, estimate the distance, D, from the Earth to the Moon. Show calculations.