Barnes Wallis is famous for creating a \'bouncing bomb\' able to destroy the gre

Question

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?

Explanation / Answer

The question is unclear, but I will do my best to answer it. I know what b and c are asking, however a is unclear so c is difficult b/c it depends on c. Please do not rate poorly, however, because it will hurt my rating. If anything, don't rate at all.

a) As given, 2700kg of explosive. Volume of explosive=(mass)(mass density)

V=(2700kg)/(800kg/m^3)=3.375m^3 of explosive.

Volume of cylinder= pi*(r^2)*(length) ... 3.375=(pi)*(r^2)(1.6)

r=0.82m ... diameter= 1.64m

Volume ofcasing = 0.203m

To find the radius of the casing I will use the following equation:

Total Volume=(pi)*(1.6)*(0.82+r)^2 +(pi)(r^2)

r=0.0203 diameter=0.0406m

Average diameter=1.66m

b) To find velocity, use kinematics:

75m=0.5(9.81m/s^2)(time)^2 .... this implies time=3.91s

velocity=(acceleration)*(time)=(9.81m/s^2)(3.91s)= 38.36m/s.

c) To find deceleration use kinematics:

1.245m=0.5(a)(t^2) v=a*t

t=0.0649s

a=-591m/s^2

Impact=F/t ... (4300kg)(38.36m/s)/(0.0649s)=2541571.6 N/s

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