A simple gun can be made from a uniform cylinder of length Lo and radius n. One end of the cylinder is sealed with a movable plunger and the other end is plugged with a cylindrical cork bullet. The bullet is held in place by friction with the walls of the cylinder. Initially it is necessary to squeeze the bullet to get in to the cylinder in the first place. The bullet normally has a radius 'r that is slightly larger than the inside radius of the cylinder. The bullet has a length h<< Lo. The walls of the cylinder apply a pressure P to the cork bullet. When a pressure P is applied to the bullet along a given direction the bullets dimensions in that direction changes by Ax Ax such that , where y is the young's modulus of cork. The poison's ratio for =-- х y cork is zero such that we can assume that the compression along one direction does not cause expansion in any other direction. P, is the atmosphere pressure and u be the coefficient of friction between cork and the cylinder. The temperature of the gas (air) inside the cylinder is To. 15. The minimum pressure P, of the gas inside the cylinder required to slide the bullet out of the cylinder is 2 µhy(r –ro) 2hy(r-ro) B) 2hy (r-r) C) P + rro D) P +- 2 µhy(r-ro) A) rro rro rro 16. Assume that we launch the bullet by heating the gas in the cylinder without moving the plunger. The minimum temperature of the gas to launch the bullet is A) To(14 2lo(r-n) rm Po 2µhy(r-ro) B) To A) To| 1+ Po 2 µhy(r-n) rrm Po То D) 2hy (r-n) Po + C) Tо 1+ rro
A simple gun can be made from a uniform cylinder of length Lo and radius n. One end of the cylinder is sealed with a movable plunger and the other end is plugged with a cylindrical cork bullet. The bullet is held in place by friction with the walls of the cylinder. Initially it is necessary to squeeze the bullet to get in to the cylinder in the first place. The bullet normally has a radius 'r that is slightly larger than the inside radius of the cylinder. The bullet has a length h<< Lo. The walls of the cylinder apply a pressure P to the cork bullet. When a pressure P is applied to the bullet along a given direction the bullets dimensions in that direction changes by Ax Ax such that , where y is the young's modulus of cork. The poison's ratio for =-- х y cork is zero such that we can assume that the compression along one direction does not cause expansion in any other direction. P, is the atmosphere pressure and u be the coefficient of friction between cork and the cylinder. The temperature of the gas (air) inside the cylinder is To. 15. The minimum pressure P, of the gas inside the cylinder required to slide the bullet out of the cylinder is 2 µhy(r –ro) 2hy(r-ro) B) 2hy (r-r) C) P + rro D) P +- 2 µhy(r-ro) A) rro rro rro 16. Assume that we launch the bullet by heating the gas in the cylinder without moving the plunger. The minimum temperature of the gas to launch the bullet is A) To(14 2lo(r-n) rm Po 2µhy(r-ro) B) To A) To| 1+ Po 2 µhy(r-n) rrm Po То D) 2hy (r-n) Po + C) Tо 1+ rro
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Transcribed Image Text:A simple gun can be made from a uniform cylinder of length Lo and radius n.
One end of the cylinder is sealed with a movable plunger and the other end is
plugged with a cylindrical cork bullet.
The bullet is held in place by friction with the walls of the cylinder.
Initially it is necessary to squeeze the bullet to get in to the cylinder in the first
place. The bullet normally has a radius'r' that is slightly larger than the inside
radius of the cylinder. The bullet has a length h<< Lo. The walls of the cylinder
apply a pressure P to the cork bullet. When a pressure P is applied to the bullet
along a given direction the bullets dimensions in that direction changes by Ax
Ax
such that
, where y is the young's modulus of cork. The poison's ratio for
y
cork is zero such that we can assume that the compression along one direction
does not cause expansion in any other direction. Po is the atmosphere pressure
and u be the coefficient of friction between cork and the cylinder. The
temperature of the gas (air) inside the cylinder is To.
The minimum pressure P, of the gas inside the cylinder required to slide the bullet
out of the cylinder is
15.
2µhy(r-n)
B)
rro
2hy(r-ro)
2hy(r-n)
C) P +
2 µhy(r–ro)
D) Po +
A)
rro
rro
16.
Assume that we launch the bullet by heating the gas in the cylinder without
moving the plunger. The minimum temperature of the gas to launch the bullet is
2hy(r-ro)
rrm Po
2µthy(r -ro)
2 uhy(r–ro)
B) To
Po
A) To| 1+
2hy(r-)
To
D)
Po +
Po
C) To| 1+
rro Po
rro
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