How much the gas has increased the speed of the plug?

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In summary: B]In summary, the cannon shoots a plug which, according to the equation Vplug=dπl, has a volume of 7.065 cm3.
  • #1
kaspis245
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Homework Statement


The cannon is made from V=30ml test tube completely closed with a plug (diameter d=1,5cm; length l=3cm; mass m=5g). Before closing the test tube, V'=1ml of water is poured into it. Room temperature is 20oC , pressure p=105 Pa , relative humidity is σ=20%. When the temperature in the test tube becomes t'=40oC the plug is shot. I need to find how much the escaping gas has increased the speed of the plug after it had been shot.

I know that the initial speed with which the plug starts to move is v=12.134m/s.

image.jpg


Homework Equations


Ideal gas laws.

The Attempt at a Solution


I know that:

Vplug=dπl=14.13 cm3
Vfree space=30ml-14.13ml=15.87ml
t/Vfree space=t'/V

What now?[/B]
 
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  • #2
kaspis245 said:

Homework Statement


The cannon is made from V=30ml test tube completely closed with a plug (diameter d=1,5cm; length l=3cm; mass m=5g). Before closing the test tube, V'=1ml of water is poured into it. Room temperature is 20oC , pressure p=105 Pa , relative humidity is σ=20%. When the temperature in the test tube becomes t'=40oC the plug is shot. I need to find how much the escaping gas has increased the speed of the plug after it had been shot.

I know that the initial speed with which the plug starts to move is v=12.134m/s.

Homework Equations


Ideal gas laws.

The Attempt at a Solution


I know that:

Vplug=dπl=14.13 cm3
Vfree space=30ml-14.13ml=15.87ml
t/Vfree space=t'/V

What now?[/B]
Where did you get the formula Vplug = dπl ?
 
  • #3
V=Ssurface*length

V=2πr*l=dπl
 
  • #4
kaspis245 said:
V=Ssurface*length

V=2πr*l=dπl
That's not the formula for the volume of a cylindrical plug. In general, surface area × length ≠ volume :frown:
 
  • #5
SteamKing said:
That's not the formula for the volume of a cylindrical plug. In general, surface area × length ≠ volume :frown:
I'm not sure what Ssurface is intended to mean, but what kaspis has actually done is circumference x length.
 
  • #6
haruspex said:
I'm not sure what Ssurface is intended to mean, but what kaspis has actually done is circumference x length.
Whatever. It's not a volume.
 
  • #7
Vplug=(d/2)2π=7.065cm3
Vfree space=30ml-7.065ml=22.935cm3
Ok?
 
  • #8
  • #9
kaspis245 said:
Vplug=(d/2)2π=7.065cm3
Vfree space=30ml-7.065ml=22.935cm3
Ok?
Notice how you squared a distance but showed the units as cm cubed. That should be a clue that your formula is wrong..
 
  • #10
Vplug=21.195cm3
Vfree space=8.805ml
 
  • #11
kaspis245 said:
Vplug=21.195cm3
Vfree space=8.805ml
No, this is not correct.

The diameter of the plug = 1.5 cm x length = 3 cm.
The capacity of the entire test tube is only 30 ml. According to your calculations, it is taken up mostly by the plug, which is wildly improbable.

In the calculation you made in Post #7, you forgot to divide d by 2 when doing the arithmetic. :oops:
 
  • #12
Vplug=5.3ml
Vfree space=24.7ml
 
  • #13
kaspis245 said:
Vplug=5.3ml
Vfree space=24.7ml
That's the correct volume for the plug. :smile:
 
  • #14
What now?
 

FAQ: How much the gas has increased the speed of the plug?

How is the speed of a plug affected by gas?

The speed of a plug is affected by gas through the process of combustion. When fuel is ignited by a spark, it creates an explosion that pushes the piston down and creates power. This power is then transferred to the wheels of a vehicle, increasing its speed.

What factors determine the amount of gas needed to increase the speed of a plug?

The amount of gas needed to increase the speed of a plug depends on various factors such as the type and quality of the fuel, the size and efficiency of the engine, and the driving conditions. Other factors that may affect the gas consumption include the weight of the vehicle, the speed and acceleration rate, and the maintenance of the engine.

Can using a higher octane gas increase the speed of a plug?

Using a higher octane gas does not directly increase the speed of a plug. However, it can improve engine performance and efficiency, which can indirectly contribute to an increase in speed. High octane gas is designed for high-performance engines and can withstand higher compression ratios, providing more power to the engine.

Does the gas mileage affect the speed of a plug?

Gas mileage, or the distance a vehicle can travel per gallon of gas, does not have a direct impact on the speed of a plug. However, a vehicle with better gas mileage can cover more distance with the same amount of fuel, allowing it to travel at a higher speed for a longer period of time.

How does the type of gas used affect the speed of a plug?

The type of gas used can affect the speed of a plug in terms of its octane rating and the quality of the fuel. Higher octane gas and better quality fuel can provide more power and efficiency to the engine, resulting in an increase in speed. Using lower quality fuel or the wrong type of gas for a specific engine can negatively impact its performance and speed.

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