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RslM
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Hello, could someone please let me know if I have worked this problem out correctly, or if I need to try again? Thank you.
A 40.0 g projectile is launched by the expansion of hot gas in an arrangement showing in Figure P12.4a (attached file). The cross-sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 32 cm. As the gas expands, the pressure varies as shown in Figure P12.4b. The values for the initial pressure and volume are Pi = 11 x 105 Pa and Vi = 8.0 cm3 while the final values are Pf = 1.0 x 105 Pa and Vf = 40.0 cm3. Friction between the projectile and the launch tube is negligible.
A) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube?
B) If instead the projectile is launched into air at a pressure of 1.0 x 105 Pa, what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube?
I chose to use:
Work = the area under a curve
KE = 1/2mV2
Area under the curve:
Pi = 11 x 105 Pa
Pf = 1.0 x 105 Pa
Vi = 8.0 cm3
Vf = 40.0 cm3
ΔP = 1.0 x 105 Pa - 11 x 105 Pa = -10 x 105 Pa
ΔV = 40 cm3 - 8.0 cm3 = 32 cm3
= 3.2 x 10-5 m3
Area of triangle under curve = (1/2)(-10 x 105 Pa)(3.2 x 10-5 m3) = -16 J
Area of rectangle under curve = (-1.0 x 105 Pa)(3.2 x 10-5 m3) = -32 J
W = -32 J + (-16 J) = -48 J
KE = 1/2mv2
v = √(2KE/m)
KE = 48 J
m = 0.040 kg
V = √((2(48J))/0.040 kg) = 48 m/s
B) W = (-1.0 x 105 Pa)(3.2 x 10-5 m3) = -32 J
-32 J/-48 J = 2/3
2/3 of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube.
Homework Statement
A 40.0 g projectile is launched by the expansion of hot gas in an arrangement showing in Figure P12.4a (attached file). The cross-sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 32 cm. As the gas expands, the pressure varies as shown in Figure P12.4b. The values for the initial pressure and volume are Pi = 11 x 105 Pa and Vi = 8.0 cm3 while the final values are Pf = 1.0 x 105 Pa and Vf = 40.0 cm3. Friction between the projectile and the launch tube is negligible.
A) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube?
B) If instead the projectile is launched into air at a pressure of 1.0 x 105 Pa, what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube?
Homework Equations
I chose to use:
Work = the area under a curve
KE = 1/2mV2
The Attempt at a Solution
Area under the curve:
Pi = 11 x 105 Pa
Pf = 1.0 x 105 Pa
Vi = 8.0 cm3
Vf = 40.0 cm3
ΔP = 1.0 x 105 Pa - 11 x 105 Pa = -10 x 105 Pa
ΔV = 40 cm3 - 8.0 cm3 = 32 cm3
= 3.2 x 10-5 m3
Area of triangle under curve = (1/2)(-10 x 105 Pa)(3.2 x 10-5 m3) = -16 J
Area of rectangle under curve = (-1.0 x 105 Pa)(3.2 x 10-5 m3) = -32 J
W = -32 J + (-16 J) = -48 J
KE = 1/2mv2
v = √(2KE/m)
KE = 48 J
m = 0.040 kg
V = √((2(48J))/0.040 kg) = 48 m/s
B) W = (-1.0 x 105 Pa)(3.2 x 10-5 m3) = -32 J
-32 J/-48 J = 2/3
2/3 of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube.
