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kozerog [31]
3 years ago
11

The typical area of a commercial airplane's passenger window is 80.0 in^2 . At an altitude of 3.00 × 104 ft above the sea level,

the atmospheric pressure is 0.350 atm. Determine the net force on the passenger window during flight at that altitude for both the English Engineering (EE) and SI unit systems. Use appropriate units and unit conversions in all steps of your calculations.
Engineering
1 answer:
nikdorinn [45]3 years ago
3 0

Answer:

The force over the plane windows are 764 lbf in the EE unit system and 3398 N in the international unit system.

Explanation:

The net force over the window is calculated by multiplying the difference in pressure by the area of the window:

F = Δp*A

The pressure inside the plane is around 1 atm, hence the difference in pressure is:

Δp = 1atm - 0.35 atm = 0.65 atm

Expressing in the EE unit system:

Δp = 0.65 atm * 14.69 lbf/in^2 = 9.55 lbf/in^2

Replacing in the force:

F = 9.55 lbf/in^2 * 80 in^2  = 764 lbf

For the international unit system, we re-calculate the window's area and the difference in pressure:

A = 80 in^2 * (0.0254 m/in)^2 = 0.0516 m^2

Δp =  0.65 atm * 101325 Pa  = 65861 Pa  = 65861 N/m^2

Replacing in the force:

F = 65861 N/m^2  *0.0516 m^2  = 3398 N

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c. 96.676 sq. Inches and 0.671 sq. Feet

Explanation:

From the list of the given option, we are told to chose the correct area in sq. inches that correspond to sq. Feet.

If we recall from the knowledge of our conversion  table that,

1 sq feet = 144 sq inches

Then, let's confirm if the option were true.

a.  966.76 sq. Inches and 8.056 sq. Feet

Assuming

if 1 sq feet = 8.056

in sq inches, we have ( 8.056 × 144 ) sq inches

= 1160.064 sq. inches

So, 1160.064 sq. inches is equal to 8.056 sq. Feet. Then option 1 is wrong

b. 96.676 sq. Inches and 8.056 sq. Feet

if 1 sq feet = 8.056

in sq inches, we have ( 8.056 × 144 ) sq inches

= 1160.064 sq. inches

So, 1160.064 sq. inches is equal to 8.056 sq. Feet. Then option 2 is wrong/

c. 96.676 sq. Inches and 0.671 sq. Feet

if 1 sq feet = 0.671

in sq inches, we have ( 0.671 × 144 ) sq inches

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While playing a game of catch on the quadrangle, you throw a ball at an initial velocity of 17.6 m/s (approximately 39.4 mi/hr),
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Answer:

a) The y-component of velocity just before the ball hits the ground is -14.860 meters per second.

b) The ball is in the air during approximately 2.890 seconds.

c) The horizontal distance covered by the ball is 32.695 meters.

d) The magnitude of the velocity of the ball just before it hits the ground is approximately 18.676 meters per second.

e) The angle of the total velocity of the ball just before it hits the ground is approximately 52.717º below the horizontal.

Explanation:

a) The ball experiments a parabolic motion, which is a combination of horizontal motion at constant velocity and vertical motion at constant acceleration. First, we calculate the time taken by the ball to hit the ground:

y = y_{o} + (v_{o}\cdot \sin \theta) \cdot t+\frac{1}{2}\cdot g\cdot t^{2} (1)

Where:

y_{o}, y - Initial and final vertical position, measured in meters.

v_{o} - Initial speed, measured in meters per second.

\theta - Launch angle, measured in sexagesimal degrees.

g - Gravitational acceleration, measured in meters per square second.

t - Time, measured in seconds.

If we know that y_{o} = 2\,m, y = 0\,m, v_{o} = 17.6\,\frac{m}{s}, \theta = 50^{\circ} and g = -9.807\,\frac{m}{s^{2}}, then the time taken by the ball is:

-4.904\cdot t^{2}+13.482\cdot t +2 = 0 (2)

This second order polynomial can be solved by Quadratic Formula:

t_{1} \approx 2.890\,s and t_{2} \approx -0.141\,s

Only the first root offers a solution that is physically reasonable. That is, t \approx 2.890\,s.

The vertical velocity of the ball is calculated by this expression:

v_{y} = v_{o}\cdot \sin \theta +g\cdot t (3)

Where:

v_{o,y}, v_{y} - Initial and final vertical velocity, measured in meters per second.

If we know that v_{o} = 17.6\,\frac{m}{s}, \theta = 50^{\circ}, g = -9.807\,\frac{m}{s^{2}} and t \approx 2.890\,s, then the final vertical velocity is:

v_{y} = -14.860\,\frac{m}{s}

The y-component of velocity just before the ball hits the ground is -14.860 meters per second.

b) From a) we understand that ball is in the air during approximately 2.890 seconds.

c) The horizontal distance covered by the ball (x) is determined by the following expression:

x = (v_{o}\cdot \cos \theta)\cdot t (4)

If we know that v_{o} = 17.6\,\frac{m}{s}, \theta = 50^{\circ} and t \approx 2.890\,s, then the distance covered by the ball is:

x = 32.695\,m

The horizontal distance covered by the ball is 32.695 meters.

d) The magnitude of the velocity of the ball just before hitting the ground (v), measured in meters per second, is determined by the following Pythagorean identity:

v = \sqrt{(v_{o}\cdot \cos \theta )^{2}+v_{y}^{2}} (5)

If we know that v_{o} = 17.6\,\frac{m}{s}, \theta = 50^{\circ} and v_{y} = -14.860\,\frac{m}{s}, then the magnitude of the velocity of the ball is:

v \approx 18.676\,\frac{m}{s}.

The magnitude of the velocity of the ball just before it hits the ground is approximately 18.676 meters per second.

e) The angle of the total velocity of the ball just before it hits the ground is defined by the following trigonometric relationship:

\tan \theta = \frac{v_{y}}{v_{o}\cdot \cos \theta_{o}}

If we know that v_{o} = 17.6\,\frac{m}{s}, \theta_{o} = 50^{\circ} and v_{y} = -14.860\,\frac{m}{s}, the angle of the total velocity of the ball just before hitting the ground is:

\theta \approx -52.717^{\circ}

The angle of the total velocity of the ball just before it hits the ground is approximately 52.717º below the horizontal.

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3 years ago
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