Reconsider Prob. 1-102 . Using EES (or other) software,...

Reconsider Prob. $1-102 .$ Using EES (or other) software, investigate the effect of the number of people carried in the balloon on acceleration. Plot the acceleration against the number of people, and discuss the results.

Key Concepts

Newton's Second Law

Newton's Second Law, which states that force equals mass times acceleration, is fundamental here. As the number of people in the balloon increases, the total mass increases, which, for a fixed net force, results in a decrease in acceleration. This principle is critical for understanding how additional mass influences the dynamics of any system.

Parametric Analysis

Parametric analysis involves evaluating how changes in a key parameter—in this case, the number of people—affect an output variable such as acceleration. By systematically varying the number of occupants and observing the resulting acceleration, one can determine the sensitivity and behavior of the system under different conditions.

Computational Simulation

Computational simulation utilizes tools like EES to model complex physical systems by solving the underlying equations numerically. It allows for the investigation of system behavior over a range of parameters, providing insights that might be difficult to obtain analytically. This is especially useful in problems like this, where the interplay between forces and mass needs detailed study.

Graphical Data Analysis

Graphical data analysis involves plotting variables such as acceleration against the number of people to visually interpret trends and patterns. This approach not only aids in confirming theoretical predictions but also helps in identifying any nonlinearities or unexpected behaviors in the system, making it a powerful tool in both research and practical applications.

Transcript

00:01 All right, so what we have is a hot air balloon of diameter 12 meters.

00:04 We know that the mass of each person on board the balloon is 85 kilograms each.

00:09 The density of air is given to us as 1 .16 kilograms per cubic meter.

00:13 We know the density of helium, which is being able, which is being used to fill up this hot air balloon, has a density that is 1 -7th, the density of air.

00:21 We're asked to vary the number of passengers from basically 1 to 10, and we're asked to find the net acceleration just when the balloon is released.

00:30 So the first thing we're going to do is go ahead and solve for the volume of a balloon.

00:35 We're going to assume that the balloon is a sphere.

00:37 Therefore, the volume of the balloon will be equal to four -thirds pi -r cubed.

00:43 This gives us a volume equal to 904 .8 cubic meters.

00:51 Next, what we can do is we can use the equation for the force of buoyancy and use the density of air in this volume to solve for the buoyancy force.

00:58 So we can say that fb, which is our buoyancy force, is equal to row of air times gravity times bb.

01:09 And this gives a total buoyancy force of 10 ,296 newons.

01:14 Next, what we need to do is calculate our total mass.

01:17 So what we can do is solve for first the mass of helium that's inside our balloon and say that mhe is equal to row h .e times the volume of the balloon.

01:28 Which gives us a total mass of helium equal to 149 .9 kilograms...

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