Script Name: prob1 Script Variables: parallel force (double) - The parallel comp

Question

Script Name: prob1 Script Variables: parallel force (double) - The parallel component of the force applied to the rope. WorkOnSled (double) - the work done on the sled by pulling on the rope. Problem Statement: Write a script named "prob1" that will calculate the parallel component of the force applied to a hand sled and the work done on the sled. The sled is being pulled by a rope that forms a 35 degree angle with the ground. The force applied to the rope is 45 N. The sled is pulled a horizontal distance of 20 m. [Refer to the following website if you're stuck: http://www.physics247.com/physics-homework-help/work-power.php] The script should compute the following: What is the parallel component of the force on the sled? Store this value in a variable called "parallel_force". Use "paralle_force" to calculate the work done on the sled. Store this value in the variable "WorkOnSled". Note: the MATLAB functions sin() and cos() take angles in radians. You will need to convert the given angle to radians before using it in the sin() or cos() function.

Explanation / Answer

function sol = prob2 % This problem considers a cardiovascular model, which can be found in % 'Modelling of the Baroflex-Feedback Mechanism With Time-Delay' by J.T. % Ottesen in J. Math. Biol., 36 (1997), 41-63. (This is reference % 14 of the tutorial). % Copyright 2004, The MathWorks, Inc. % Problem parameters, visible in nested functions. p.ca = 1.55; p.cv = 519; p.R = 1.05; p.r = 0.068; p.Vstr = 67.9; p.alpha0 = 93; p.alphas = 93; p.alphap = 93; p.alphaH = 0.84; p.beta0 = 7; p.betas = 7; p.betap = 7; p.betaH = 1.17; p.gammaH = 0; P0 = 93; Paval = P0; Pvval = (1 / (1 + p.R/p.r)) * P0; Hval = (1 / (p.R * p.Vstr)) * (1 / (1 + p.r/p.R)) * P0; history = [Paval; Pvval; Hval]; for tau = [1 7.5] sol = dde23(@prob2f,tau,history,[0, 350]); figure plot(sol.x,sol.y(1,:)) title(['Problem 2. Baroflex Feedback Mechanism with' ... ' au = ',num2str(tau),'.']) xlabel('time t') ylabel('P_a(t)') axis([0 350 82 96]) end %----------------------------------------------------------------------- % Nested function % function yp = prob2f(t,y,Z) %PROB2F The derivative function for Problem 2 of the DDE Tutorial. % Local variables are used to express the equations in terms % of the physical quantities of the model. ylag = Z(:,1); Patau = ylag(1); Paoft = y(1); Pvoft = y(2); Hoft = y(3); dPadt = - (1 / (p.ca * p.R)) * Paoft + (1/(p.ca * p.R)) * Pvoft ... + (1/p.ca) * p.Vstr * Hoft; dPvdt = (1 / (p.cv * p.R)) * Paoft ... - ( 1 / (p.cv * p.R) + 1 / (p.cv * p.r) ) * Pvoft; Ts = 1 / ( 1 + (Patau / p.alphas)^p.betas ); Tp = 1 / ( 1 + (p.alphap / Paoft)^p.betap ); dHdt = (p.alphaH * Ts) / (1 + p.gammaH * Tp) - p.betaH * Tp; yp = [ dPadt; dPvdt; dHdt ]; end % prob2f %----------------------------------------------------------------------- end % prob2

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