Dynamics Chapter 2 Problem 2.15 | Georgia Southern University - Edubirdie

University:
Georgia Southern University
Course:
ENGR 2232 | Dynamics of Rigid Bodies
Academic year:

2024
Views:

347

Pages:

2
Author:

Jalen W.

Problem 2.15: A car passes through a bend whose curvature increases proportionally to the covered distance. At time \( t_0 = 0 \), the car is at \( s_0 = 0 \) and has an initial speed \( v_0 \). At which speed, where, and when does the car 'skid off the bend' if: a) it moves with constant speed. b) it brakes with constant deceleration. MATLAB Code: % Constants A = 35; % m mu0 = 0.6; % coefficient of static friction a0 = 9.81 / 4; % g/4 m/s^2 v0 = 72 * 1000 / 3600; % initial speed in m/s % Calculate the curvature syms s rho s = A^2 / rho; % Velocity when the car moves with constant speed % v = sqrt(mu0 * g * rho) % v^2 / rho = mu0 * g % v^2 = mu0 * g * rho % v = sqrt(mu0 * g * A^2 / s) % We want to find v when the car skids off the bend, so let's set s = A v_constant_speed = sqrt(mu0 * 9.81 * A); % Time taken to cover distance A with constant speed t_constant_speed = A / v0; % Velocity when the car brakes with constant deceleration % v^2 = v0^2 - 2 * a0 * s % v = sqrt(v0^2 - 2 * a0 * A) v_braking = sqrt(v0^2 - 2 * a0 * A); % Time taken to brake t_braking = (v0 - v_braking) / a0; % Results fprintf('a) Velocity when moving with constant speed: %.2f m/s\n', v_constant_speed); fprintf(' Time taken to cover distance A: %.2f seconds\n', t_constant_speed); fprintf('b) Velocity when braking with constant deceleration: %.2f m/s\n', v_braking); fprintf(' Time taken to brake: %.2f seconds\n', t_braking);

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