Dynamics Chapter 2 Problem 2.14 | Georgia Southern University

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

2024
Views:

192

Pages:

2
Author:

Jalen W.

Problem 2.14: A hockey puck (mass \( m \)) in an ideally smooth ice field (no friction) is shot with speed \( v_0 \) into the half-circular part of the boards and slides along the boards. At the end of the curved part, the speed is measured to be \( 0.6 \, v_0 \). Determine the friction coefficient \( \mu \) of the boards. matlab % Given data v0 = 10; % initial speed of the puck final_speed = 0.6 * v0; % final speed of the puck radius_of_curvature = 2; % radius of curvature of the half-circular part of the boards % Conservation of mechanical energy: Initial kinetic energy = Final kinetic energy % 0.5 * m * v0^2 = 0.5 * m * final_speed^2 % m cancels out, solving for final_speed % v0^2 = final_speed^2 % v0 = final_speed % Initial kinetic energy initial_ke = 0.5 * v0^2; % Final kinetic energy final_ke = 0.5 * final_speed^2; % Work done by friction = Change in mechanical energy % Work = friction_force * distance = friction_coefficient * normal_force * distance % Change in mechanical energy = final_ke - initial_ke % distance = 2 * pi * radius_of_curvature (half-circular path) % normal_force = m * g (weight of the puck) % friction_coefficient = (final_ke - initial_ke) / (m * g * distance) % Since m and g cancels out, we can simplify the equation % Constants g = 9.81; % acceleration due to gravity % Calculation distance = 2 * pi * radius_of_curvature; friction_coefficient = (final_ke - initial_ke) / (g * distance); disp(['Friction coefficient μ of the boards: ' num2str(friction_coefficient)]);