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{
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"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 1: Classical Mechanics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1.10: Common_velocity_of_a_car_truck_system.sce"
]
},
{
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"source": [
"// Scilab Code Ex1.10: : Page-14 (2008)\n",
"clc; clear;\n",
"m1 = 1200; // Mass of the car, kg\n",
"m2 = 3600; // Mass of the truck, kg\n",
"u1 = 30; // Speed of the car, m/s\n",
"u2 = 20; // Speed of the truck, m/s\n",
"theta = 60; // Direction of motion of the truck w.r.t. that of car, degree\n",
"// As m1*u1 + m2*u2 = (m1 + m2)*v, solving for v along x and y directions\n",
"v_x = (m1*u1 + m2*u2*cosd(theta))/(m1 + m2); // Common speed along x-direction, m/s\n",
"u1 = 0; // The speed of the car after interlocking with the truck, m/s\n",
"v_y = (m1*u1 + m2*u2*sind(theta))/(m1 + m2); // Common speed along y-direction, m/s\n",
"v = sqrt(v_x^2 + v_y^2); // Common speed of the car-truck system, m/s\n",
"theta = atand(v_y/v_x); // Direction of common velocity w.r.t. that of car, degree\n",
"printf('\nThe common speed of the car-truck system = %4.1f m/s', v);\n",
"printf('\nThe direction of common velocity = %4.1f degree north of east', theta);\n",
"// Result \n",
"// The common speed of the car-truck system = 19.8 m/s"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1.11: Velocity_of_third_piece_of_the_exploded_object.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex1.11: Page-14 (2008)\n",
"clc; clear;\n",
"v1 = 20; // Velocity of first piece, m/s\n",
"v2 = 30; // Velocity of second piece, m/s\n",
"// From conservation of momentum, in x-direction \n",
"// m*v1*cosd(0)+m*v2*cosd(45)+m*v3*cosd(theta) = 0, solving for v3*cosd(theta)\n",
"v3_cos_theta = -(v1*cosd(0)+v2*cosd(45)); // x-component of v3 along theta, m/s\n",
"// From conservation of momentum, in y-direction \n",
"// m*v1*sind(0)-m*v2*sind(45)+m*v3*sind(theta) = 0, solving for v3*sind(theta)\n",
"v3_sin_theta = -(v1*sind(0)-v2*sind(45)); // y-component of v3 along theta, m/s\n",
"theta = atand(v3_sin_theta/v3_cos_theta); // Direction of velocity of third piece, degree\n",
"v3 = -(v1*cosd(0)+v2*cosd(45))/cosd(theta+180); // Velocity of third piece, m/s\n",
"printf('\nThe velocity of third piece is %4.1f m/s towards %d degree north of west', v3, ceil(theta+180));\n",
"// Result \n",
"// The velocity of third piece is 46.4 m/s towards 153 degree north of west "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1.5: Force_of_contact_between_two_masses.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex1.5: Page-11 (2008)\n",
"clc; clear;\n",
"m1 = 2; // Mass of first body, kg\n",
"m2 = 1; // Mass of second body, kg\n",
"F = 3; // The horizontal force applied to the mass m1, N\n",
"F_prime = m2/(m1 + m2)*F; // Force of contact between m1 and m2, N\n",
"printf('\nThe force of contact between m1 and m2 = %3.1f N', F_prime);\n",
"F_prime = m1/(m1 + m2)*F; // Force of contact when F is applied to m2, N\n",
"printf('\nThe force of contact when F is applied to m2 = %3.1f N', F_prime);\n",
"// Result \n",
"// The force of contact between m1 and m2 = 1.0 N\n",
"// The force of contact when F is applied to m2 = 2.0 N "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1.6: Direction_of_motion_of_a_ball_after_momentum_conservation_during_collision.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex1.6: Page-12 (2008)\n",
"clc; clear;\n",
"v = 1; // Let the speed of the ball B be unity, unit\n",
"v_prime = v/2; // Speed of the ball after the collision, unit\n",
"theta = atand(v_prime/v); // The direction of motion of the ball A after collision, degree\n",
"printf('\nThe direction of motion of the ball after collision = %2.0f degree', theta);\n",
"// Result \n",
"// The direction of motion of the ball after collision = 27 degree "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1.9: Angular_velocity_of_the_combination_of_two_wheels.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex1.9: Page-14 (2008)\n",
"clc; clear;\n",
"omega1 = 500; // Angular speed of rotating shaft, r.p.m.\n",
"omega2 = 0; // Initial angular speed of the second wheel, r.p.m.\n",
"I = 1; // For simplicity assume moment of ineria of the wheels to be unity\n",
"I1 = I, I2 = I; // Moment of inertia of wheels A and B, kg-Sq.m\n",
"// As I1*omega1 + I2*omega2 = (I1 + I2)*omega, solving for omega\n",
"omega = (I1*omega1 + I2*omega2)/(I1 + I2); // Angular speed of the combination of two wheels, r.p.m.\n",
"printf('\nThe angular speed of the combination of two wheels = %3.0f r.p.m.', omega);\n",
"// Result \n",
"// The angular speed of the combination of two wheels = 250 r.p.m. "
]
}
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