Introduction to Mechanics

R_{max} = P + Q

R_{min} = P - Q

If two forces acting at a point of a rigid body are represented by two sides of a triangle, their resultant is represented by the third side taken in the opposite order.

<p>( \frac{P}{\sin \gamma} = \frac{Q}{\sin \alpha} = \frac{R}{\sin \beta} )</p> Signup and view all the answers

<p>It involves replacing a single force F acting on a body with two or more forces that have the same effect as F.</p> Signup and view all the answers

<p>Rectangular components are the components of force that are perpendicular to each other.</p> Signup and view all the answers

<p>( R_X = \sum F_X ) and ( R_Y = \sum F_Y )</p> Signup and view all the answers

<p>The angle influences the calculation of both the maximum and minimum resultant values.</p> Signup and view all the answers

<p>Statics focuses on the study of forces and conditions of equilibrium of bodies at rest or moving with zero acceleration.</p> Signup and view all the answers

<p>Dynamics studies the motion of rigid bodies and the forces causing that motion, while statics examines bodies at rest or in constant velocity.</p> Signup and view all the answers

<p>A particle is a body whose dimensions can be neglected when studying its motion or equilibrium.</p> Signup and view all the answers

<p>Newton's First Law implies that a body remains in its state of rest or uniform motion unless acted upon by an external force.</p> Signup and view all the answers

<p>Newton's Second Law states that the acceleration of a particle is proportional to the impressed force, expressed as F = ma.</p> Signup and view all the answers

<p>A rigid body is assumed to have no deformation under applied forces, contrasting with bodies that may change shape.</p> Signup and view all the answers

<p>Continuum refers to a model of matter where it is treated as a continuous mass distribution without voids or gaps.</p> Signup and view all the answers

<p>Force is defined as any action that changes a body’s state of rest or uniform motion and is a vector quantity.</p> Signup and view all the answers

<p>The resultant R is given by the formula $R = \sqrt{R_X^2 + R_Y^2}$.</p> Signup and view all the answers

<p>The resultant lies in the second quadrant.</p> Signup and view all the answers

<p>The direction is given by $\alpha = \tan^{-1}\left(\frac{R_Y}{R_X}\right)$.</p> Signup and view all the answers

<p>The resultant lies in the fourth quadrant.</p> Signup and view all the answers

<p>The angle is calculated using $\alpha = \tan^{-1}\left(\frac{R_Y}{R_X}\right)$.</p> Signup and view all the answers

<p>The magnitude can be found using $R = \sqrt{R_X^2 + R_Y^2}$ where R_X and R_Y are the components from the forces.</p> Signup and view all the answers

<p>The angle will be in the third quadrant, indicating a heading towards the negative X and Y directions.</p> Signup and view all the answers

<p>The magnitude is $R = 155.8 \text{ N}$, and the direction is $\alpha = 76.6°$.</p> Signup and view all the answers

<p>Coplanar forces are forces that lie in the same plane, while non-coplanar forces are those that do not lie in the same plane.</p> Signup and view all the answers

<p>Concurrent forces are forces whose lines of action intersect at a common point; for example, two forces acting at a junction in a structure.</p> Signup and view all the answers

<p>Collinear forces are forces whose lines of action lie on the same line, meaning they can be in the same or opposite directions.</p> Signup and view all the answers

<p>Parallel forces are forces that have lines of action that are parallel; like parallel forces act in the same direction, while unlike parallel forces act in opposite directions.</p> Signup and view all the answers

<p>Non-concurrent forces do not intersect at a common point, making their analysis more complex compared to concurrent forces.</p> Signup and view all the answers

<p>Combined force systems consist of multiple forces acting together; an example of a non-concurrent force system is four forces that do not intersect at a single point.</p> Signup and view all the answers

<p>Non-coplanar forces are forces that do not lie in the same plane and are significant in three-dimensional space analysis, such as in engineering applications.</p> Signup and view all the answers

<p>The types of parallel forces are like parallel forces, which act in the same direction, and unlike parallel forces, which act in opposite directions.</p> Signup and view all the answers

<p>They are forces whose lines of action intersect at a common point and lie in the same plane.</p> Signup and view all the answers

<p>They are forces that lie in the same plane but do not intersect at a common point, such as forces acting on a ladder resting against a wall.</p> Signup and view all the answers

<p>Coplanar parallel forces are those whose lines of action are parallel and lie in the same plane, like vertical forces acting on a beam.</p> Signup and view all the answers

<p>Non-coplanar concurrent forces do not lie in the same plane but intersect at a common point, such as forces acting on a tripod.</p> Signup and view all the answers

<p>They are forces that do not lie in the same plane and do not intersect, such as the forces acting on a moving bus.</p> Signup and view all the answers

<p>Coplanar collinear forces have their lines of action in the same line and plane, which differs from non-collinear systems.</p> Signup and view all the answers

<p>These forces are parallel but do not lie in the same plane, like the weight of benches, impacting the structure's stability.</p> Signup and view all the answers

<p>Forces acting at a hinge point of a door are an example of coplanar concurrent forces, as they determine how the door swings.</p> Signup and view all the answers