Vectors Engineering I Grayson HS

Vectors A scalar is a physical quantity that has only magnitude and no direction. – Length – Volume – Mass – Speed – Time Therefore: A 10kg mass.

Vectors A vector is an object defined by both magnitude and direction. – Example: Force = Mass * Acceleration Therefore: That 10 kg Mass * 9.8m/s 2 (acceleration due to gravity) =98 kg-m/s 2 (Newton) – Forces, Moments, Velocity, Displacement, and Acceleration.

Vectors Forces can be specified by magnitude, direction and point of application. Forces that are encountered in a mechanical system are either contact or body forces. Contact forces result from an actual physical contact between two bodies such as friction. Body forces are those resulting from remote action, such as gravitational force.

Vectors Forces that act on a body may be either: Concentrated Distributed

Vectors Forces are classified into categories based on a line of action, point of application or plane of action. Collinear Forces act along the same line of action. Concurrent forces pass through the same point in space. Coplanar forces lie in the same plane.

Vectors Resultant force: the net sum of the forces acting on a body. Expressing a force in terms of its components is referred to as the resolution of forces.

Vectors Translation is when a force is applied to a body it has the tendency of displacing the body in the direction of the line of action of the applied force. This may cause the body to rotate. The measure of the tendency of a force to cause the rotation of a body about a point is called moment. If the rotation is about an axis it is called torque. Torque is a moment that tends to twist a body about its longitudinal axis.

Vectors It is standard practice to label vectors with bold letters; A,B, C, etc. Vectors are drawn using a line that terminates on one end with an arrowhead. The direction of the arrow indicates the direction of the vector. The length of the vector should be representative of the magnitude.

Vectors Vectors must obey the parallelogram law or addition. Stated: two vectors A 1 and A 2 can be replaced by their equivalent A, which is the diagonal of the parallelogram formed by A 1 and A 2 and its two sides.

Vectors

Example: Two Soccer players kick a soccer ball at the same time. Player A kicks it with 100 N of force at 45 o from zero. Player B kicks it with 200 N of force at 90 o from zero. Where will it go? Draw diagram. A B

Vectors Parallelogram Law of Addition: A B

Vectors Use Trigonometry and Pythagorean Theorem to solve for angles and lengths. AUTOCAD to solve Vector Equations.

Vectors A third soccer player is introduced to the scenario. He is the goalie and kicks the ball with 400N of force at 270 o from zero. Now where does the soccer ball wind up. (Assume no friction.) Draw diagram. A B C

Vectors What do we do first??? Associative Law of Addition. States: If three or more vectors are added together the resultant is independent of how the individual vectors are grouped together. Or.. (A+B)+C = A+(B+C)

Vectors CAD and the Associative Law of Addition