* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 3. forces
Survey
Document related concepts
Newton's theorem of revolving orbits wikipedia , lookup
Frictional contact mechanics wikipedia , lookup
Hooke's law wikipedia , lookup
Virtual work wikipedia , lookup
Work (thermodynamics) wikipedia , lookup
Fictitious force wikipedia , lookup
Fundamental interaction wikipedia , lookup
Electromagnetism wikipedia , lookup
Centrifugal force wikipedia , lookup
Mass versus weight wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Centripetal force wikipedia , lookup
Transcript
3. FORCES 3.1 TYPES OF FORCES FORCE - vector quantity; action of one body to another; tends to move a body in the direction of its action. TERMINOLOGY LINE OF ACTION - the straight line collinear with the force vector - a particular set of forces Two-dimensional (coplanar) - the lines of action of the forces lie in a plane Three-dimensional - otherwise Concurrent - the lines of action of the forces intersect at a point Parallel - the lines of action of the forces are parallel SYSTEM OF FORCES EXTERNAL FORCE - exerted by a different object INTERNAL FORCE - exerted by another part of the same object BODY FORCE - acts on the volume of the object (e.g., gravitational force) SURFACE FORCE - acts on the surface of the object (e.g., contact forces) GRAVITATIONAL FORCE - the force exerted on an object by the earth’s gravity - acts toward the center of the earth through the center of mass of the body - the magnitude of an object’s gravitational force (weight) is related to its mass | W | mg g - the acceleration due to gravity at sea level g 9.81 m/s 2 in SI units g 32.2 ft/s 2 in U.S. Customary units - gravitational forces act at a distance (electromagnetic forces also), and the objects they act on are not necessarily in contact with the objects exerting forces CONTACT FORCES SURFACES - exerted on objects by contact with surfaces of other objects, by ropes, cables and springs - the contact force F can be resolved into a component N that is normal to the surface (normal force; always compressive), and a component f that is parallel to the surface (friction force; opposed to a motion) - smooth surfaces – the friction force can be neglected - rough surfaces – the friction force cannot be neglected - if the contact surfaces are curved, the normal and friction forces are perpendicular and parallel to the plane tangent to the surfaces at their point of contact ROPES AND CABLES - the force exerted by a cable or a rope is always a tension away from the body in the direction of the cable/rope - if the weight of the rope/cable can be neglected, the rope/cable can be considered as straight and the tension along its length as constant force; otherwise, the cable will sag and the tension will vary along its length (for now, we will assume that the weight of the rope/cable is negligible) SPRINGS - spring force is tensile if the spring is stretched and compressive if compressed (acts toward the unstretched/uncompressed position) - the magnitude of the spring force depends on the material it is made of, its design, and the change in length (if this change is not too large compared to the unstretched length, the force may be considered as a linear function of the change in length) | F | k | L L0 | k - spring constant, stiffness; depends on the material and design; it is the force required to deform the spring a unit distance - springs can be used to model situations in which forces depend on displacements (e.g., the force necessary to bend the steel beam) | F | k - if is not large, the force-deflection behavior of the beam can be modeled with a linear spring 3.2 EQUILIBRIUM AND FREE–BODY DIAGRAMS EQUILIBRIUM - each point of an object has the same constant velocity (velocity is measured relative to an inertial reference frame, where Newton’s laws are valid) EQUILIBRIUM EQUATION - the vector sum of the external forces acting on an object is zero ΣF 0 - this equation can be used to determine unknown forces acting on an object in equilibrium FREE-BODY DIAGRAM - a drawing of an object and the external forces acting on it How to draw it? 1. Identify the object you want to isolate. 2. Draw a sketch of the object isolated from its surroundings, and show relevant dimensions and angles. 3. Draw vectors representing all of the external forces acting on the isolated object, and label them. 4. Choose a coordinate system in order to express the forces in terms of components. 3.3 TWO–DIMENSIONAL FORCE SYSTEMS (coplanar) Equilibrium (vector) equation: Σ F (ΣFx ) i (ΣFy ) j 0 The vector is zero only if each of its components is zero, so we have 2 scalar equations: ΣFx 0 ΣFy 0 3.4 THREE–DIMENSIONAL FORCE SYSTEMS Equilibrium (vector) equation: Σ F (ΣFx ) i (ΣFy ) j (ΣFz ) k 0 The vector is zero only if each of its components is zero, so we have 3 scalar equations: ΣFx 0 ΣFy 0 ΣFz 0