Forces and Newton’s Laws of Motion Chapter 4

Force A force is a push or pull. Forces are often categorized as contact forces or at-a-distance forces. Contact forces: arise from the physical contact between two objects. At-a-distance forces: Gravity, electrical forces Forces are VECTOR QUANTITIES. We use arrows to represent magnitude and direction.

Mass and Inertia Mass is the amount of matter in an object. Mass is a scalar quantity. Inertia is a property of matter that depends on mass. Inertia is a resistance to change in motion. Inertia is dependent on mass. Inertia is the “lazy factor.”

Newton’s 1st Law of Motion An object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force. Net force is the vector sum of all forces acting on a body. Often called the Law of Inertia. This law helps explain why we fly over handlebars and how and why seatbelts work.

Newton’s 2nd Law of Motion Acceleration is proportional to the net force acting on an object. Again, net force is the vector sum of all forces. ΣF is used to signify net force. Also, for a given force, the magnitude of the acceleration is inversely proportional to the mass.

2nd Law Mathematics When a net external force acts on an object of mass m, the acceleration that results is directly proportional to the net force and has a magnitude that is inversely proportional to the mass. The direction of the acceleration is the same as the direction of the net force. SI unit of Force: a derived unit kgm/s2 = Newton (N)

Problem Solving Hints Start with a FREE BODY DIAGRAM! Determine the net force. Remember force is a vector quantity and may need to be broken into x and y components to solve for ΣF. You may need to use kinematics equations as a means of solving for acceleration. Substitute this information into F=ma. Label everything clearly to eliminate confusion.

Vector Nature of Newton’s 2nd Law When dealing with projectile motion, we broke motion into x- and y- components. When dealing with forces, it is important to realize we often need to do the same thing. ΣFx = max ΣFy = may After solving for the x- and y- components, Net Force can be solved using pythagorean theorem.

Newton’s 3rd Law of Motion Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body. “Action – Reaction” law

Types of Forces Common types of forces include: Gravitational force Normal force Frictional force Tension force Each of these types of forces could be acting on the same body. Newton’s Laws hold true for ALL types of forces.

Fundamental Forces These forces are the ones that are truly unique, in the sense that all other forces can be explained in terms of them. The three known fundamental forces are:: Gravitational Force Strong nuclear force – primary role in stability of nucleus of the atom Electroweak force Electromagnetic force – electrically charged particles exert on one another Weak nuclear force – radioactive disintegration of certain nuclei

Nonfundamental Forces Except for gravity all forces dealt with in this chapter are nonfundamental The rest are related to electromagnetic force Physicists are still trying to narrow the number of fundamental forces!

The Gravitational Force Every particle in the universe exerts an attractive force on every other particle. This equation is not perfect for objects too large to be considered particles. However, assuming the objects are spheres with uniform distribution of mass, as long as r is used as the distance between the centers of the spheres the equation is a good approximation of gravitational force. G = 6.63 x 10-11 Nm2/kg2 G is the universal gravitational constant

Weight The weight of an object on or above the earth is the gravitational force that the earth exerts on the object. The weight always acts downward, toward the center of the earth. SI unit of Weight: newton(N) On Earth Fw =mg This equation works because the mass of the Earth and the radius from the center are fairly constant and g can be substituted in for constants in the universal gravitation equation. Of course, slight variations are expected and can be easily solved for.

The Normal Force One component of the force that a surface exerts on an object with which it is in contact – namely, the component that is perpendicular to the surface. The key part of the definition here is that the normal force acts PERPENDICULAR to the surface an object is in contact with. The normal force is consistent with Newton’s 3rd Law of Motion.

Special Situations :Normal Force In “normal” situations, In “normal” cases where an object is lying on a horizontal surface, the normal force will be equal and opposite to the weight of the object. However, if an additional downward force is applied to the object, that force must be included in determining the normal force. Likewise, if an upward force is applied to the object (not causing motion) that force must be subtracted from the weight.

Apparent Weight Apparent weight is the force that the object exerts on the scale with which it is in contact. Think about an elevator…. Accelerating up: apparent weight > true weight Accelerating down: apparent weight < true weight Constant velocity: apparent weight = true weight + or - FN is apparent weight Always Positive

Friction: Contact Force Acting PARALLEL to the surface Static Friction Kinetic Friction When maximum static frictional force is exceeded, an object will move. Not affected by surface area Directly affected by normal force Opposes the relative sliding motion Usually less than static friction Independent of area of contact Independent of the speed (when small) Proportional to the normal force. Friction: Contact Force Acting PARALLEL to the surface

Static Friction Kinetic Friction µ is the coefficient of friction (static or kinetic). No units are associated with this value. This value depends on the surfaces in contact with one another. If kinetic friction is exactly opposite the vector sum of applied forces, the Net Force will equal zero. In these cases, there will be no acceleration. However, an object could still be moving with constant velocity. Friction Equations

The Tension Force Forces applied through ropes or cables. A Force is applied to one end of a rope. Satisfying the 3rd Law, each particle applies the same force to the next. The original force applied is then applied to the object. For ease, we consider the rope to be “massless. “

Equilibrium Applications of Newton’s Laws of Motion In physics, equilibrium is achieved when an object has zero acceleration. Problem Solving Strategy Select object to analyze. If necessary, treat two or more objects separately. Free body diagram for each object chosen. Choose a set of x,y axes for each object and resolve all forces in the free body diagram. Apply equations at left. Solve the two equations for the desired unknown quantities. Remember, two equations can give answers for only two unknowns at most.

Nonequilibrium Applications of Newton’s Laws of Motion Net force does not equal zero so the object is accelerating! We cannot set the forces equal to zero according to the 2nd Law. Apply the same reasoning strategy as in equilibrium problems. However, use these equations in step 4.

Hints and Websites Read this chapter and work through ALL sample problems. They are helpful for developing concepts and will reinforce notes. http://www.wiley.com/college/cutnell check out Chapter 4 features http://wps.prenhall.com/esm_giancoli_physicsppa_6/16/4351/1113925.cw/index.html great site for extra practice www.physicsclassroom.com Forces and dynamics