Download Newton's Laws of Motion: Equilibrium and Friction and more Study notes Physics in PDF only on Docsity! 1 Chapter 5 The Laws of Motion Applications of Newton’s Law l Assumptions l Objects can be modeled as particles l Masses of strings or ropes are negligible l When a rope attached to an object is pulling it, the magnitude of that force, T, is the tension in the rope l Interested only in the external forces acting on the object l can neglect reaction forces l Initially dealing with frictionless surfaces 2 Objects in Equilibrium l If the acceleration of an object that can be modeled as a particle is zero, the object is said to be in equilibrium l Mathematically, the net force acting on the object is zero 0 0and 0x y F F F = = = ∑ ∑ ∑ Equilibrium, Example 1 l A lamp is suspended from a chain of negligible mass l The forces acting on the lamp are l the force of gravity (Fg) l the tension in the chain (T) l Equilibrium gives 0 0y gF T F= → − =∑ gT F= 5 Newton’s Second Law, Example l Suppose the person pulls with a force that is equal to 100 N and the friction force between the crate and the floor is 20 N, solve for the acceleration if the mass of the crate is 10 kg. Ff Note About the Normal Force l The normal force is not always equal to the gravitational force of the object l For example, in this case l n may also be less than Fg 0y gF n F F= − − =∑ and gn F F= + 6 Inclined Planes l Forces acting on the object: l The normal force, n, acts perpendicular to the plane l The gravitational force, Fg, acts straight down l Choose the coordinate system with x along the incline and y perpendicular to the incline l Replace the force of gravity with its components l What is the acceleration if the car is sliding along the icy incline? Take the incline angle to be 10o. Multiple Objects l When two or more objects are connected or in contact, Newton’s laws may be applied to the system as a whole and/or to each individual object l Whichever you use to solve the problem, the other approach can be used as a check 7 Multiple Objects, Example 1 l First treat the system as a whole: l Apply Newton’s Laws to the individual blocks l Solve for unknown(s) l Check: |P21| = |P12| systemx xF m a=∑ Multiple Objects, Example 2 l Forces acting on the objects: l Tension (same for both objects, one string) l Gravitational force l Each object has the same acceleration since they are connected l Draw the free-body diagrams l Apply Newton’s Laws l Solve for the unknown(s) 10 Forces of Friction, cont. l Friction is proportional to the normal force l ƒs ≤ µsn and ƒk= µkn l These equations relate the magnitudes of the forces, they are not vector equations l The force of static friction is generally greater than the force of kinetic friction l The coefficient of friction (µ) depends on the surfaces in contact Forces of Friction, final l The direction of the frictional force is opposite the direction of motion and parallel to the surfaces in contact l The coefficients of friction are nearly independent of the area of contact 11 Static Friction l Static friction acts to keep the object from moving l If F increases, so does ƒs l If F decreases, so does ƒs Kinetic Friction l The force of kinetic friction acts when the object is in motion l Although µk can vary with speed, we shall neglect any such variations l ƒk = µk n 12 Some Coefficients of Friction Friction in Newton’s Laws Problems l Friction is a force, so it simply is included in the ΣF in Newton’s Laws l The rules of friction allow you to determine the direction and magnitude of the force of friction
