Lecture 8 Physics I Chapter 6 Friction forces Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi
Today we are going to discuss: Chapter 6: Some leftover (Ch.5) Kinetic/Static Friction: Section 6.4 Gravity: Section 6.3 (read if you want. We will get to this in Ch.13)
Exam I Results Average 52.3 points out of 90 points Average 58.1% MCQ Pr.1 Pr.2 Pr.3 Max 30 20 20 20 Average 20 11.6 8.0 12.7 I added three problems to your current homework!
Some leftover Ch5.
Newton s laws In 1687 Newton published his three laws in his Principia Mathematica. These intuitive laws are remarkable intellectual achievements and work spectacular for everyday physics
Newton s 1 st Law (Law of Inertia) In the absence of force, objects continue in their state of rest or of uniform velocity in a straight line i.e. objects want to keep on doing what they are already doing It helps to find inertial reference frames
Inertial reference frame Inertial reference frame A reference frame at rest Or one that moves with a constant velocity An inertial reference frame is one in which Newton s first law is valid. This excludes rotating and accelerating frames (non-inertial reference frames), where Newton s first law does not hold. How can we tell if we are in an inertial reference frame? - By checking if Newton s first law holds!
Inertial Reference Frame (Example) A physics student cruises at a constant velocity in an airplane. A ball placed on the floor stays at rest relative to the airplane. There are no horizontal forces on the ball, so when. Newton s first law is satisfied, so this airplane is an inertial reference frame.
Non-Inertial Reference Frames (Example) A physics student is standing up in an airplane during takeoff. A ball placed on the floor rolls toward the back of the plane. There are no horizontal forces on the ball, and yet the ball accelerates in the plane s reference frame. Newton s first law is violated, therefore this airplane is not an inertial reference frame. In general, accelerating reference frames are not inertial reference frames.
Newton s Second Law of Motion Newton s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass. F ma New unit of force Newton N kg m 2 s It takes a force to change either the direction or the speed of an object. More force means more acceleration; the same force exerted on a more massive object will yield less acceleration.
F ma Mass Proportionality defines mass of object. Mass is the measure of inertia of an object, sometimes understood as the quantity of matter in the object. In the SI system, mass is measured in kilograms. Mass is not weight. Mass is a property of an object. Weight is the force exerted on that object by gravity. If you go to the Moon (gravitational acceleration is about 1/6 g), you will weigh much less. Your mass, however, will be the same.
Force to stop a car. Example What average net force is required to bring a 1000-kg car to rest from a speed of 20 m/s within a distance of 100 m? Assume acceleration is constant
ConcepTest A very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck? Truck on Frozen Lake A) it is too heavy, so it just sits there B) it moves backward at constant speed C) it accelerates backward D) it moves forward at constant speed E) it accelerates forward When the fly hit the truck, it exerted a force on the truck (only for a fraction of a second). So, in this time period, the truck accelerated (backward) up to some speed. After the fly was squashed, it no longer exerted a force, and the truck simply continued moving at constant speed.
Friction Static Kinetic Kinetic/Static Friction: Section 6.4
A new contact force friction Friction is always present when two solid surfaces slide along each other. The microscopic details are not yet fully understood.
Friction. Static-vs-Kinetic If a horizontal force is applied on an object, the object does not move. It means a second force, Static Friction, must be opposing the applied force. N N N N m F A m F A m F A m mg no motion static mg f s no motion static 0 F x ma x F A f f s s F A 0 S N Static friction f s mg Static. Limit. Motion is about to start f s N S F S coefficient of static friction N An object remains at rest as long as f s < f s max. The object just begins to slip when f s = f s max. f s S A S N f k f fr Sliding. Friction (kinetic) is constant 45 fs F A f N K k K coefficient of kinetic friction Kinetic friction f k F K N F A
Static friction Static friction applies when two surfaces are at rest with respect to each other (such as a book sitting on a table). Static friction points opposite the direction in which the object would move if there were no static friction. The static frictional force is as big as it needs to be to prevent slipping, up to a maximum value. f s N S N
Kinetic friction Sliding friction is called kinetic friction. N The kinetic friction force is directed opposite to the velocity of the object relative to the surface Approximation of the kinetic frictional force: N is the normal force μ k f N K k is the coefficient of kinetic friction, which is different for each pair of surfaces. Usually it is easier to keep an object sliding than it is to get it started. Movie New in Town (6.09)
Coefficients of Friction Note that, in general, μ s > μ k.
Summary
Example A 10-kg box moves on a horizontal surface. The system has coefficients of friction μ K =0.5. [Use g=10 m/s 2 ] A horizontal force of 60N is applied. What is the acceleration? y F fr x =μ K N N m F g =mg F A F y ma y N mg F K N fr K mg F x F A F mg K A Ffr ma ma a F Kmg m 60N 0.510kg 10 m A 2 s 1m 2 s 10kg
ConcepTest A box of weight 100 N is at rest on a floor where s = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? Will It move? A) moves to the left B) moves to the right C) the box does not move D) moves down E) moves up F fr F S N Smg 0.5100 50N The static friction force has a maximum of s N = 50 N. The tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction. m T=30N Follow-up: What happens if the tension is 55 N?
Demonstration Two Interleaved Books Simply lay the pages of two phone books on top of each other one by one before attempting to pull them apart. F fr NxF fr http://www.youtube.com/watch?v=ahq82d78igg F A F pull F perp It increases friction It pulls books apart
How to measure μ S? F x ma x Given: μ s, with friction N Find: θ F y ma y F fr N mg cos 0 0 About to start moving mg A block lies on an inclined plane with μ k. The angle of the incline is slowly increased. At what angle does the block start to move? F y F x mgsin F fr 0 mgsin s mgcos 0 mgsin s mgcos N mg cos F S N fr mg S cos sin cos tan s By measuring angle, when an object gets lose, we can find static friction coefficient
Thank you See you on Monday
ConcepTest A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block? Going Up A) N > mg B) N = mg C) N < mg (but not zero) D) N = 0 E) depends on the size of the elevator v=const a The block is moving at constant speed, so v it must have no net force on it. The forces on it are N (up) and mg (down), so N = mg, just like the block at rest on a table. m
Example: Apparent weight loss. A 65-kg woman descends in an elevator that briefly accelerates at 0.20g downward. She stands on a scale that reads in kg. What does the scale read? Woman is a described object m Y direction y ) ) Although her weight is still mg, the scale would read less, 0.8mg
ConcepTest A 50-kg student (mg = 490 N) gets in an elevator at rest and stands on a metric bathroom scale. Sadly, the elevator cable breaks. What is the student s weight during the few second it takes the student to plunge to his doom? Going Up I A) > 490 N B) 490 N C) < 490 N (but not zero) D) N = 0 E) depends on the size of the elevator If an object is accelerating downward with a y = g 0 a y = g An object in free fall has no weight! He is weightless like an astronaut. m y m