Lecture 6 Chapter 4 Physics I 02.10.2013 Dynamics: Newton s Laws of Motion Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1spring.html
Outline Chapter 4: Sections 4.1 4.6 Force, Mass Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal Force/Tension
Kinematics to Dynamics In Kinematics we studied HOW things move Motion Forces Now in Dynamics we will study WHY things move Motion Forces
Force A force is a push or pull An object at rest needs a force to get it moving A moving object needs a force to change its velocity Force has magnitude and direction: VECTOR!
There are two types of forces Contact forces: exerted by one object in contact with another Non-contact forces: gravity
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 to see if Newton s first law holds!
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.
Example 4-3 Force to stop a car. 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
Newton s 3 rd Laws But where do forces on an object come from? Forces come from other objects
Newton s Third Law of Motion Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. For every action force, there is an equal and opposite reaction force NOTE: Action and Reaction forces act on different objects!
Newton s 3 rd Law When a hammer hits a nail, the hammer stops very quickly i.e. the hammer changes velocity, i.e. it decelerates (a) So, nail must also exert a Force on the hammer (F=ma).
Action-Reaction Forces F OnPersonbyGround F OnGroundbyPerson A key to the correct application of the third law is that the forces are exerted on different objects. Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source. F F PG GP Make sure you don t use them as if they were acting on the same object.
Newton s Third Law of Motion Rocket propulsion can also be explained using Newton s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket. Hero s engine - water-propelled engine from a soft drink cans. Water flowing out of holes in the can cause the can to rotate in the direction opposite to the stream, explained by Newton's Third Law of motion.
Falling ball exerts force on Earth
Weight the Force of Gravity Weight is the force exerted on an object by gravity. Newton s 2 nd Law On earth s surface Force of gravity (weight) F ma a g 9.8 m s 2 Non-contact force all objects dropped near the surface of the Earth accelerates with g towards Earth.
Reaction Forces: Normal Force An object at rest must have no net force on it. If it is standing on a ground, the force of gravity is still there; what other force is there? The force exerted perpendicular to a surface is called the normal force,. F N It is exactly as large as needed to balance the force from the object. F G F N
When you solve problems using forces Need to decide motion of which object we want to describe To find motion of an object, need to know forces acting ON that object
Determine the normal force exerted on the box by the table. y Use Newton s 2 nd Law a (no motion) Box is a described object m y 40N m a (no motion) The normal force is greater
Determine the normal force exerted on the box by the table. Use Newton s 2 nd Law y a No motion m The normal force is smaller
Example 4 8: 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? Y direction Woman is a described object y m ) ) Although her weight is still mg, the scale would read less, 0.8mg
ConcepTest 1 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 I 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
Reaction Forces: Tension If a flexible cord pulls an object, the cord is said to be under TENSION F t2 m F t1 Cord is a described 0 object =0 (assume, the mass of the cord is negligible)
ConceptTest 2. Tension Which situation gives us the largest rope tension? (A) Fcw=Ft wall Fwc=Ft F t ceiling (C) (B) F t F t (D) Tensions are equal. The tension in the rope is F t in all of the above F t
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ConcepTest 7 A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? Going Up II 1) N > mg 2) N = mg 3) N < mg (but not zero) 4) N = 0 5) depends on the size of the elevator The block is accelerating upward, so it must have a net upward force. The forces on it are N (up) and mg (down), so N must be greater than mg in order N m mg a > 0 to give the net upward force! Follow-up: What is the normal force if the elevator is in free fall downward? F = N mg = ma > 0 N > mg
ConcepTest 8 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 1) it is too heavy, so it just sits there 2) it moves backward at constant speed 3) it accelerates backward 4) it moves forward at constant speed 5) 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.