The first exam will be held next Tuesday, on September 29, in room 114 Richardson from 7 to 9:10 p.m. Section 807 and half of section 808 (students with last names beginning from letters A through M) should come at 6:55 p.m. for an exam that starts at 7:00 and ends at 8:00 p.m. The rest of section 808 and section 809 should come at 8:00 for an exam that starts at 8:10 and ends at 9:10 p.m. Those who take the first exam cannot leave before 8 p.m.

A help session will be held on Monday, September 28, at 7:00 pm, In room 205 ENPH Please come with questions!

Dynamics Finally, we talk about what causes the motion! Connection between force and motion The concept of force gives us a quantitative description of the interaction between two bodies or between a body and its environment Johannes Kepler was probably the first who suggested that it is some force which is responsible for the orbital motion of Mars

Aristotle: a natural state of an object is at rest; a force is necessary to keep an object in motion. It follows from common sense. Galileo: was able to identify a hidden force of friction behind common-sense experiments B.C.

Galileo: If no force is applied to a moving object, it will continue to move with constant speed in a straight line Galilean principle of relativity: Laws of physics (and everything in the Universe) look the same for all observers who move with a constant velocity with respect to each other. Inertial reference frames

Newton’s Laws 1st Law: A body acted on by no net force moves with constant velocity (which may be zero) 2st Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. 3rd Law: For every action there is an equal, but opposite reaction

The First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion. The First Law contains implications about the fundamental symmetry of the universe in that a state of motion in a straight line must be just as "natural" as being at rest. If an object is at rest in one frame of reference, it will appear to be moving in a straight line to an observer in a reference frame which is moving by the object. There is no way to say which reference frame is "special", so all constant velocity reference frames must be equivalent.

2 nd Law From experiments we know: 1.A force is needed to change the state of motion 2.Force is a vector 3.The direction of acceleration vector is the same as the direction of the force vector 4.The magnitude of the force and acceleration are related by a constant which intuitively is a “quantity of matter”.

I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Isaac Newton “I do not feign hypotheses”

Newton’s 2 nd Law of Motion 2.The acceleration a of a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force. a = F/m  F = m a

Newton’s second law The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

Units of Force British system: units of mass: units of force: One pound is kg One pound is the weight of kg on the Earth

Newton’s 3 rd Law of Motion 3.To every action, there is an equal and opposite reaction. The same force that is accelerating the boy forward, is accelerating the skateboard backward.

Skater Skater pushes on a wall The wall pushes back –Equal and opposite force The push from the wall is a force –Force provides an acceleration –She flies off with some non-zero speed

Clockwork universe

Types of forces Gravity Spring force, tension force Friction Normal force, “contact” force Fundamental forces

Matter is effected by forces or interactions (the terms are interchangeable) There are four fundamental forces in the Universe: gravitation (between particles with mass) electromagnetic (between particles with charge) strong nuclear force (between quarks) weak nuclear force (that changes quark types)

The Standard Model (SM) describes all these particles and 3 of 4 forces. We have confirmed the existence of those in the laboratory experiments. The Standard Model + Higgs boson Higgs has not yet been discovered The mass is constrained from LEP and Tevatron data: 114 GeV<M H <154 GeV Precision Cosmology at the LHC 19

Large Hadron Collider went online on Sept Counter propagating proton beams accelerated to 7x10 12 eV make 11,000 revolutions per second and collide in four points 27 km ring

CMS detector

Some goals of LHS: To discover the Higgs boson responsible for the origin of mass To discover the dark matter particle To confirm the Supersymmetry theory

Dark matter dominates in all galaxies! > 90% of mass is invisible Dark matter corona

Gravity is a strange force. It has a unique property: M m R All bodies in the same point in space experience the same acceleration! Galileo, about 1600

Weight, the force of gravity, and the normal force A person in an elevator

A Recipe for Solving Problems 1.Sketch Isolate the body (only external forces but not forces that one part of the object exert on another part) 2. Write down 2 nd Newton’s law Choose a coordinate system Write 2 nd Newton’s law in component form: 3. Solve for acceleration

Force exerted by a spring: Hooke’s law: If spring is stretched or compressed by some small amount it exerts a force which is linearly proportional to the amount of stretching or compressing. The constant of proportionality is called the spring constant. - is deviation from the natural length “stress is proportional to strain”

Hooke’s law is an approximation for small strain Steel

Friction Two types of friction: 1.Kinetic: The friction force that slows things down 2.Static: The force that makes it hard to even get things moving

Refrigerator If you push a refrigerator when there is no friction what happens? In the real world what happens? Especially when it’s fully loaded and on a sticky kitchen floor? –When does static friction kick in? –When does kinetic friction kick in?

Friction There is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates. The maximum of the force of friction varied linearly with the amount that the block pushes on the table.  - coefficient of friction, is the vertical force exerted by the block on the table The friction force only exists when there is another force trying to move an object

Kinetic Friction For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write F Friction =  Kinetic F Normal Here  is a constant Warning: –THIS IS NOT A VECTOR EQUATION!

Static Friction This is more complicated For static friction, the friction force can vary F Friction   Static F Normal Example of the refrigerator: –If I don’t push, what is the static friction force? –What if I push a little?

What is the normal force? What is the velocity of the block when it reaches the bottom? H No friction:  =0 m

 Pulling Against Friction A box of mass m is on a surface with coefficient of kinetic friction . You pull with constant force F P at angle  The box does not leave the surface and moves to the right. 1.What is the magnitude of the acceleration? 2.What angle maximizes the acceleration?

A Recipe for Solving Problems 1.Sketch Isolate the body (only external forces but not forces that one part of the object exert on another part) 2. Write down 2 nd Newton’s law Choose a coordinate system Write 2 nd Newton’s law in component form: 3. Solve for acceleration

Is it better to push or pull a sled? You can pull or push a sled with the same force magnitude, F P, and angle , as shown in the figures. Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, , which is better? FPFP FPFP

P m1m1 m2m2 No friction m1m1 Free body diagram m1m1 m1gm1g P N1N1 F 21 m2gm2g F 12 N2N2 m2m2 F 12 =F 21

A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is If the larger block is on a frictionless table, what is the largest horizontal force that can be applied to it without the small block slipping?