This property of all matter to continue in its present state of motion (straight line, constant speed) is called inertia. What determines how much inertia an object has? mass, measured in SI units of kilograms. Newton’s 1st law, the Law of Inertia: Every material object continues in its state of rest, of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

The 1st law mentions forces as the agents responsible for affecting the motion of objects. If the velocity has been changed by the force, what has occurred? an acceleration Force is closely related to acceleration.

contact surface Normal N friction Static f s Kinetic f k Ropes/rods T Non-contact Gravity W Electric f e Force Categories

When two systems interact they each exert equal forces on each other, but the two forces are in opposite direction. These two forces are called action-reaction pairs This is Newton’s 3rd law, the Law of Action-Reaction An important corollary to this law is that action and reaction forces never act on the same object.

Unbalanced forces cause masses to accelerate. Force and mass are directly related Mass and acceleration are inversely related These results are consistent with Newton’s Second Law: Net F = m a The net force is the vector sum of all the force acting on the system. units of force are or Newtons (N)

Example: A 50 kg crate is pulled horizontally by a boy with a rope while his girl friend pushes from behind the crate with a force of 40 N. The tension in the rope is 60 N. and the force of kinetic friction is 20 N. What is the acceleration. 60 N 40 N Net F = = 80 N 80 = 50 a a = 1.6 m/s/s + 20 N

Inclines: Which way is up? W N x y W Because the object is constrained to move up or down the incline, it makes sense to find the force components along this direction. This also means that there will be zero net force perpendicular to the incline. Why? No acceleration in this direction.

When several objects are interacting, you can apply 2 nd law to any of them individually, or to any group of them. Example: Two steel beams connected by a cable are hoisted by a crane with its cable attached to the upper beam. The lower beam has a mass of 200 kg, while the upper one has a mass of 300 kg. The system accelerates up at 0.5 m/s 2. Find the tensions in both cables N T N T2 T2-T1-3000=300a T2-T1-3000=150 T2-T1=3150 T1-2000=200a T1-2000=100 T1=2100 +

2000 N T N T2 + Alternatively, we can apply the law to the system as a whole: Net F = ma T T1+T1-2000=500a T2-5000=250 T2=5250 N. Note that the internal forces exerted between parts of the system cancel in this equation. Why?

Pulleys: A change in direction m1 m2 A pulley merely changes the direction of the tension force. It is easiest to choose a “rotation” direction as + or - T W1 T W2

Friction For two surfaces sliding past each other, the kinetic friction force depends on how much the surfaces are pressed into each other. What force gets bigger as surfaces are pressed together? Normal force. Thus expect f k to depend on the normal force N. Static friction can vary from zero to some maximum value, f s max. We expect the value of f s max to depend on N also. Why? Equality when slipping about to begin

Example: A 50 kg crate is pulled horizontally by a boy with a rope while his girl friend pushes from behind the crate with a force of 40 N. The tension in the rope is 60 N directed at 37 o. and the coefficient of kinetic friction is.12. What is the acceleration? 60 N 40 N + fkfk W N 48 36

Example: A.5 kg mass sits on top of a 1.5 kg mass. The larger mass is on a smooth surface and is pulled horizontally by a rope. It is found that when the rope tension exceeds 8 N. the top mass starts to slip. Find the coefficient of static friction between the two masses. T N W fsfs

Centripetal Force When an object moves in a circle, it accelerates toward the center of the circle with an acceleration of All accelerations are caused by forces, and the generic name for the net force acting toward the center is the centripetal force, F cp. Centripetal force is not a “real” force like gravity, or friction. Rather, it is just a name we give to one or more of the real forces when they are involved in making an object move in a circle. We say the centripetal force is supplied by the real forces. We can apply Newton ‘s 2 nd law in the direction toward the center of the circle at a given instant to obtain:

When solving problems involving circular motion, the first thing to do is determine where the center of the circle is. This determines how forces will be broken into components: along the line connecting the object and the center and perpendicular to this line. Examples where one force only supplies F cp : 1) ball on string whirling in horizontal circle 2) flat circular race track 3) rotor (amusement park ride) 4) earth-moon system When several forces have components along the radial direction, we must sum them all to find the centripetal force.

Example: Ball moving in a vertical circle. Top: Bottom: General:

Banked Track N mg θ Toward center: to center: