Dynamics What changes the motion of bodies? Forces. Why things move? Describing forces What changes the motion of bodies? Forces. What keeps bodies moving? No need of forces. Aristotle (384-322 B.C.) Galileo Galilei (1564-1642) Isaac Newton (1642-1727) Proposed a theory to explain the motion of all objects (celestial or not). Most important in PHY101: Newton’s 3 laws of motion and his law of gravitation. More an observer than an experimenter. Performed several careful experiments with falling objects, and published a lot. He challenged Aristotle’s views. was first demonstrated by Galileo.

Types of forces Contact Forces Field Forces Frictional Force Gravitational Force Tension Force Electrical Force Normal Force Magnetic Force Air Resistance Force Applied Force Spring Force

The bigger the mass, more resistance to changes in the motion. Accidents Inertia Inertia is an object tendency to continue in its motion, in the absence of a force. It is related to mass. The bigger the mass, more resistance to changes in the motion.

Also known as law of inertia or law of equilibrium. Newton’s First Law An object remains at rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposed force. Also known as law of inertia or law of equilibrium. If Fnet = 0 (no net force acting on the body) and the body is a rest and the body is moving with constant velocity then the body remains with v = 0. then the body remains moving with constant velocity. v Even today people still believe that a force is required to keep an object moving.

Balanced forces is the case described by the 1st Law of Newton. What does “balanced forces” mean??

The forces on the person are balanced. The floor pushes upward on the person The forces on the book are balanced. The table pushes upward on the book Gravity pulls downward on the book Gravity pulls downwards on the person

Newton’s Second Law The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is in the same direction as that of the imposed force. UNIT of force: 1 newton= 1N = 1 kg m/s2 F a m1 m2 The smaller-mass object experiences a larger acceleration than the larger-mass object when identical forces are applied to the two objects.

Unbalanced forces is the case described by the 2nd Law of Newton.

Just like acceleration, velocity and position. FORCE IS A VECTOR !!!! Just like acceleration, velocity and position. + + = 3 N 5 N 3 N 1 N

Two equal-magnitude horizontal forces act on a box Two equal-magnitude horizontal forces act on a box. Is the object accelerated horizontally? Since the two forces are equal in size, and are in opposite directions, they cancel each other out and there is no acceleration. Yes. No. You can’t tell from this diagram.

Is it possible that the box is moving, since the forces are equal in size but opposite in direction? Even though there is no acceleration, it is possible the object is moving at constant speed. Yes, it is possible for the object to be moving. No, it is impossible for

Two equal forces act on an object in the directions shown Two equal forces act on an object in the directions shown. If these are the only forces involved, will the object be accelerated? Yes. No. It is impossible to determine from this figure. The vector sum of the two forces results in a force directed toward the upper right corner. The object will be accelerated toward the upper right corner.

A ball hangs from a string attached to the ceiling A ball hangs from a string attached to the ceiling. What is the net force acting on the ball? The net force is downward. The net force is upward. The net force is zero. Since the ball is hanging from the ceiling at rest, it is not accelerating so the net force is zero. There are two forces acting on the ball: tension from the string and force due to gravitation. They cancel each other.

Two masses connected by a string are placed on a fixed frictionless pulley. If m2 is larger than m1, will the two masses accelerate? Yes. No. You can’t tell from this diagram. The acceleration of the two masses will be equal and will cause m2 to fall and m1 to rise.

1) An object can move even when no force acts on it. Quick Quizzes Answer True or False: T 1) An object can move even when no force acts on it. F 2) If an object isn't moving, no external forces act on it. T 3) If a single force acts on an object, the object accelerates. T 4) If an object accelerates, a force is acting on it. F 5) If an object isn’t accelerating, no external force is acting on it. F 6) If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction.

Quick Quiz Consider the two situations shown in the figure below, in which there is no acceleration. In both cases the men pull with a force of magnitude F. How does the reading on the scale in part (i) of the figure relate to the reading on the scale in part (ii)? The scale in situation (i) gives the greater reading. The scale in situation (ii) gives the greater reading. The scales in both situations give identical readings.

Quick Quiz For the woman being pulled forward on the toboggan in the figure below, the magnitude of the normal force exerted by the ground on the toboggan is equal to the total weight of the woman plus the toboggan. greater than the total weight. less than the total weight. possibly greater than or less than the total weight, depending on the size of the weight relative to the tension in the rope.

Apparent weight and weightlessness

Quick Quizzes 1) Which has a greater value, a newton of gold won on Earth or a newton of gold won on the Moon? the newton of gold on the Earth the newton of gold on the moon the value is the same, regardless. True or False? F 2) No force of gravity acts on an astronaut in an orbiting space station. 3) At three Earth radii from the center of Earth, the acceleration of gravity is 1/9 its surface value. 4) One kilogram of gold would have greater value on Earth than on the Moon. T F

Newton’s Third Law (“action/reaction”) For every action (force), there is an equal but opposite reaction (force).

Third-Law Action/Reaction Pair If the cart pulls back on the mule equal and opposite to the mule’s pull on the cart, how does the cart ever move?

Third-Law Action/Reaction Pair The car pushes against the road, and the road, in turn, pushes against the car.

Friction Tread designs channel water away from the bearing surfaces on wet roads to combat the tendency to skid. Website about friction of cars: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/frictire.html#c1

Quick Quizzes 1) If you press a book flat against a vertical wall with your hand, in what direction is the friction force exerted by the wall on the book? 1. downward 2. upward 3. out from the wall 4. into the wall 2) A crate is sitting in the center of a flatbed truck. As the truck accelerates to the east, the crate moves with it, not sliding on the bed of the truck. In what direction is the friction force exerted by the bed of the truck on the crate? 1. to the west 2. to the east 3. There is no friction force, because the crate is not sliding.

Quick Quiz situation (a) situation (b) Suppose you're playing with your niece in the snow. She's sitting on a sled and asks you to move her across a flat, horizontal field. You have a choice of (a) pushing her from behind by applying a force downward on her shoulders at 30° below the horizontal (Fig. a), or (b) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal (Fig b). {image} Which option would be easier? Quick Quiz Suppose your friend is sitting on a sled and asks you to move her across a flat, horizontal field. You have a choice of (a) pushing her form behind by applying a force downward on her shoulders at 30° below the horizontal (figure a), or (b) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal (figure b). Which option would be easier? situation (a) situation (b)

Two types of friction forces: Static friction, or also called starting friction: when the object is about to start moving. Kinetic friction, or also called sliding friction: when the object is MOVING.

So, which force of friction is greater, in general? Kinetic or peak static friction force? KINETIC FRICTION It is moving! STATIC FRICTION No motion yet! fk is the force of kinetic friction fs is the force of static friction

Static Friction Kinetic Friction Tire is rolling: it is safer. Wheels are locked and tire is skidding.

v = 2 vcm v = vcm v = 0 Very blurred because at that point: The image is sharper at the bottom because there: v = 0

Rolling motion of a wheel as a combination of purely rotational motion and purely translational motion. ROTATIONAL LINEAR COMBINATION The purely rotational motion: all points on the wheel move with the same angular speed ω. Points on the outside edge of the wheel all move with the same linear speed v = vcm. The purely translational motion: all points on the wheel move to the right with the same linear velocity v as the center of the wheel. The rolling motion of the wheel is the combination of (a) and (b).

FN FN FN

Cool website about Physics of cars: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/frictire.html#c1