Chapter 4: The Laws of Motion Forces  There seem to be two kinds of forces in Nature: Contact forces and field forces.  A contact force is transferred from one object to another by physical contact.  A field force is transferred in space without physical contact. However, according to modern physics contact forces are field forces in disguise! All the fundamental forces in Nature are all field forces.

Forces  Examples of forces:

Forces There are four know fundamental forces: An example: Free neutron decay  Fundamental forces

Forces  Examples of forces: An example of weak interaction Free neutron decay: n -> p + e -  e -

Newton’s First Law  Galileo’s thought experiment Galileo thought about an object moving on a frictionless surface. He posed a question: what will happen if no force is applied to the object? He concluded that it’s not the nature of an object to stop, once set in motion, but rather to continue in its original state of motion.  Newton’s first law of motion An object moves with a velocity that is constant in magnitude and direction, unless acted on by a non-zero net force. External forces come from the object’s environment. If an object’s velocity is not changing in either magnitude or direction, then it’s acceleration and the net force acting on it must both be zero. Internal forces originate within the object itself and cannot change the object’s velocity (although they can change the object’s rate of rotation).

Newton’s First Law  Inertia It is much easier to throw a golf ball over a longer distance than a bowling ball – a bowling ball resists to move more than a golf ball. Q: Why is that? A: Inertia. The tendency of an object to continue in its original state of motion is called inertia.  Mass Mass is a measure of the object’s resistance to changes in its due to a force: more precisely inertial mass.

Newton’s First Law  Examples of inertia Ooops!Seat belt motion of car

Newton’s Second Law  Motion of an object under influence of net non-zero force How does an object under influence of net force? Experiments show that, if you push an object with twice as strong force, the object is accelerated twice as much….  Newton’s second law The acceleration a of an object is directly proportional to the net force acting on it and inversely proportional to its mass where the constant of proportionality is one. inertial mass net force acceleration

Newton’s Second Law  Units of force and mass SI unit of force : newton (N) SI unit of mass : kilogram (kg) Newton’s second law: 1 N = 1 kg m/s 2 =0.225 lb..

Newton’s Second Law  Examples Example 4.1: Airboat (a) Find the acceleration of the airboat. (b) Starting from rest, find the time needed to reach a speed of 12.0 m/s. const. force=const. accel. (c) After reaching the speed, the engine is turned off and drifts to a stop over a distance of 50.0 m. Find the resistance force.

Newton’s Second Law  Examples Example 4.2: Horses and a barge x-components: 30.0 o o y-components: acceleration:

Newton’s Second Law  Gravitational force Is the mutual attractive force between any two objects Is described by Newton’s law of universal gravitation:. Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. G= 6.67 x Nm 2 /kg 2 universal gravitation constant

Newton’s Second Law  Weight Is the magnitude of the gravitational force acting on an object of mass m near Earth’s surface. SI unit : newton (N) Relation between g and G M E : mass of Earth R E : radius of Earth depends on environment

Newton’s Third Law  Newton’s 3 rd law Forces in nature always exists in pairs. If object 1 and object 2 interact, the force F 12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F 21 exerted by object 2 on object 1. action reaction

Newton’s Third Law  An example of Newton’s 3 rd law A TV on a table (TV at rest) action reaction normal force gravitational force TV at rest Newton’s 2 nd law

Friction  Friction and force Friction as a function of applied force (see the graph) Static region (Object at rest) Kinetic region (Object in motion) normal force coefficient of friction normal forcecoefficient of friction const.

Friction  Coefficients of friction

Application of Newton’s Laws  An example of Newton’s 3 rd law A piece of rope at rest under constant tension along it Newton’s 2 nd law No acceleration A crate pulled by a man Forces on the crate Free-body diagram Newton’s 2 nd law

Application of Newton’s Laws  Objects in equilibrium Objects that are either at rest or moving with constant velocity are said to be in equilibrium. Newton’s 2 nd law Net force is zero.

Application of Newton’s Laws  Examples Example 4.5: A traffic light at rest

Application of Newton’s Laws  Examples Example 4.5: A traffic light at rest T 1x T 2x T 1y T 2y T 3y

Application of Newton’s Laws  Examples Example 4.6: Sled (at rest) on a frictionless hill

Application of Newton’s Laws  Examples Example 4.8: The runaway car  =20.0 o (a) Determine the acceleration of the car. (b) Time taken for the car to reach the bottom? (c) velocity at the bottom?

Application of Newton’s Laws  Examples Example 4.9: Weighing a fish in an elevator (a) Find the weight when a>0. (b) Find the weight when a<0. a=2.00 m/s 2 a=-2.00 m/s 2 (c) Find the weight when the cable breaks (a=-g).

Application of Newton’s Laws  Examples Example 4.10: Atwood’s machine m 2 >m 1

Application of Newton’s Laws  Examples Example 4.11: A block on a ramp (static friction)

Application of Newton’s Laws  Examples Example 4.12: A sliding hockey puck (kinetic friction) v 0 =20.0 m/s -> v=0  x=1.20x10 2 m

Application of Newton’s Laws  Examples Example 4.13: Connected objects m 1 =4.00 kg m 2 =7.00 kg   =0.300 (a) Find acceleration and tension I. For Object 1: For Object 2: (2)-(4)

Application of Newton’s Laws  Examples Example 4.13: Connected objects m 1 =4.00 kg m 2 =7.00 kg   =0.300 (b) Find acceleration and tension II (system approach). For a system made of Object 1+2:

Application of Newton’s Laws  Examples Example 4.14: Two blocks and a cord For top object 1: For bottom object 2: m=5.00 kg M=10.0 kg  s =0.350 What is the max. force by the string without causing the top object to slip?