Newton s Laws of Motion

Newton s Laws of Motion

Observation #1 An object at rest remains at rest, unless something makes it move. Observation #2 A object in motion continues in motion with constant velocity, unless something makes it change its velocity. Constant velocity = constant speed in the same direction. Observation #3 An object will not change its velocity unless a net external force acts on it.

Combining Observations 1 & 2 An object left alone will not change it s velocity. Something must cause a change in velocity. A force is something that causes an acceleration or change in velocity Change in speed Change in direction By definition is a push or a pull

orce SI unit of force is the Newton (N) 1 N = 0.225 lb 1 lb. = 4.448 N A orce is a Vector It has a magnitude, measured in N or lbs. It acts in a particular direction. Can exist during physical contact (tension, friction, applied force) = Contact orce Can exist with NO physical contact, called field forces(gravitational, electric)= Noncontact orce

Newton s irst Law An object in motion remains in motion in a straight line and at a constant speed (velocity) or an object at rest remains at rest, unless acted upon by an external (unbalanced) force. TWO conditions and one constraint. Condition #1 The object CAN move but must be at a CONSTANT SPEED Condition #2 The object is at REST Constraint As long as the forces are BALANCED. If all the forces are balanced the SUM of all the forces is ZERO. The bottom line: There is NO ACCELERATION in this case AND the object must be at EQILIBRIUM ( All the forces cancel out). accel 0 0

Inertia Another way to say Newton s irst Law is to say the Law of Inertia Inertia is the tendency of objects to resist changes in motion. The amount of inertia an object has is determined by its mass. Quantity of matter, also called MASS. Italian for LAZY. Unit for MASS = kilogram.

Inertial Reference rame Newton s Law require measurements to be made in a reference frame that is not accelerating to be valid. (moving at constant velocity) This excludes situations where the rotation of the Earth is noticeable. Large air currents and ocean currents. Long range missiles.

Newton s irst Law Inertia Examples

Types of orces Contact orces- result from physical contact between two objects. ield orces- (Noncontact) force that can exist between two objects even in the absence of physical contact. (Action-at-a-Distance orce) Common Types of orces: Gravitational orce Normal orce rictional orce Tension orce

Common orces orce of gravity ( g ) pulls straight down. riction ( f ) occurs between two objects that can slide against each other. It opposes motion.

Common orces Normal force ( N ) is the support force from a surface. It is called normal because it is always perpendicular to the surface. Tension ( T ) is the force in a rope or string. The tension is the same in every part of a rope.

Determining the orce of Gravity The magnitude of the force of gravity on something is called the weight. Is how MASS is effected by gravity Weight = mass x gravity g = 9.81 N/kg W mg NOTE: MASS and WEIGHT are NOT the same thing. MASS never changes. What is the weight of an 85.3-kg person on earth? What is the weight of same person on Mars (g=3.2 m/s 2 )? W W mg W (85.3)(9.8) MARS (85.3)(3.2) 272. 96 835.94N N

Equilibrium Model A system moving at a constant speed (velocity) or at rest MUST be at EQUILIBRIUM. net = 0 According to Newton s irst Law, objects in equilibrium have a net external force equals 0., Δv = 0, = 0 TIPS for solving problems: Draw a free body diagram Resolve anything into COMPONENTS Write equations of equilibrium Solve for unknowns

Determining Net External orce The net external force is the sum of all the forces acting on the object. Since forces are vectors, we must use vector addition to find the sum, or resultant. ree-body diagrams are useful for determining the net force acting on an object.

ree-body Diagram ree-body diagrams consider just one object and the forces that act on it. To draw a free body diagram Draw a dot to represent the object. Draw and label vector arrows representing all the forces acting on the object. All the vectors should be shown as acting at a single point.

A pictorial representation of forces complete with labels. f ree Body Diagrams N W 1,g 1 or m 1 g T T m 2 g Weight(mg) Always drawn from the center, straight down orce Normal( N ) A surface force always drawn perpendicular to a surface. Tension(T or T ) force in ropes and always drawn AWAY from object. riction(f)- Always drawn opposing the motion.

ree Body Diagrams f N a mg

Example A 10-kg box is being pulled across the table to the right at a constant speed with a force of 50N. a) Calculate the orce of riction a) Calculate the orce Normal N 50N a f f a mg ( 10)(9.8) 98N n mg

Example Suppose the same box is now pulled at an angle of 30 degrees above the horizontal. a) Calculate the orce of riction b) Calculate the orce Normal ax f a ax cos 50cos 30 43.3N 43.3N N a f 30 mg ax ay N N mg! ay mg N mg ay (10)(9.8) 50sin 30 N 73N

Newton s Second Law m(a) "The acceleration of an object is directly proportional to the NET ORCE AND inversely proportional to the mass." Acceleration is directly proportional to the NET orce. a NET DIRECTLY = They do the same thing. If the force increases, the acceleration increases. If the force decreases, the acceleration decreases. a 1 m Acceleration is inversely proportional to the mass. INVERSELY = They do the opposite. If the mass decreases, the acceleration will increase. If the mass increases, the acceleration will decrease.

Newton s 2 nd Law N.S.L. works based on these direct and inverse relationships. As 2 of the variable change, ONE of them must remain constant. If the force is constant, the acceleration and mass change as shown above. (net)=ma 2=m(2a) 3=m(3a) If we add a second dog pulling with 100N just like the first dog, we could pull the sled with twice the acceleration, provided the mass of the sled was constant.

Putting it all Together NET a 1 a m 10 N 3 N 10 kg a NET NET NET NET ma m Total orce 0 Magnitude of NET = Direction = Acceleration = RIGHT 7 N 0.70 m/s 2

Newton s 2nd Law Tips 1. Draw a free body diagram 2. Break vectors into components if needed 3. ind the NET force by adding and subtracting forces that are on the same axis as the acceleration. 4. Set net force equal to ma this is called writing an EQUATION O MOTION. NOTE: To avoid negative numbers, always subtract the smaller forces from the larger one.

Example An elevator with a mass of 2000 kg rises with an acceleration of 1.0 m/s 2. What is the tension in the supporting cable? T NET ma Equation of Motion T mg ma T ma mg T (2000)(1) (2000)(9.8) mg T 21,600 N

Example A 50 N applied force drags an 8.16 kg log to the right across a horizontal surface. What is the acceleration of the log if the force of friction is 40.0 N? 40 N n 50 N a NET a f ma ma mg 50 10 40 8.16a 8.16a a 1.23 m/s 2

Example A sled is being accelerated to the right at a rate of 1.5 m/s 2 by a rope at a 33 degree angle above the + x. Calculate the rictional orce if the mass of the sled is 66 kg and the tension in the rope is 150 N. f N mg Tcos Tsin NET ma T cos f ma T cos ma f 150cos 33 (66)(1.5) f f 26.8 N

Newton s Third Law or every action there is an EQUAL and OPPOSITE reaction. This law focuses on action/reaction pairs (forces) They NEVER cancel out All you do is SWITCH the wording! PERSON on WALL WALL on PERSON

Newton s Third Law This figure shows the force during a collision between a truck and a train. You can clearly see the forces are EQUAL and OPPOSITE. To help you understand the law better, look at this situation from the point of view of Newton s Second Law. m Truck Truck A Truck Train M Train a Train There is a balance between the mass and acceleration. One object usually has a LARGE MASS and a SMALL ACCELERATION, while the other has a SMALL MASS (comparatively) and a LARGE ACCELERATION.

Newton s 3 rd Law Examples Action: HAMMER HITS NAIL Reaction: NAIL HITS HAMMER Action: Earth pulls on YOU Reaction: YOU pull on the earth

Newton s Law of Gravitation What causes YOU to be pulled down? THE EARTH.or more specifically the EARTH S MASS. Anything that has MASS has a gravitational pull towards it. Mm g What the proportionality above is saying is that for there to be a ORCE DUE TO GRAVITY on something there must be at least 2 masses involved, where one is larger than the other.

Newton s Law of Gravitation As you move AWAY from the earth, your DISTANCE increases and your ORCE DUE TO GRAVITY decrease. This is a special INVERSE relationship called an Inverse-Square. g 1 The r stands for SEPARATION DISTANCE and is the distance between the CENTERS O MASS of the 2 objects. We us the symbol r as it symbolizes the radius. Gravitation is closely related to circular motion as you will discover later. r 2

N.L.o.G Putting it all Together G m1m2 2 r constant of G Universal Gravitational Constant G g g 6.67x10 G m1m 2 r 2 11 proportionality Nm 2 kg 2 g g mg Use this when you are on theearth G m m r 1 2 2 Use this when you are LEAVING the earth

Try this! Let s set the 2 equations equal to each other since they BOTH represent your weight or force due to gravity r g g Mm mg G 2 r M g G 2 r M Massof radius of mg G m m r Use this when you are on theearth 1 2 2 g the Earth 5.97x10 the Earth 6.37x10 Use this when you are LEAVING the earth 6 24 kg m SOLVE OR g! 11 (6.67x10 )(5.97x10 6 2 (6.37x10 ) 24 ) 9.81m / s 2

Which has more force? When the boxer hits the bag, which has more force, the boxer on the bag or the bag on the boxer?

Newton s Third Law If an object, A, pulls or pushes on an object, B, then B also pulls or pushes on A. The force on each object has the same magnitude, but the forces are oppositely directed.

Action-Reaction Pairs

Action-Reaction Pairs A pair of forces between two objects is called an actionreaction pair.

Newton s Laws Simplified orce is required to cause an acceleration. orce = mass x acceleration All forces come in pairs.

Constant orce Model vs. Equilibrium Model Equilibrium = 0. Object will be at rest or move with constant velocity. Position vs. time graph- Constant orce = constant. Object will accelerate in the direction of the net force. Position vs. time graph-

Normal orce Normal orce ( N ) if one component of a force that a surface exerts on an object with which it is in contact, perpendicular to the surface Block on table, block s weight pushes down on table, the table pushes back up on block ollows Newton s 3 rd Law, for every action there is an opposite reaction Size of N indicates how hard two object press against each other If object is resting on horizontal surface and no other forces act, then N = W

Tension orce orce often applied by means of cables or ropes that are used to pull an object ( T ) Tension is often defined as the tendency of a rope or a cable to be pulled apart T of a rope that is pulling an object is the same size as the force being applied to the object being pulled Assume rope is massless, tension can be transmitted undiminished through rope unless stated otherwise (then tension would be different along different areas of the rope)

rictional orces rictional forces oppose the applied force. They act in the opposite direction of the motion Two Types of riction Static Kinetic riction Applied

Static riction Static friction ( s ) is the frictional force that acts on a static (nonmoving) object. When an object is not moving, the frictional force will equal the applied force but be in the opposite direction. S Applied s = - applied

Static riction There is a maximum amount of static friction, s,max. Once the applied force exceeds s,max the object breaks free and begins moving. S Applied

Kinetic riction Kinetic friction is the frictional force on a moving object. The force of kinetic friction is less than the maximum static friction. The net force on a moving object is equal to applied - k K Applied

orce of riction The orce of riction is directly related to the Normal orce. Mostly due to the fact that BOTH are surface forces f sf kf N constant of coefficien t of s k N N proportionality friction The coefficient of friction is a unit less constant that is specific to the material type and usually less than one. Note: riction ONLY depends on the MATERIALS sliding against each other, NOT on surface area.

riction & Newton s 1 st Law If the coefficient of kinetic friction between a 35-kg crate and the floor is 0.30, what horizontal force is required to move the crate to the right at a constant speed across the floor? n f mg a a f f k N a k N N a a a mg mg k (0.30)(35)(9.8) 102.9 N

riction & Newton s 2 nd Law f Suppose the same 35 kg crate was not moving at a constant speed, but rather accelerating at 0.70 m/s/s. Calculate the applied force. The coefficient of kinetic friction is still 0.30. ma mg n a NET ma a a k N a a a a f ma mg ma k ma mg k (35)(0.70) (0.30)(35)(9.8) 127.4 N

Inclines f N mg cos mgsin mg Tips Rotate Axis Break weight into components Write equations of motion or equilibrium Solve

riction & Inclines A person pushes a 30-kg shopping cart up a 10 degree incline with a force of 85 N. Calculate the coefficient of friction if the cart is pushed at a constant speed. a mg cos mg sin mg f n mg sin a f f k N mg sin mg cos a k N N mg cos mg sin a k mg sin mg cos a k a mg sin mg cos k 85 (30)(9.8)(sin10) k 0.117 (30)(9.8)(cos10)

A 5-kg block sits on a 30 degree incline. It is attached to string that is thread over a pulley mounted at the top of the incline. A 7.5-kg block hangs from the string. a) Calculate the tension in the string if the acceleration of the system is 1.2 m/s/s b) Calculate the coefficient of kinetic friction. ma m 2 gcos30 T m 1 m 1 g T 30 m 2 gsin30 f m 2 g N 30 Example NET m g T m a 1 1 T ( m g sin ) m a N f m g cos 2 2 2

Example Cont. NET 1 1 1 1 ma m g T m a m g m a T (7.5)(9.8) (7.5)(1.2) T 64.5 N T T ( m g sin ) m a f 2 2 2 2 2 T m g sin m a f 2 2 T m g sin m a k N 2 2 T m a m g sin T m2a m2g sin k N T m2a m2g sin k mgcos 64.5 (5)(1.2) (5)(9.8)(sin 30) k (5)(9.8)(cos30) k 0.80 N k N N m g cos 2

Coefficient of riction Example A 24 kg crate, initially at rest, requires a 75 N force to set it in motion. Once moving, a force of 53 N is needed to keep it moving with constant velocity. ind the coefficient of static friction and the coefficient of kinetic friction.

Coefficient of riction Example s X s, max 0 n S,Max n 75 N 75 N - S, Max S, MAX 75 N 0 gravity=mg n n Y 0 mg mg 0 s S 75 N mg 0.32 75 N (24 kg)(9.81 m/s 2 )

Coefficient of riction Example k k n n k k k n 53 N mg mg k mg 0.23 0 53 N (24 kg)(9.81 m/s 2 ) k n 75 N gravity=mg

Air Resistance The force of air resistance ( R ) is a form of friction. R depends on velocity. R g

Terminal Speed At some speed, the air resistance will be equal in magnitude to the force of gravity. ( R = - g ). Once an object reaches that speed, it will no longer accelerate. It will continue to fall at a constant speed. R g