Forces and Motion Chapter 5 and 6

Focus  Force: a push or a pull  Acts on objects to change its velocity

Newtonian Mechanics  The study of the relation between a force and the acceleration it causes as discovered by Isaac Newton  It does not apply to some situations  Very fast moving bodies  Ex: Bodies traveling near the speed of light  Must replace with Einstein’s theory of relativity  Interacting bodies on the scale of atomic structure  Ex: Electrons of an atom  Must replace with quantum mechanics  Newtonian mechanics is a special case of the two more comprehensive theories

Newton’s Laws  1 st Law: If no net force acts on a body, the body’s velocity cannot change (it cant accelerate  2 nd Law: The net force on a body is equal to the product of the body’s mass and its acceleration (F net = ma)  Only forces acted on a body are included in the net force of the body  Net force can be broken into three components (x y z)  A component force can only cause an acceleration in that component  If F net = 0, the forces are balance and the body is said to be in equilibrium  3 rd Law: When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction  F BC = F CB (Equal magnitude but opposite direction)  Third Law force pair

Force  The unit of force must be defined in terms of the mass and acceleration (Newton = kg × m/s 2 )  Vector quantity  Principle of superposition for forces  A single force that has a magnitude and direction of the net force has the same effect on the body as all the individual forces together  Two or more forces have a net force/resultant force  Free body diagram  Drawing all the external forces that act on a defined system  Net force not included  Centripetal force not included  Internal forces (forces between bodies in a system) not included

Examples of Forces  Gravitational Force (F g )  Attraction of two bodies towards each other  Ground of earth is inertial reference frame  F g = mg (For relatively small distances of an object from earth)  Weight (W)  The magnitude of the net force required to prevent a body from falling freely  Inertial reference frame is the ground of earth  W – F g = F net = 0 or W = F g

Examples of Forces (cont.)  Normal Force (F N )  The force a surface exerts on an object  direction is perpendicular to and away from the surface  Friction ( f )  The resistance force from the bonding between two objects  Direction opposite the direction of intended motion  Tension ( T )  The force resulting from a cord attached to a body being pulled taut  The force on the object being pulled and the tension force are equivalent  For simplification, a cord is often said to be massless and unstretchable

Closer Look at Friction  Static Friction ( f s )  Friction opposes the motion of a stationary object  Is only present when there is another force being exerted on the object  Equal in magnitude of that force  Opposite in direction of that force  Kinetic Friction ( f k )  Friction that opposes the motion of a moving object  Has a set magnitude that is independent of any other forces on the object and of the velocity of the object

Properties of friction  If a force F tries to push a stationary body…  If the body doesn’t move, f s and the component of F parallel to the surface are in equilibrium  f s = μ s F N  If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to f k where f k = μ k F N  μ of the friction forces are dimensionless and must be determined experimentally

Uniform Circular Motion  a c = v 2 /r  F c = mv 2 /r  A centripetal force accelerates a body by changing the direction of the body’s velocity without changing the body’s speed  Tension and friction commonly contribute to centripetal forces

Drag Force ( D )  Force from a fluid that opposes the motion of an object and points in the direction the fluid flows relative to the body  Terminal Speed  When considering drag force, a falling object will eventually achieve a constant speed (terminal velocity)  This happens when the net force on the object is 0  D – F g = F net = 0 or D = F g

The sum of all forces acting on an object is also known as? The net force

True of False? An applied force always causes an acceleration False, only a net force

What does a net force equal to?  F or ma

True or False? Some forces can cause an acceleration opposite the direction of the force False, a force can only cause an acceleration in the same direction as the force

True of False? A static friction force can be a net force on an object False, static friction is strictly a reaction forces which balances all other forces that oppose it

An 80 kg boy pushes a 25 kg girl with a force of 50 N. How much force does the tiny girl exert back on the big boy? 50 N (Newton’s third law)

A centripetal force of 10N acts on a 5 kg object. What is the magnitude of the acceleration? 0 m/s 2, only the direction of the velocity changes

Which force goes in a free body diagram? Centripetal Force Net Force Static Friction Internal Forces

True or False? Static friction acts opposite the direction of the motion of a sliding object False, this is kinetic friction

A force is a… Push or a pull

A normal force is… A force acted on by an object from a surface that is perpendicular to the surface

All forces have equal and opposite forces is which one of Newton’s laws? 3 rd law

Terminal velocity is achieved when.. Drag force is equal to gravitational force

Newton’s First Law is… An object cannot accelerate without experiencing a force

Kinetic friction applies when objects are… Moving relative to their surface

Which force is greater? Maximum static friction or kinetic friction? Maximum static friction

What force is an object experience when it is being attracted by the earth? Gravitational force

True of False? The magnitude of the normal force is always equal to the magnitude of the gravitational force. False

True of False? A Force is a vector quantity. True, force has a direction and magnitude

If net force is zero, all forces acting are said to be in… Equilibrium

5 kg F – f s,max = F net F – f s,max = 0 F = f s,max F = µ s mg F = 5 N What is the maximum magnitude of F before this block becomes on the verge of slipping? µ s = 0.1 F

Two horizontal forces, F1 = 5N and F2 = -7N, act on a 2 kg on a frictionless surface. How much does the block accelerate? 5N 7 N F1 + F2 = F net F1 + F2 = ma (F1 + F2)/m = a -1 m/s s = a

A 8.0 kg block slides across the floor at a constant speed. The coefficient of kinetic friction between the floor and the block is What is the magnitude of the force F on the block? F 8 kg F net = F - f ma = F - f 0 N = F - f f = F µmg = F 20 N = F

A block, m = 10 kg, is placed on a ramp and θ = 30°. The coefficient of static friction between the block and ramp is μ s = Does the block slide down the ramp? θ F N = Fgcosθ Fg x = Fgsinθ F s,max = F N μ s F N = mgcos 30 Fg x = mgsin30 F s,max = 52 N F N = 87 N Fg x = 50 N No, the block does not slide since the maximum static friction force is greater than the component of the force of gravity parallel to the ramp

Two blocks are connected by a massless rope on a frictionless surface, and then the two blocks are pulled by another rope with a force of T1= 30 N. m1 = 5 kg and m2 = 10kg. What is the magnitude of T2? m2 m1 T2T1 F net = T1 ma = T1 a = T1/(m1 + m2) a = 2 m/s 2 F net = T2 ma = T2 m2*a = T2 20 N = T2

A 20 kg monkey swings from a vine of length L = 10 m to save his banana in a lake. The monkey must grab the banana at the bottom of his swing. The maximum tension T in the vine before it snaps is 405N. Will the monkey safe retrieve his banana if his velocity at the bottom of his swing is10 m/s? F c = ma c T – Fg = mv 2 /L T = mv 2 /L + mg T = 400 N He barely does, but yes the monkey gets his banana safely T Fg

A system of blocks is pushed by a force F = 105 N on a frictionless surface. m1 = 25kg and m2 = 10 kg. The top block is on the verge of slipping. What is μ s between the two blocks? F F net = F ma = F a = F/(m1 + m2) a = 3 m/s 2 F net = f s m2*a = μ*m2*g μ = a/g μ =.31

F A block is being held on a wall by a force F perpendicular to the wall. The coefficient of static friction between the wall and block is The block has m = 20kg. What is the minimum force F needed to keep the block on the wall without slipping? F s,max = Fg F N μ = mg F = mg/μ F = 20 N

A drag force on a given object (m= 50 kg) is given by D = 5kv 2. What value of k would give a terminal velocity of 5.0m/s for the object? D = Fg 5kv 2 = mg k = mg/5v 2 k = 4 N/m

A vertical force of 12 N and a horizontal force of 9.0 N act on an object. What is the magnitude of the net force? What is the direction of the net force? F net = √[(F v ) 2 + (F h ) 2 ] F net = 15 N tan  = F v /F h  = arctan(F v /F h )  = 53° (north of east)