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Vectors and Newton's Laws (12) (ELCA)

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Class Notes For:
Honors Physics (12) (ELCA)

Newton's Law and VectorsEdit

Changes in MotionEdit

ForceEdit

Force – A push or a pull.

  • Force can cause a change in velocity (Acceleration)
  • Force can cause a change in direction
  • The SI unit of force is Newton (N)
    • Derived Mass and Acceleration
    • Force(N) = Mass (kg) • Acceleration (m/s2)

Force = ma
Fw = mg

Two Types of ForcesEdit

1) Contact Force

  • Forces that are in contact with another
    • Baseball hitting a baseball bat
    • Defensive tackle hitting a quarterback

2) Field

  • Forces that do not involve physical contact.
    • Electromagnetic Force
    • Gravity

Forces as Vectors ("Oh happy days!"- Ms.Hodges)Edit

Forces effect depends upon magnitude of the force.
Forces effect on an object depends upon the direction of the force.

Therefore, force is a vector.

Force DiagramsEdit

File:Force Diagram.jpg

  • Force diagram, show force as arrows.
    • Tail of the arrow is attached to the object on which the force is acting.
    • Assume all forces act on a perpendicular point, no matter where the force is applied.

Steps to drawing the DiagramsEdit

  1. Draw a sketch representing just the isolated object.
  2. Position the object in the same way as in the situation.
  3. Show the force exerted on the object.
    1. Draw as an arrow and label with words or size of the force acting on the object.

Normal ForceEdit

Normal force is the force that is perpendicular to the force being place upon an object.

Example: gravity is pushing one down and the earth is pushing one up.

  • Normal–force that pushes back up on an object from the surface.

Newton's Laws (notes from Powerpoint)Edit

Newton's First Law of Motion (Introduction)Edit

  • Newton's First law of motion deals with force and inertia.
  • Force–A push or a pull that has the ability to make a change in an objects motion.
    • Force's can...
      • increase the speed of an object.
      • decrease the speed of an object.
      • change the direction in which the object is moving.
    • Force does not have to change the motion of an object, but it must hav the ability to do so.
    • Forces can be created by different processes, such as gravity, air movement, electricity, and magnetism, even light.

Forces and MotionEdit

  • Forces create change in motion.
  • Their can be NO change in motion without having a force.
  • Example: a ball rolling down hill stops when it hits a wall. The wall exerted a force that stopped the ball.

InertiaEdit

  • Inertia is a term that measures the ability of an object to resist a change in its state of motion.
  • More mass means more inertia; more inertia means more force required to either start an object moving or to stop it from moving.

Newton's First Law of MotionEdit

  • Newton's First Law of Motion is also known as the Law of Inertia.
  • An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a straight line) unless the object experiences a net external force.
  • In the absence of forces a body will preserve its state of motion. If the net external force is zero, its acceleration (change in velocity) is zero.

How Newton's First Law is AppliedEdit

  • Seat belts and Air Bags
    • While driving along, if you suddenly slam on brakes, your body wants to continue moving at the same rate that it had been moving your seat belt applies a force to counteract you inertia and slow your body down with the car.

Newton's Second LawEdit

  • The acceleration of an object is equal to the force you apply dived by the mass of the object.
    • F=ma

Thoughts on Newton's 2nd LawEdit

  • If you apply more force to an object, it accelerates at a higher rate.
  • If an object has more mass it accelerates at a lower rate because mass has inertia.
  • The rate of acceleration is the ration of force divided by mass.

Acceleration and Newton's 2nd LawEdit

  • Coasting at constant speed (hence, no acceleration) requires no force (assuming no friction)
  • Increasing or decreasing speed, or turning (all forms of acceleration) requires a force.

In a nut shellEdit

  • Force causes acceleration.
  • Mass resists acceleration.

Units of ForceEdit

  • English system: pounds (lb.)
    • Defined by gravity
      • When you weigh yourself on the bathroom scale, you are measuring the force of gravity on your mass.
  • SI: newtons (N)
    • Force it takes to accelerate 1 kg at 1 m/s

Those Wonderful ConversionsEdit

  • The newton (N) is a smaller unit that the pound
  • 1 pound = 4.45 N

What is a NewtonEdit

  • 1 Newton is equal to 1-kg mass being accelerated at a rate of 1 m/s2
  • In problems, when you have newtons and need to solve for something else
    • A N can be replaced with the derived unit, kg•m/s2

Net ForceEdit

  • The force referred to in Newton's 2nd law of motion is a net force.
  • Net means total.
  • To solve problems with multiple forces, you have to add up all the forces, you have to add up all the force, you have to add up all the forces to get a single net force befor you calculate acceleration.

Using Newton's 2nd LawEdit

  • When working with Newton's 2nd law in calculations, mass must be in kilograms, acceleration must be in m/s2, and force must be in newtons.
  • You may have to convert before doing the problem.

Example:

Moving ObjectsEdit

  • Dynamic refers to motion.
  • In dynamic problems, Newtons 2nd law is used to calculate the acceleration of an object when you know the force and mass.
  • Acceleration is in the same direction as the net force.
  • Speed increases when the net force is in the same direction as the motion.
  • Speed decreases when the net force is in the opposite direction as the motion.

Showing directionEdit

  • Positive and negative numbers are used to show direction of force and acceleration
  • When speed, force, and acceleration point to the right, they are positive.
  • When speed, force, and acceleration point in the left direction, they are negative.

The Sign of AccelerationEdit

  • Acceleration always has the same sign as the net force.
  • When both speed and acceleration have the same sign, the speed increases with time.
  • When both speed and acceleration have opposite signs, speed decreases with time.

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Take another look at 2nd lawEdit

  • If you know mass and acceleration, you can determine the required force to make the object accelerate at a specific rate.
  • You can also determine how much force must have been present to cause an observed acceleration.

Zero Net forceEdit

  • When acceleration is zero, Newton's 2nd law allows us to calculate unknown forces in order to balance other known forces

File:Gymnast.jpg

  • This gymnast is hanging motionless
  • No acceleration, no force?
  • Force of gravity pulling down = 700N
  • Net force = 0, how?

EquilibriumEdit

  • The condition of zero acceleration is called equilibrium.
  • In equilibrium, all forces cancel out leaving a zero net force
  • In the previous example, to only way that equilibrium can be achieved is by each of the ropes pulling upward with 350 N each.

Static ProblemEdit

File:Dogseatpeople.jpg

  • Static Problems have no motion.
  • Zero net force
  • How much force does the woman have to exert to keep the dogs from moving.

Newton's 3rd LawEdit

  • For every action there is an equal and opposite reaction.
  • Discusses pairs of objects and the interaction between them.
  • In nature, forces always occur in pairs.

Moving in spaceEdit

  • In space, there is nothing to push against, so moving around is difficult.
  • The solution to the problem is to throw something opposite the direction you want to move.

Action-Reaction PairsEdit

  • The two forces in a pair are called action and reaction.
  • Anytime you have one, you also have the other.
  • If you know the strength of one, you also know the strength of the other since both forces are always equal.
  • The action-reaction forces always point in exactly opposite directions and act on different objects.

Comparing Newton's 3rd lawEdit

  • Newton's 1st and 2nd laws apply to single objects
    • 1st – an object will remain at rest until acted upon by an external force.
    • 2nd – the net force causes acceleration and mass resists acceleration for an object

Newton's 3rd lawEdit

  • Applies to pairs of objects
  • "For every action force there is a reaction force that is equal in strength and opposite in direction."
  • Action/reaction forces act on separate objects, not on the same object.

Example of action-reaction PairsEdit

File:Skateph.jpg

  • To move a skateboard, you push your foot against the ground.
  • The reaction force is the ground pushing back against your foot.

Results of ForceEdit

  • The reaction force makes you move because it acts on you.
  • You don't make the ground move because the earth is too massive to move with your puny effort.

Canceling Forces?Edit

  • Action-reaction pairs don't cancel each other out because they act on different objects.
  • The action force of your foot acts on the Earth
  • The Earth reaction force acts on you.

Which is WhichEdit

  • It doesn't matter which is the action force and which is the reaction.
  • The action force makes its counterpart the reaction
  • You have to recognize which force acts on which object, so you can apply the 2nd law properly and identify the forces acting on the object for which you're trying to find the acceleration.

Problem SolvingEdit

File:Cartstuff.jpg

  • Small cart attached to a spring.
  • You push the spring against a wall, creating a force.
  • When the cart is released, the force from the spring accelerates the cart away from the wall.

Which force created the acceleration?Edit

  • The force from the spring is pushing on the wall.
  • The reaction force of the wall pushes back on the spring, accelerating the cart

ClarificationEdit

  • Action-Reaction forces always act on different objects
  • Any force created by an object cannot accelerate the object itself.

File:Folksonrug.jpg

Forces SketchEdit

  • How much force will keep the rug from slipping?
  • 3 force of 250 N each are being applied
  • Each person applies a force to teh cart and the cart applies an equal and opposite force to the person.

File:Manpushingbox.jpg

  • The force on the rug is the sum of the reaction forces acting on each person.
  • The total force that must be applied to the rug is 750N in order to equal the reaction forces from all 3 people.

LocomotionEdit

How does locomotion apply Newton's 3rd law?

  • On land?
  • On sea?
  • On air?
  • With Jets?

Forces in Two Dimensions (Chapter 7.3)Edit

The force vector is a way to precisely describe the strength and direction of a force.

File:Force35angle.jpg If you push a block from the horizontal, some of your force accelerates the block and some of the force pushes the block into the table.

Written as x,y coordinates: F=Fx(cosø), Fy(sinø)

The magnitude of the force vector is the strength of the force. The x- and y- components of a force vector can be thought of as actual forces. If the x and y component forces were applied along their axes, their effect would be exactly the same as the single resultant force.

Equalibrium of forcesEdit

If an object is in equilibrium, all the forces acting on it are balanced and the net force is zero. If the forces act in 2 dimensions, then all of the forces in the x-direction and y-direction balance separately. So, the forces in the x-direction must equal zero, and the forces of y must equal zero.

A gymnast with a weight of 700N supports himself with 2 rings. If he is at rest (an in equilibrium), the net force on his body is zero. Gravity pulls down with a force of 700N, so the ropes must pull on his arms with a force of 350N each (½ of his weight supported by each arm)

If the gymnast is holding himself with his arms outstretched at 45º angles, the work is more strenuous because only part of the force from each arm is vertical. The total force must be large because the veritcal component of force in each arm must still equal ½ his weight.

Equilibrium in y-direction
350N = Fy = F (sin(ø)) 350N = F sin 45º F = (350N / sin (45º) ) = 495 N

The horizontal components of force from the left and right arms cancel each other because they have equal magnitude and are in opposite direction.

Incline PlaneEdit

An inclined palne is a straight surface, usually with a slope. The angle of the incline is the angle relative to the horizontal direction. When objects move along an incline, the move parallel to the surface.

A block sliding down a ramp has 3 forces acting on it:

  1. Gravity
  2. The Reaction Force form the surface (Normal Force)
  3. Friction

Motion along the ramp depends on the sum of these 3 forces. Because the ramp is usually at an angle, these 3 forces must be treated as vectors. The best coordinates to use for an inclined plane are aligned with the surface. By lining up the coordinates with the incline, motion in the x-direction is along the surface.

Usually there is no mater in the y-direction because this would mean the object is lifting off or going through the ramp.

Resolving Weight Vectors in Ramp CoordinatesEdit

The force of gravity on an object always acts in a direction towars the center of the Earth. When the surface is a ramp, the direction of gravity is still straight towards the ground, but it is NOT perpendicular to the surface of the ramp.

To treat the force of gravity, it must be resolved into components parallel (x) and perpendicual (y) to the ramp. If the angle is ø, then the weight of the block is represented by the vector Fw = mg (sin (ø) ), mg (cos (ø) ).

Force along the inclineEdit

A block accelerates down a ramp because its weight creates a force parallel to the incline. Analyzing the force, the force parallel to the surface is Fx = mg (sin (ø) ).

NormalEdit

Normal means perpendicular. For a block on a ramp, equilibrium of forces perpendicular to the ramp is what prevents the block from going through the ramp or lifting off of it. To make equilibrium in the y-direction, the normal force on the block is equal and opposite to the component of the block's weight perpendicular to the ramp (Fy). Fn = + mg ( cos (ø) )

Equilibrium in the y-direction: Fy + Fn = 0

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