Hockey Puck Dynamics and Net Force

Newton's Laws of Motion

• Dynamics studies the relationship of motion to its causes
• The principles of dynamics were clearly stated for the first time by Sir Isaac Newton

Newton's Laws of Motion and Classical Mechanics

• Newton did not derive the laws of motion
• Instead Newton deduced them from experiments by other scientists, e.g., Galileo
• Classical mechanics, also called Newtonian mechanics, are founded on Newton's Laws
• Only need modification only for situations involving extremely high speeds (near the speed of light) or very small sizes (such as within the atom).

Adjusting Understanding to Physical Experiments

• The job of studying physics means helping you to recognize how "common sense" ideas can lead astray
• Physical understanding must be consistent with experiments

Force and Interactions

• Force is a push or pull, therefore it is an interaction
• The interaction occurs between two objects or between an object and its environment
• That is why we always refer to the force that one object exerts on a second object
• Force is a vector quantity; you can push or pull an object in different directions

Contact Forces

• Contact force involves direct contact between two objects, such as a push or pull
• Normal force is exerted on an object by any surface with which it is in contact and acts perpendicular to the surface
• Friction force is exerted on an object by a surface and acts parallel to the surface, opposing sliding
• Tension force is the pulling force exerted by a stretched rope or cord on an object and acts along the rope

Long-Range Forces

• Long-range forces act even when objects are separated by empty space
• The gravitational force that the earth exerts on your body is called your weight

Measuring Force

• The SI unit of magnitude of force is the newton, abbreviated N
• A common instrument for measuring force magnitudes is the spring balance

Superposition of Forces

• When two forces F₁ and F₂ act at the same time at the same point on an object, the effect is the same as if a single force R were acting equal to the vector sum, or resultant, of the original forces: R = F₁ + F₂.
• Any number of forces applied at a point on an object have the same effect as a single force equal to the vector sum of the forces
• Important principle is called superposition of forces

Solving Force Problems

• Forces are vector quantities and add like vectors
• Therefore use all of the rules of vector mathematics to solve problems involving vectors

Adding Forces by Components

• Easiest to add vectors by using components
• Describe a force F in terms of its x- and y-components Fx and Fy
• Net force acting on an object is the vector sum (resultant) of all forces:
  • R = ∑F = F₁ + F₂ + F₃ + …The net force acting on an object is the vector sum, or resultant, of all individual forces acting on that object.
• The x-component of the net force is the sum of the x-components of the individual forces, and likewise for the y-component:
  • Rx = ΣFx Ry = ΣFy
• Magnitude calculation:
  • R = √(Rx^2) + (Ry^2)
• The angle θ between R and the +x-axis to the relationship
  • Tanθ = Ry/Rx

Newton's First Law of Motion

• It is impossible for an object to affect its own motion by exerting a force on itself Forces that affect an object's motion are external forces, those exerted on the object by other objects in its environment
• The question that needs answering is this: How do the external forces that act on an object affect its motion?
• With zero net external force, then an object at rest, will remain at rest
  • But what if there is zero net external force acting on an object in motion?

Motion

• A big mistake is thinking that in motion naturally come to rest and that a force is required to sustain motion.
• Instead, when no net external force acts on an object, the object either remains at rest or moves with constant velocity in a straight line
• No net external force is needed to keep it moving and not force is required to sustain motion

Newton's First Law Definition

• An object acted on by no net external force has a constant velocity (which may be zero) and zero acceleration

Inertia

• Inertia is the tendency of an object to keep moving once it is set in motion (or stay at rest)

Real World Inertia

• The net external force is what matters in Newton's first law
• For example, a physics book at rest on a horizontal tabletop has two forces acting on it: an upward supporting force, or normal force, exerted by the tabletop and the downward force of the earth's gravity
• The upward push of the surface is just as great as the downward pull of gravity, so the net external force acting on the book (that is, the vector sum of the two forces) is zero
• Therefore the book remains at rest and the same principle applies when an object slides on a frictionless surface - vector sum is zero, therefore the motion is constant

Equilibrium

• When an object is either at rest or moving with constant velocity, we say that the object is in equilibrium
• For an object to be in equilibrium, it must be acted on by no forces, or by several forces such that their vector sum, - that is, the net external force-is zero:
  • ΣF = 0

Inertial Frames Of Reference

• A frame of reference is central to Newton's laws of motion
• Newton's laws are valid in some frames of reference and not valid in others
• A frame of reference in which Newton's first law is valid, is called an inertial frame of reference

Law of Inertia

• When the bus is accelerating with respect to the earth and is not a suitable frame of reference for Newton's first law, the passenger's velocity relative to the vehicle changes
• Therefore an observer in the vehicle's frame of reference might be tempted to conclude that there is a net external force acting on the passenger
  • However it should be emphasized that The vehicle observer's mistake is in trying to apply Newton's first law in the vehicle's frame of reference, which is not an inertial frame and in which Newton's first law isn't valid - Use inertial frames of reference

Inertial Frame Variety

• Many inertial frames exist.
• If we have an inertial frame of reference A, in which Newton's first law is obeyed, then any second frame of reference B will also be inertial if it moves relative to A with constant velocity vB/A (we don't need to define that constant velocity to prove it)

Force, Velocity And Frames Of Reference

• There is no single inertial frame of reference that is preferred over all others for formulating Newton's laws
• If one frame is inertial, then every other frame moving relative to it with constant velocity is also inertial - state of rest and the state of motion with constant velocity are not very different; both occur when the vector sum of forces acting on the object is zero.

Newton's Second Law Law

• When an object is acted on by zero net external force, the object moves with constant velocity and zero acceleration
• A hockey puck is sliding to the right on wet ice
  • There is negligible friction, so there are no horizontal forces acting on the puck; the downward force of gravity and the upward normal force exerted by the ice surface sum to zero
• If the net external force acting on the puck is zero, the puck has zero acceleration, and its velocity is constant

Applying Force

• Applying a constant horizontal force to a sliding puck in the same direction that the puck is moving means
  • ΣF is constant and in the same horizontal direction as v
  • We find that during the time the force is acting, the velocity of the puck changes at a constant rate and it is under constant acceleration

Force Opposite vs Acceleration

• Reversing the direction of the force on the puck so that ΣF acts opposite to v also means that the puck has an acceleration
• In each case, an acceleration occurs if and only if ΣF is constant

Force Conclusions About Acceleration

• The force exerted on an object causes the object to accelerate in the same direction as the acceleration and net external force (direct relationship)
• The greater the force placed on the object means an equivalent increase to the acceleration

Mass And Force

• For a given object, the ratio of the magnitude | ΣF| of the net external force to the magnitude a = |a| of the acceleration is constant, regardless of the mag-nitude of the net external force.
• Call this ratio the inertial mass, or simply the mass, of the object and denote it by m

Mass Equation

• m = |Σ̅̅F̅ | / |a| | Σ̅̅F̅ | = ma
• The greater an object's mass, the more the object resist

Mass And Inertia

• Mass is a quantitative measure of intertia

The Newton

• One newton is the amount of net external force that gives an acceleration of 1 meter per second squared to an object with a mass of 1 kilogram
• 1 newton =(1 kilogram)(1 meter per second squared) or 1N = 1 kg*m / s^2

Stating Newton's Second Law of Motion

• Experiment shows that the net external force on an object is what causes that object to ac-celerate
• superposition of forces principle also holds true when the net external force is not zero and the object is accelerating
• Equations (4.4) relate the magnitude of the net external force on an object to the mag-nitude of the acceleration that it produces
• Newton's Second law:
  • THE second law of motion: IF a net external force acts on an object, the object accelerates.
  • The direction of acceleration is the same as the direction of the net external force. The mass of the object times
  • The the acceleration vector of object equals the net external force vector.

Newton's Second Law Summary

In symbols, ∑F = ma - the object accelerates in the same direction as the net external force is on an object.

Newton's Second Law Importance

• Newton's second law is a fundamental law of nature, the basic relationship between force and motion
• Equation (4.6) has many practical applications and actually been used
• For example In your inner ear, microscopic hair cells are attached to a gelatinous substance that holds tiny crystals of calcium carbonate called otoliths. - They sense the magnitude and direction of your acceleration

Using Newton's Second Law

• First, the relationship between forces must be a vector equation and used in component form - Newton's second law: The component of acceleration equation: , where all terms equals the object's mass times the corresponding acceleration component.
• Second, the statement refers ton external forces
  • Ex] A kicked soccer ball only moves because of external forces

Newton's Second Law Validations

• Equation (4.7) is valid only when the mass m is constant
  • Must avoid systems that have mass change like a leaking tank truck
• Newton's second law is valid in inertial frames of reference only, just like the first law
  • Do NOT use the law to non-inertial references like an accelerating car

Do Not Overlook "mass x acceleration" as external force

Do not use m*a as equal to all of the individual force sum, acceleration is that force causes from its use and Also avoid applying Newton's second law to solve problems if not an initial force reference

Newton's Third Law Of Motion

• A force acting on an object is always the result of its interaction with another object, so forces always come in pairs
• The force you exert on the other object is in the opposite di-rection to the force that object exerts on you
• Newton's third law of motion: if object a exerts a force on object b ("action"), then abject b exerts a force on object a which is called as reaction. These forces have the same magnitude but are opposite

Examine the relationship between net external forces and motion, focusing on scenarios involving hockey pucks. Understand how forces affect velocity, acceleration, and direction. Questions cover constant velocity, acceleration, and free-body diagrams.