Introduction to Force

Introduction to Force

• Force is a push or pull on an object and attempts to change its state of rest or motion.
• The symbol for force is F.
• The SI unit is the Newton, symbolized as N.
• Force has magnitude and direction and is a vector.
• When exerting a force, two objects are involved and interact, either by direct contact or without it.

Kinds of Forces: Contact and Non-Contact Forces

• Most forces are contact forces, exerted when objects touch.
• An applied force is externally applied to an object (e.g., a push or pull).
• Normal force is the force exerted by a flat surface (plane) on an object in contact with it, and always acts at right angles (perpendicular) to the surface.
• For example using values of 20kg and 9.11ms-1, N = 196N and is equal to the gravitational force and all other forces acting on the surface

Frictional Force

• Frictional force, denoted as f or F_tr, resists the movement of an object and is caused by one surface moving or scraping over another.
• It is parallel to the surface, acting in the opposite direction to the object's motion.
• A frictional force is a contact force exerted by a surface on an object, parallel to the surface, to resist the object's movement over it.
• Static frictional force is experienced by an object at rest when forces act on it.
• No static frictional force is experienced when there is no applied force on an object at rest.
• The static frictional force is = applied force (f = F₁ when an object is at rest)
• Increase the applied force to the point of breaking contact (fsmax)
• The static frictional force increases to a maximum as the forces trying to set the object in motion increase.
• Maximum static frictional force on an object relies on the normal force (N) exerted by the plane on the object.
• A greater weight leads to a greater normal force, requiring more applied force for movement
• The types of surfaces (texture and material composition) dictate the friction magnitude, which is indicated by static friction coefficient (μs) .
• mu_{s} is a constant of proportionality without a unit, ranging from 0 (frictionless) to a maximum value (maximum Friction)
• f s max = mu s .N where fs max = maximum static frictional force in newtons (N)
• μs = coefficient of static friction; N = normal force in newtons (N).
• The frictional force f_s while an object is at rest is less than fs frax
• On a horizontal plane N = Fg
• On an inclined plane, gravity pulls directly downwards, so the force is not perpendicular to the surface.
• On an inclined plane the weight is 2D and resolved in 2 components:
• Parallel component tends to slide the object down the plane, and increases with the angle of inclination.
• The perpendicular component pushes the object toward the plane, and decreases as the angle of inclination increases.
• The angle between F_{g} and F_{0} equates to the angle of inclination 8.
• When an object is at rest on an inclined plane, the forces are in equilibrium such as F - a =0 -F
• On a horizontal plane the frictional force is a maximum f soax
• The greatest angle at which the object remains at rest and forces are in equilibrium = frictional force is a maximum f soax
• mu_{n} = tan theta is dependent on surface types
• The kinetic frictional force (f_{x}) occurs as soon as an object is set in motion
• A smaller force is required to keep an object moving at a constant velocity than from rest, therefore, f 3 <f 3 = ax.
• Kinetic frictional force depends on the plane's normal force, the type of materials.
• Frictional force is independent of contact area and velocity of motion.
• Friction coefficients are usually < 1 and depend on surfaces in contact.
• The counteractive force an object experiences moving over another with contact is kinetic frictional force.
• Non-contact forces are exerted over a distance, without touching.
• E.g. Weight/gravitational pull (F) is when Earth exerts a gravitational pull on any object with mass near its surface calculated as: Wmg (gravitational acceleration g = 9.8 m.s²
• Earth weight force is directed towards the earth's centre, i.e. directly downwards.
• Magnetic forces, either attractive or repulsive, between magnetic objects are non-contact forces
• Electrostatic forces are attractive or repulsive, between charges on charged objects are non-contact forces

Force and Free-Body Diagrams

• Both show forces on a single object
• A force diagram draws objects and represents forces using arrows.
• The object is drawn, and all the forces on the object are indicated by arrows.
• The length of the arrow indicates the magnitude of the force and the arrow shows the direction.
• A pull/brake force originates on the object and points away from it.
• External push force originates elsewhere and ends on the object
• The object is represented by a dot in a free-body diagram and all the forces acting on the object are shown as arrows from the dot.
• Opposite signs denote forces in opposite directions when substituting into equations.
• If vertical motion is absent, vertical forces are in equilibrium and the vertical resultant vector is zero.
• F gj is always one such force acting parallel to an inclined plane, F_{T} and f may be included
• Friction force is opposite to the direction of motion (Delta*x)

Newton's First Law of Motion

• Before the mid-16th century, scholars believed forces were needed for continuous motion.
• Galileo realized friction impacts motion.
• Galileo proved reduced friction means objects take longer to stop.
• Galileo concluded eliminating friction would allow constant, unrestricted linear motion at constant velocity, no forces needed.
• Isaac Newton (1643-1727) expanded on Galileo's studies.
• Newton's First Law: An object remains at rest or in uniform motion in a straight line unless acted upon by a resultant force.
• When the net force equals zero (Finet = 0 N), the forces are in equilibrium and the object maintains its state of rest or motion.
• Inertia lets a body resist changes in motion.
• The greater mass leads to greater inertia.
• Without resultant force the state of rest/motion is maintained
• Safety belts protect vehicle occupants by counteracting their inertia when the vehicle suddenly stops.
• A person in a moving vehicle travels at the same velocity as the vehicle so when the vehicle stops the passengers will also continue at the same rate due to his inertia

Newton's Second Law of Motion

• From Newton's First Law, if the net force on an object is zero (F rat =0 N), its state of rest or motion will remain unchanged
• Change only occurs if a non-zero net force is applied.
• When a resultant force (F ruul /F ruo >0) is applied to an object, it will accelerate in the direction of the force.
• The acceleration is directly proportional to the force and inversely proportional to the mass (a α F net, a α 1/m).
• 1 Newton is the force applied when a 1 kg object accelerates at 1 m/s².
• Vector addition of forces gives resultant along horizontal, vertical, or inclined planes
• If F rax =0, then a = 0. The object moves at a constant velocity
• An object will accelerate in the direction of the resultant force.
• F cac = ma or a = F mat m
• F is a vector sum of forces.
• Determining missing values may require considering forces.
• Problems are those where one object of one or more forces act
• An object of 8kg accelerates to the left at 2ms^-2
• Solution 1 is to find frictional force f with F net =ma F_{T} + f = ma 20 + f = 8(2), where 14 f = 4N right.
• m = 8kg Fr 20 N lelt a= 2m .s^ 2 left where calculated N= 8 *9.8 =78.4N and the mu{k} is calculated at 0.05
• Consider two objects in contact and accelerating jointly, two blocks are connected by a light string
• Push force F_{1} on A (or B) accelerates system, with A and B sharing acceleration.
• The blocks push equally against each other.
• A pull force Fs on B (or A) tightens the string and Tension (Tis is present at both ends of the string
• A and B have the same acceleration, therefore they experience an equal tensile force (T) in opposite directions
• When two objects A and B are connected by a light string over a frictionless pulley: equal tension T acts on A and B in opposite directions, gravitational force accelerates the system.
• Steps in problem-solving include:
• Draw a force or free-body diagram for each object.
• Determine Fret for each object
• State a separate equation and Fnet ma for both objects
• If acceleration a and one force is unknown, use to simultaneous calculations
• Substitute to calculate contact force between objects or tension in string

Newton's Third Law of Motion

• Newton II (Fma applies to a single object
• Nawtion III is where at least wo objects interact
• Newton III: When two objects interact, they simultaneously exert equal but oppositely directed forces.
• Forces work in pairs the two forces
• Have of equal magnitude
• Act in opposite directions
• Act on different objects and therefore don't balance each other out
• If a book on a table exerts downward force, the table exerts a equal upward force equal to the normal force (N).
• A second such force pair includes the gravitational pull of the book to earth, in return earth exert a equal but opposite force on earth
• The earth (A) exerts an attractive force on a planet (P,) and P exerts an equal but oppositely directed force on A

Newton's Law of Universal Gravitation

• Newton's Law of Universal Gravitation was inspired by realizing the earth attracts a falling apple.
• Gravitational force is described as attractive and non-contact, existing between objects with mass in the universe as long as mass is involved.
• Earth pulls the apple and moon, and conversely, the apple/moon attract Earth.
• This magnitude relies on:
• Magnitudes of their masses
• Distance between their centres
• It gravitational force is directly proportional to the product of masses and inversely proportional to the square of the distance between them
• Each particle exerts a gravitational pull on every other particle. The force is directly proportional to the product of masses and inversely proportional to the square of the distance between them This translates into Fu=Gm1.m2d^2
• gravitational pull F_{g} in newtons (N)
• Masses of the objects, m_{1} m_{2} in kilograms (kg)
• The distance d between their centres in metres (m)
• G = universal gravitational constant =6.67* t0^-11 N. m^2kg^-2
• An example has been calculated for you in these notes
• Mass of the earth (M) = 5.98 * 10 ^ 24 *k ;radius (2) 6.38x10 m
• Barth, solut, 21, 22 values are used in an example given on page 46 of your notes
• Similarly 10 000m distance is calculated (please see the original document) note that the earth exerts an attractive force on
• Even at a great distance the height of 10 000m is still comparitively small
• Wei,T, F,g values are used in an example on page 47

Weight

• This gravitational pull that can be calculated by W = mg (with gravitational pull of the earth on/near its surface g=9.8 m.s^ -2)
• Weight always forces on an object, down towards centre of earth.
• In the absence verticle motion, gravitational of g follows F nat =ma
• Gravitational acceleration (g) can be affected by air resistance, particularly objects falling from the same object that have different masses
• Free-falling objects have equal acceleration when air resistance is eliminated at mathfrak g = 9.8 =9.8 m.s^ -2
• g is independent of mass of the object such taht mg = G * (mM)/(d^2) g = G * M/( d^2)
• Dependence relies earth mass and distance from its centre
• g near planets can be calculated using their mass and radius.
• Comparison between Earth/moon highlights Earth's stronger pull due to larger mass.
• Moon weight is about one-sixth Earth weight.
• A person's weight on the moon is about a sixth of theirearth weight, causing buoyancy instead of walking.
• The value of y differs depending on where you are in the world such as:
• Cape Town g= 0.976m .s^ -1
• Poland g = 9,785m *z^2 g = 9.632m
• The planets varies and therefore the weight of an object. However, the mass of an object is the same everywhere

Distinction Between Mass and Weight

• Mass is the matter quantity that remains fixed in the universe.
• Inertia is a measure and inertial mass can increase/decrease
• The Si unit for mass is the kilogram (kg).
• Weight is gravitational pull, varies by planet.
• The St unit for weight is the newton (N)
• Weightlessness happens when no gravitation is on it.
• Yet a sense of weight can be experienced in a gravitational field
• Sensation from gravity is caused by the pressure of upwents fromon that floors against each other, and an object is determined by the nomal exerted by the surface on which they rest
• Objects experiences weightteesmess such as when an floor is in freewill or gravitational is the only force acting on him such as when the floor gives way