Physics: Tension, Forces, and Newton's Laws
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Questions and Answers

What causes the top string to break when it is pulled down slowly?

  • The weight of the ball. (correct)
  • The density of the ball.
  • The volume of the ball.
  • The mass of the ball.

    • According to Newton's 2nd Law, how is acceleration related to net force and mass?

  • Acceleration is directly proportional to net force and inversely proportional to mass. (correct)
  • Acceleration is inversely proportional to net force.
  • Acceleration does not depend on mass.
  • Acceleration is directly proportional to mass.

    • If both the net force and the mass of an object are doubled, what happens to the acceleration?

  • Acceleration increases by a factor of four.
  • Acceleration doubles.
  • Acceleration remains unchanged. (correct)
  • Acceleration is halved.

    • What occurs to acceleration if the net force acting on an object is quadrupled while the mass remains constant?

    <p>Acceleration will quadruple.</p> Signup and view all the answers

    If a car can accelerate at $2 ext{ m/s}^2$, what is the acceleration when towing another car of equal mass?

    <p>1 m/s²</p> Signup and view all the answers

    How does increasing an object's mass affect its acceleration when a constant net force is applied?

    <p>Acceleration decreases.</p> Signup and view all the answers

    Under which condition would an object's acceleration be most affected?

    <p>When the mass is increased and net force is constant.</p> Signup and view all the answers

    What relationship does Newton's 2nd Law establish between force, mass, and acceleration?

    <p>Force is equal to mass multiplied by acceleration.</p> Signup and view all the answers

    What does the term 'normal' refer to in the context of forces?

    <p>The force exerted perpendicular to a surface</p> Signup and view all the answers

    If a person evenly distributes their weight across two bathroom scales, what will each scale read?

    <p>Half of their weight</p> Signup and view all the answers

    In the context of a gymnast hanging from two rings, how do the scale readings compare to her total weight when evenly distributed?

    <p>Half her weight in each scale</p> Signup and view all the answers

    In static equilibrium, what is the relationship between the sum of forces and motion?

    <p>The sum of forces equals zero, and the object is at rest</p> Signup and view all the answers

    If a gymnast supports more weight on one ring than the other, how will the scale on the ring with less weight behave?

    <p>Read less than half her weight</p> Signup and view all the answers

    What type of motion is characterized by constant speed in a straight line?

    <p>Dynamic equilibrium</p> Signup and view all the answers

    What can be inferred about the forces acting on an object in equilibrium?

    <p>The sum of forces acting on the object is zero</p> Signup and view all the answers

    Which statement correctly describes a situation when two scales measure the weight of an object?

    <p>The scales will read different values if the weight is unevenly distributed</p> Signup and view all the answers

    What does Newton's 3rd Law state about forces in interactions?

    <p>Forces always occur in pairs.</p> Signup and view all the answers

    Why does Earth not 'jump up' when a boulder exerts a force on it?

    <p>Earth's mass is much larger than that of the boulder.</p> Signup and view all the answers

    What is the relationship between mass and acceleration as per Newton's 3rd Law?

    <p>Acceleration is inversely proportional to mass.</p> Signup and view all the answers

    In a scenario where a cannon fires a cannonball, why does the cannonball accelerate more than the cannon?

    <p>The cannonball has a smaller mass.</p> Signup and view all the answers

    What occurs when a balloon is released and the trapped air escapes?

    <p>The balloon recoils and climbs upwards.</p> Signup and view all the answers

    When swimming, how do the forces between a swimmer and water operate?

    <p>The swimmer pushes water backward, and water pushes the swimmer forward.</p> Signup and view all the answers

    How does the interaction between the tires of a car and the road contribute to motion?

    <p>The tires push against the road, and the road pushes back on the tires.</p> Signup and view all the answers

    What primarily determines the acceleration experienced by an object when subjected to force?

    <p>The amount of force and the object's mass.</p> Signup and view all the answers

    What is necessary for a system to accelerate?

    <p>The presence of external forces</p> Signup and view all the answers

    In the context of the horse-cart system, what role do the forces exerted by the horse on the cart and the cart on the horse play?

    <p>They cancel each other out and do not contribute to acceleration</p> Signup and view all the answers

    What forces interact to provide acceleration for the horse-cart system as a whole?

    <p>The forces between the horse and the ground</p> Signup and view all the answers

    What happens when the apple pushes against the floor?

    <p>There is a simultaneous reaction force from the floor</p> Signup and view all the answers

    In a situation involving interatomic forces within a baseball, how do these forces affect the ball's acceleration?

    <p>They combine to zero, having no impact on acceleration</p> Signup and view all the answers

    Why does the farmer focus on the net force exerted on the cart system?

    <p>The horse's acceleration is irrelevant to the cart</p> Signup and view all the answers

    What is the role of the ground in the horse's movement?

    <p>The ground interacts and pushes the horse forward</p> Signup and view all the answers

    What contributes to the acceleration of the entire horse-cart system?

    <p>The interaction with the ground</p> Signup and view all the answers

    What is the equation for the net force acting on the cart?

    <p>∑ 𝑭𝑭 = 𝑃𝑃 - 𝑓𝑓</p> Signup and view all the answers

    According to Newton’s laws, what happens if the net force on an object is not zero?

    <p>The object will accelerate according to Σ𝐹⃗ = 𝑚𝑎⃗.</p> Signup and view all the answers

    What is the primary direction of Nellie Newton's force when pulling the sled?

    <p>A combination of horizontal and vertical.</p> Signup and view all the answers

    What are the two other forces acting on the sled, apart from Nellie's force?

    <p>Weight and normal force.</p> Signup and view all the answers

    Which of the following statements accurately represents Newton’s Third Law of Motion?

    <p>For every action, there is an equal and opposite reaction.</p> Signup and view all the answers

    In a free-body diagram (FBD) for an object, what does each vector represent?

    <p>The direction and magnitude of all forces acting on the object.</p> Signup and view all the answers

    What happens to the vertical component of a vector when an object is projected at an angle?

    <p>It changes depending on the angle of projection.</p> Signup and view all the answers

    If an object is not accelerating, what can be inferred about the net force acting on it?

    <p>The net force is zero.</p> Signup and view all the answers

    What is escape speed necessary for an object to leave the gravitational influence of Earth?

    <p>11 km/s</p> Signup and view all the answers

    What happens to an object that achieves escape velocity from Earth?

    <p>It will forever leave Earth's gravitational influence.</p> Signup and view all the answers

    What is the escape speed required to leave the solar system from Earth's distance from the Sun?

    <p>42 km/s</p> Signup and view all the answers

    If an object reaches the escape speed, it primarily alters its trajectory from which of the following types of orbits?

    <p>Elliptical to parabolic or hyperbolic</p> Signup and view all the answers

    Which statement about escape velocity is incorrect?

    <p>Escape velocity is dependent on the mass of the object.</p> Signup and view all the answers

    How does an increase in rotational speed affect tangential speed?

    <p>It increases tangential speed.</p> Signup and view all the answers

    What is the relationship between the radius from the axis and linear speed?

    <p>Linear speed increases with an increasing radius.</p> Signup and view all the answers

    What direction does centripetal acceleration point?

    <p>Towards the center of the circle.</p> Signup and view all the answers

    What essential condition allows a car to remain on a curved path while driving?

    <p>There must be sufficient centripetal force.</p> Signup and view all the answers

    What happens to water in a washing machine during the spinning cycle?

    <p>It flies off tangentially due to insufficient centripetal force.</p> Signup and view all the answers

    Centripetal force is dependent on which of the following factors?

    <p>Mass, tangential speed, and radius of the circle.</p> Signup and view all the answers

    If a friend sits halfway to the center of a rotating disk, what is her rotational speed compared to yours, sitting at the edge?

    <p>Her rotational speed is equal to yours.</p> Signup and view all the answers

    What occurs if the force of friction is insufficient for a car navigating a curve?

    <p>The car will skid off the road.</p> Signup and view all the answers

    What two factors determine centripetal acceleration?

    <p>Linear speed and radius</p> Signup and view all the answers

    What provides the centripetal acceleration for a car rounding a banked curve?

    <p>The horizontal component of the normal force and possibly friction</p> Signup and view all the answers

    What does the term 'centrifugal force' refer to in circular motion?

    <p>An apparent force perceived due to inertia when an object moves in a circle</p> Signup and view all the answers

    When analyzing a conical pendulum, what is the y-direction force equation associated with the bob's weight?

    <p>ΣF_y = Ty - mg</p> Signup and view all the answers

    In the context of a conical pendulum, which component of tension provides the centripetal acceleration?

    <p>Tx</p> Signup and view all the answers

    What must happen for an object in circular motion once the centripetal force is removed?

    <p>The object will move in a straight line tangent to the circle</p> Signup and view all the answers

    What does the tension in the string of a conical pendulum represent when resolved into components?

    <p>Both horizontal and vertical forces acting on the bob</p> Signup and view all the answers

    In a conical pendulum, when the bob is not moving vertically, what can be inferred about the net force in the y-direction?

    <p>The net force is zero</p> Signup and view all the answers

    What is the period of a geosynchronous satellite at about 6.5 Earth radii?

    <p>Approximately 24 hours</p> Signup and view all the answers

    What shape do orbits generally take around a planet?

    <p>Ellipses</p> Signup and view all the answers

    How does the altitude of a satellite affect its orbital period?

    <p>Higher altitude leads to a greater period</p> Signup and view all the answers

    What is the expected vertical distance a horizontally thrown rock will fall after one second?

    <p>5 meters</p> Signup and view all the answers

    What factor is primarily responsible for a satellite's speed at different positions in its orbit?

    <p>The distance from the planet</p> Signup and view all the answers

    What period does the International Space Station (ISS) complete an orbit in?

    <p>About 90 minutes</p> Signup and view all the answers

    For a projectile with high speed, where is the center of Earth likely located in an elliptical orbit?

    <p>At the near focus</p> Signup and view all the answers

    In a satellite's orbit, which position will it have the least speed?

    <p>At the farthest point from the planet</p> Signup and view all the answers

    What is the result of doubling both masses and tripling the distance between them in terms of gravitational force?

    <p>The gravitational force decreases to one-ninth of its original value.</p> Signup and view all the answers

    What is the gravitational field strength at the surface of Earth as per the provided formula?

    <p>$9.8 m/s^2$</p> Signup and view all the answers

    How does the presence of mass affect the gravitational field created in space?

    <p>It creates a gravitational field that affects other masses.</p> Signup and view all the answers

    What analogy is used to explain the effect of gravitational fields on space-time?

    <p>A marble rolling on a waterbed.</p> Signup and view all the answers

    What defines the variations in ocean levels referred to as tides?

    <p>The gravitational interaction between the moon and Earth.</p> Signup and view all the answers

    If the radius of Earth is approximately $6.4 imes 10^6 m$, which of the following calculations would be used to determine the gravitational force at its surface?

    <p>$G imes rac{M}{R^2}$</p> Signup and view all the answers

    What impact does the distance between two masses have on gravitational force?

    <p>The gravitational force decreases as the distance increases.</p> Signup and view all the answers

    What physical principle underpins the explanation of gravitational fields as alterations of space?

    <p>Einstein's Theory of General Relativity.</p> Signup and view all the answers

    Why is it preferable for a car to hit a haystack rather than a concrete wall when it is out of control?

    <p>The haystack provides a longer impact time, reducing force.</p> Signup and view all the answers

    How does increasing the contact time of a punch reduce the resulting force?

    <p>The force is reduced because the time for momentum transfer is increased.</p> Signup and view all the answers

    What must happen for an object to bounce?

    <p>Its momentum must come to zero and then reverse direction.</p> Signup and view all the answers

    What is required for the momentum of a system to change?

    <p>An external force must be applied to the system.</p> Signup and view all the answers

    What is the net momentum of the cannon-cannonball system before firing?

    <p>It is zero since both cannon and cannonball are at rest.</p> Signup and view all the answers

    How does the design of Lester A. Pelton's paddle improve the efficiency of a waterwheel?

    <p>It causes the water to bounce back, increasing impulse.</p> Signup and view all the answers

    What happens to the net momentum of a system if no external forces are applied?

    <p>It remains constant.</p> Signup and view all the answers

    If the impulse delivered to a bouncing object is twice that of an object stopped at rest, what can be said about the bouncing object?

    <p>It gains more velocity than when stopped.</p> Signup and view all the answers

    What does the conservation of momentum state about two colliding objects in the absence of external forces?

    <p>The total momentum before collision equals the total momentum after collision.</p> Signup and view all the answers

    In an elastic collision, what additional condition must be met besides momentum being conserved?

    <p>Kinetic energy must also be conserved.</p> Signup and view all the answers

    Which type of collision occurs when two objects couple together after the impact?

    <p>Completely inelastic collision</p> Signup and view all the answers

    If a freight car A moving towards a stationary freight car B collides and they couple together, what happens to the speed of the coupled cars compared to the initial speed of freight car A?

    <p>It becomes half of the speed of freight car A.</p> Signup and view all the answers

    In an inelastic collision, what typically happens to the total kinetic energy of the system?

    <p>Some of it is transformed into heat or deformation.</p> Signup and view all the answers

    Which statement correctly reflects Newton's second law concerning momentum?

    <p>No acceleration implies conservation of momentum.</p> Signup and view all the answers

    What defines an elastic collision compared to an inelastic collision?

    <p>Kinetic energy is conserved in an elastic collision.</p> Signup and view all the answers

    When two identical freight cars collide inelastically and couple together, what can be said about their momentum?

    <p>Momentum remains the same before and after the collision.</p> Signup and view all the answers

    What is the unit of measurement for work, which combines a unit of force and a unit of distance?

    <p>Newton-meter</p> Signup and view all the answers

    When a force is exerted but there is no displacement of the object, what can be concluded about the work done?

    <p>No work is done</p> Signup and view all the answers

    If you push a cart with a constant force and then push it twice as far, how much work have you done?

    <p>Twice as much</p> Signup and view all the answers

    What aspect of energy quantifies a system's ability to do work?

    <p>Energy</p> Signup and view all the answers

    Which of the following scenarios does not involve work being done?

    <p>Pushing a car that doesn't move</p> Signup and view all the answers

    What is the result of doubling the load lifted a certain height compared to lifting a single load the same height?

    <p>Twice as much work is done</p> Signup and view all the answers

    What is the correct equation to calculate work done when a force is applied over a distance?

    <p>W = F.d</p> Signup and view all the answers

    Which of the following statements correctly describes energy in a system?

    <p>Energy is a conserved quantity.</p> Signup and view all the answers

    What must occur to increase the kinetic energy of an object?

    <p>Work must be done on the object.</p> Signup and view all the answers

    In the presence of friction, which factor affects the net work done on a moving object?

    <p>The frictional force opposing the motion.</p> Signup and view all the answers

    If an object’s kinetic energy remains unchanged while work is being done, what can be concluded?

    <p>The net work done on the object is zero.</p> Signup and view all the answers

    What does the term 'net work' refer to in a system with friction?

    <p>The difference between the applied force and friction.</p> Signup and view all the answers

    What impact does friction have when a crate slides and comes to a stop?

    <p>It converts kinetic energy into heat and sound.</p> Signup and view all the answers

    If a cart is moving and 100 J of work is done on it, under which condition would it not gain 100 J of kinetic energy?

    <p>If the work is done against friction.</p> Signup and view all the answers

    What would indicate that no work is being done on an object that is being pushed?

    <p>The object is not moving.</p> Signup and view all the answers

    How is the work done to stop a car determined?

    <p>By multiplying the friction force and the distance the car slides.</p> Signup and view all the answers

    What is the primary function of a lever in simple machines?

    <p>To allow a small force over a large distance to induce a large force over a short distance</p> Signup and view all the answers

    How many classes of levers are identified based on the positions of the effort, load, and fulcrum?

    <p>Three</p> Signup and view all the answers

    What does a pulley achieve when it operates?

    <p>Changes the direction of the input force and multiplies force</p> Signup and view all the answers

    What principle do all simple machines operate under?

    <p>Work in = Work out</p> Signup and view all the answers

    In terms of mechanical advantage, how can the input force be adjusted?

    <p>By making the effort distance large</p> Signup and view all the answers

    What is the role of the fulcrum in a lever?

    <p>To serve as the pivot point</p> Signup and view all the answers

    What does the equation $F d = F d$ signify in the context of levers?

    <p>The output force times its distance equals input force times its distance</p> Signup and view all the answers

    What happens to the output force when using a system of pulleys?

    <p>It can be greater than the input force depending on the arrangement</p> Signup and view all the answers

    What happens to a ball's kinetic energy when it bounces?

    <p>It decreases with each bounce.</p> Signup and view all the answers

    The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.

    <p>True</p> Signup and view all the answers

    What is the formula to calculate gravitational potential energy?

    <p>PE = mgh</p> Signup and view all the answers

    During free fall, a falling object's momentum increases due to its increasing ________.

    <p>velocity</p> Signup and view all the answers

    Match the energy types with their definitions:

    <p>Kinetic Energy = Energy of motion Potential Energy = Stored energy based on position Mechanical Energy = Sum of kinetic and potential energy Thermal Energy = Energy related to temperature</p> Signup and view all the answers

    Which car experiences greater acceleration when equal forces are applied?

    <p>Compact car</p> Signup and view all the answers

    When the force is removed from the cars after accelerating, the compact car will have greater momentum than the full-size sedan.

    <p>False</p> Signup and view all the answers

    What effect does gravitational potential energy (PE) experience during the free fall of Bronco?

    <p>It decreases.</p> Signup and view all the answers

    The relationship between work done and kinetic energy is expressed as W = _____ KE.

    <p>Δ</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Kinetic Energy = Energy of motion Potential Energy = Stored energy based on position Impulse = Change in momentum Work = Force applied over a distance</p> Signup and view all the answers

    Which force impacts the motion of the cars as they accelerate?

    <p>Applied force</p> Signup and view all the answers

    The amount of work done on both cars is the same if they travel equal distances under equal forces.

    <p>True</p> Signup and view all the answers

    What two types of potential energy are changing during Bronco's slowing-down interval?

    <p>Gravitational potential energy and elastic potential energy.</p> Signup and view all the answers

    How much work is needed to lift a 200 N object to a height of 4 meters?

    <p>800 J</p> Signup and view all the answers

    The potential energy of an object increases as it is lifted higher above the ground.

    <p>True</p> Signup and view all the answers

    What is the formula for calculating power?

    <p>Power = Work / Time</p> Signup and view all the answers

    The potential energy of a mass can be found using the formula PE = ______ x height.

    <p>mass x gravitational acceleration</p> Signup and view all the answers

    Match each scenario with its corresponding energy concept:

    <p>Raising an object = Potential Energy Rolling a ball down a hill = Kinetic Energy Object falling freely = Energy Conservation Sliding without friction = Momentum During Free Fall</p> Signup and view all the answers

    What is the power output of an engine that does 60,000 J of work in 10 seconds?

    <p>6000 J/s</p> Signup and view all the answers

    If an object is sliding down a ramp with friction, it will have more kinetic energy at the bottom than without friction.

    <p>False</p> Signup and view all the answers

    What happens to the speed of an object as it falls freely under gravity?

    <p>The speed increases.</p> Signup and view all the answers

    What is the resultant vector when two vectors are added at an angle using the parallelogram rule?

    <p>The diagonal of the parallelogram formed by the two vectors</p> Signup and view all the answers

    The horizontal component of a force acting on an object is always equal to the net force acting on that object.

    <p>False</p> Signup and view all the answers

    What does the normal force represent in the context of an object resting on an inclined plane?

    <p>The perpendicular force exerted by a surface on an object resting on it.</p> Signup and view all the answers

    The component of weight parallel to the inclined plane is greater than the ______ when the plane is inclined.

    <p>friction force</p> Signup and view all the answers

    Match each force acting on a block on an inclined plane to its function:

    <p>Weight (W) = The force acting downward due to gravity Normal Force = The force acting perpendicular to the plane Friction Force = The force opposing motion down the plane Component of W Parallel = The force driving the block down the incline</p> Signup and view all the answers

    Which component of vector T at point B should be equal to W/2 for equilibrium?

    <p>Vertical component</p> Signup and view all the answers

    In a free-body diagram, each vector represents a force acting on the object.

    <p>True</p> Signup and view all the answers

    How does the horizontal component of the tension at B relate to the horizontal components at hinge A?

    <p>They should be equal in magnitude but opposite in direction for equilibrium.</p> Signup and view all the answers

    Which component of velocity remains constant while an object is in free motion along a horizontal path?

    <p>Horizontal component</p> Signup and view all the answers

    The vertical component of velocity decreases as the object travels upwards.

    <p>True</p> Signup and view all the answers

    What effect does a force have on the velocity of an object according to Newton's Third Law?

    <p>Force changes the velocity of an object by causing acceleration.</p> Signup and view all the answers

    The __________ rule is used to find the resultant vector of two or more vectors acting at a point.

    <p>parallelogram</p> Signup and view all the answers

    What happens to the resultant vector when two forces of equal magnitude act at angles of 90 degrees?

    <p>It is equal to the sum of the forces.</p> Signup and view all the answers

    Match the following forces with their corresponding effects on an object:

    <p>Gravitational force = Pulls objects towards the center of the Earth Frictional force = Opposes the motion of sliding objects Tension force = To support the weight of an object Normal force = Acts perpendicular to the surface of contact</p> Signup and view all the answers

    At what moment does the vertical component of velocity equal zero during an object's projectile motion?

    <p>At the peak height of the projectile's path.</p> Signup and view all the answers

    Velocity vectors combine with force vectors when determining an object's motion.

    <p>False</p> Signup and view all the answers

    In the context of a sailboat affected by wind, which component of force helps it to move forward?

    <p>The component parallel to the keel</p> Signup and view all the answers

    The tension in a rope must be equal to the weight of the object it is supporting.

    <p>False</p> Signup and view all the answers

    What relationship do you see between the vectors formed by the tensions in ropes A, B, and C when a lantern is suspended?

    <p>Vectors A + B are equal in magnitude and opposite in direction to vector C.</p> Signup and view all the answers

    When analyzing vector components, the _____ component causes acceleration in the direction of motion.

    <p>parallel</p> Signup and view all the answers

    Which statement is true regarding the impact of wind on sailboats?

    <p>A perpendicular wind force can help propel the boat forward.</p> Signup and view all the answers

    Match the following terms with their correct definitions:

    <p>Vector Addition = Combining two or more vectors to find the resultant Components of a Vector = Projections of a vector along the axes Newton's Third Law = For every action, there is an equal and opposite reaction Parallelogram Rule = Method to determine the resultant of two vectors</p> Signup and view all the answers

    What happens to a boat's movement if the pulling force on the rope becomes perpendicular to the track?

    <p>The boat will not move forward as acceleration requires a component of force in that direction.</p> Signup and view all the answers

    A component of force that acts perpendicular to an object's path always causes motion.

    <p>False</p> Signup and view all the answers

    Study Notes

    Tension in a String

    • The tension in the top string of a hanging object is equal to the tension in the bottom string plus the weight of the object.
    • The tension in the top string is greater than the tension in the bottom string, therefore it will break first.
    • The tension in a string is a measure of the pulling force applied to the string.

    Newton’s Second Law of Motion

    • Newton's Second Law of Motion relates the net force acting on an object to its mass and acceleration.
    • The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
    • If the net force acting on an object doubles, its acceleration doubles.
    • If the mass of an object doubles, its acceleration is halved.
    • If both the net force and the mass of an object double, its acceleration remains unchanged.

    Normal (Support) Forces

    • In physics, the word "normal" means "perpendicular".
    • The normal force of a surface on an object is the force the surface exerts perpendicular to that surface.

    Static and Dynamic Equilibrium

    • Static equilibrium occurs when an object is at rest and the net force acting on it is zero, meaning there is no motion.
    • Dynamic Equilibrium occurs when an object is moving at a constant speed in a straight line, meaning the net force acting on it is also zero.

    Newton’s Third Law

    • Newton’s Third Law states that for every force (action) there is an equal and opposite force (reaction).
    • The forces always occur in pairs, and act on different objects in the interaction.
    • The forces are equal in magnitude but opposite in direction.
    • The magnitudes of the forces are always equal, however, the accelerations caused by the forces can be different due to different masses of the objects involved.

    Action-Reaction Pairs

    • When object 'A' exerts a force on object 'B', object 'B' exerts an equal and opposite force on object 'A'.
    • While the forces are equal in magnitude, the accelerations produced depend on the masses of the objects.
    • Internal forces within a system, such as the forces between parts of a single object, cancel out and do not contribute to the acceleration of the system.
    • An external force is necessary to accelerate a system as a whole.

    Horse-Cart Problem

    • The horse-cart system is a classic example of action-reaction pairs.
    • The horse pulls the cart forward and the cart pulls the horse backwards, these forces are equal in magnitude and opposite in direction, but they are internal forces within the system.
    • The horse-cart system needs an external force, such as friction between the horse's feet and the ground, to move forward.

    Vector Components

    • Vectors are quantities that have both magnitude and direction.
    • Vector components are the projections of a vector onto the x-axis (horizontal) and the y-axis (vertical).
    • When analyzing motion in two dimensions, it's often helpful to break forces down into their horizontal and vertical components.

    Summary of Forces

    • Newton’s laws of motion are fundamental principles of physics, which explain how forces interact with and affect objects.
    • The steps to solve force problems include drawing a free body diagram for each object of interest, labelling all forces with their directions, and applying Newton’s laws to determine the net force and acceleration of each object.

    Centripetal Acceleration and Force

    • Centripetal acceleration is the acceleration that causes an object to move in a circular path.
    • The magnitude of centripetal acceleration is directly proportional to the square of the object's speed and inversely proportional to the radius of the circular path.
    • Centripetal force is the force that causes centripetal acceleration.
    • Centripetal force is always directed towards the center of the circular path.

    Conical Pendulum

    • A conical pendulum consists of a bob swinging in a circular path, with the string tracing a cone.
    • Tension in the string and gravitational force act on the bob.
    • The horizontal component of the tension provides the centripetal force, while the vertical component balances the weight of the bob.

    Banked Curves

    • The horizontal component of the normal force acting on a car rounding a banked curve provides the centripetal force.
    • Friction also contributes to the centripetal force.

    Centrifugal Force

    • There is no actual force called "centrifugal force".
    • The apparent outward force experienced by a person or object in circular motion is actually due to inertia.

    Rotational Speed

    • Rotational speed is the rate at which an object rotates.
    • It is measured in revolutions per minute (RPM).
    • Tangential speed is the linear speed of an object in circular motion.
    • Tangential speed is directly proportional to the rotational speed and the radius of the circular path.

    Gravitational Force

    • The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

    Gravitational Field

    • A gravitational field is an alteration of space around a massive object.
    • It is a vector field, representing the force that would be experienced by a test mass at each point in space.
    • The strength of the gravitational field is directly proportional to the mass of the object and inversely proportional to the square of the distance from the object.

    Ocean Tides

    • Tides are the periodic rise and fall of ocean water levels.
    • They are caused by the gravitational pull of the Moon and the Sun.
    • There are typically two high tides and two low tides each day.

    Satellite Motion

    • Satellites orbit Earth due to a balance between their inertia and Earth's gravity.
    • The period of a satellite's orbit depends on its altitude.
    • The speed of a satellite in its orbit is not constant; it is faster when it is closer to Earth and slower when it is farther away.

    Escape Velocity

    • Escape velocity is the minimum speed an object needs to escape the gravitational pull of a planet or star.
    • It is the speed at which the object's kinetic energy is greater than or equal to its gravitational potential energy.
    • For Earth, the escape velocity is approximately 11 km/s.
    • For the Sun, the escape velocity at Earth's distance is about 42 km/s.

    Impulse and Momentum

    • Impulse occurs when a force acts on an object over time.
    • The change in momentum equals the impulse on the object.
    • A boxer riding with a punch increases the contact time and reduces the impact force.
    • Momentum is conserved when no external forces are acting on a system.
    • Collisions can be elastic (conserving kinetic energy) or inelastic (some kinetic energy is lost due to heat or deformation).
    • In a completely inelastic collision, two objects collide and become one.

    Work and Energy

    • Work is done when a force is applied over a distance in the direction of the force.
    • The work-energy theorem states that the net work done on an object equals the change in its kinetic energy.
    • Work is needed to change the kinetic energy of an object.
    • Friction causes a loss of kinetic energy because energy is transferred into heat and the deformation of the object.

    Simple Machines

    • A lever is a simple machine that rotates on a fulcrum, enabling a small force over a large distance to induce a large force over a small distance.
    • A pulley is a simple machine that functions like a lever with equal arms - it changes the direction of the input force and can multiply the force.
    • All simple machines operate under the principle of work in = work out.
    • By increasing the effort distance, a smaller force is required to do a given amount of work.

    Bronco's Bungee Jump

    • Bronco’s mass is 100 kg
    • Acceleration of free fall is 10 m/s²
    • Distance traveled in free fall for 3 seconds is 45 meters (using d = ½ * a * t²)
    • Bronco's velocity after 3 seconds of free fall is 30 m/s (using v = a * t)
    • Change in momentum during the 3-second free fall is 3000 kg⋅m/s (using Δmv = m * Δv )
    • Change in momentum during the 2-second slowing down period is 3000 kg⋅m/s
    • Impulse during the 2-second slowing down period is 3000 N⋅s (using Impulse = Ft)
    • Average force exerted by the cord during the 2-second slowing down interval is 1500 N (using Ft = Δmv)
    • Bronco's kinetic energy after 3 seconds of free fall is 45,000 J (using KE = ½ * m * v²)
    • The decrease in gravitational potential energy during the 3 seconds of free fall is 45,000 J (using PE = m * g * h)
    • During the slowing down interval, both gravitational potential energy and elastic potential energy are changing

    Cars on a Cliff

    • The car with less mass will accelerate more quickly (higher acceleration).
    • The car with less mass will spend less time along the surface of the lot.
    • Since impulse is Ft and the force and time are the same, the impulse will be the same for both cars.
    • Since Ft = Δmv and the force and time are the same, the momentum at the edge of the cliff will be the same for both cars.
    • The car with less mass will have more work done on it, since W = F*d, and the force is constant but the car with less mass travels a greater distance.
    • The car with less mass will have a higher kinetic energy at the edge of the cliff, because the work done, W = ΔKE.

    Conservation of Energy

    • The total mechanical energy of a system remains constant (conserved) if no work is done on the system by external forces.
    • In a closed system, energy can be converted from one form to another, but it can't be created or destroyed
    • Mechanical energy is the sum of potential energy and kinetic energy
    • Potential energy is stored energy, such as gravitational potential energy (energy stored due to an object's position relative to Earth)
    • Kinetic energy is the energy of motion

    More on Energy

    • There is a trade-off between potential energy and kinetic energy; when one increases, the other decreases.
    • Work is defined as the force applied to an object over a certain distance
    • The amount of work done is equal to the change in energy of the object.
    • Power is the rate at which work is done.

    Friction and Energy

    • Inelastic collisions are collisions where kinetic energy is not conserved, and some energy is lost as heat, sound, or deformation.
    • Friction is a force that opposes motion, and it can cause energy to be dissipated as heat.
    • In real-world scenarios, friction will always play a role, and some energy will always be lost, meaning that the bounce will be less high over time.
    • The amount of energy lost due to friction is dependent on the coefficient of friction between the surfaces.

    Windmills and Energy

    • Windmills use wind energy to generate electricity.
    • The power generated by windmills does not affect wind speed.
    • Windmills capture kinetic energy from the wind, but this doesn't change the overall amount of energy in the system.
    • The wind behind a windmill may appear to be slower, but this is due to the wind being diverted by the blades, not due to a decrease in total wind energy.

    Resultant Vectors

    • Resultant vector C is produced when vectors A and B are at an angle to each other.
    • C is the diagonal of a parallelogram with A and B as adjacent sides
    • C is a rectangle when A and B are perpendicular to each other.

    Velocity Vectors and Components

    • Velocity vectors combine with other velocity vectors.
    • Velocity vectors do not combine with force vectors.

    Force Vectors and the Parallelogram Rule

    • The resultant vector of two rope tensions supporting a heavy ball is equal and opposite to the ball's weight.
    • The relative lengths of the sides of the parallelogram are proportional to the rope tensions.
    • When a lantern is suspended by three ropes, there is a relationship between the vectors: A + B = C, and A + C = B.

    Vectors and Sailboats

    • The component of force parallel to the direction of the boat's motion propels the boat forward.
    • The component of force perpendicular to the direction of the boat's motion is useless for propulsion.
    • A boat oriented at an angle into the wind will tack and move in a forward direction.
    • The component of force parallel to the keel of a sailboat will determine its forward direction:
      • When the component is perpendicular to the keel, the boat will not move forward.
      • When the component is parallel to the keel, the boat will move forward.

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    Description

    This quiz covers the concepts of tension in strings, Newton’s Second Law of Motion, and normal forces. It explores the relationships between forces, mass, and acceleration in physics. Test your understanding of these fundamental principles and their applications in various scenarios.

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