Forces and Gravity
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Questions and Answers

Two coccal bacteria, each with a mass of $9.5 \times 10^{-16}$ kg, are separated by a distance of $1 \mu m$. What is the gravitational force between them, given $G = 6.67 \times 10^{-11} Nm^2/kg^2$?

  • $6.0 \times 10^{-29} N$ (correct)
  • $3.0 \times 10^{-29} N$
  • $3.0 \times 10^{-23} N$
  • $6.0 \times 10^{-23} N$
  • If the radius of a planet is doubled, how does the free fall acceleration ($g$) at the surface change, assuming the planet's mass remains constant?

  • $g$ is quartered (correct)
  • $g$ is quadrupled
  • $g$ is doubled
  • $g$ is halved
  • A sphere with a mass of 20 kg is placed on the Earth's surface where $g = 9.8 m/s^2$. What is the weight of the sphere?

  • 196 N (correct)
  • 29.8 N
  • 20 N
  • 98 N
  • A box rests on a horizontal surface. A force of 15 N is applied upwards, while gravity exerts a force of 11 N downwards on the box. What is the normal force exerted by the surface on the box?

    <p>4 N (C)</p> Signup and view all the answers

    Which of the following best describes the direction of the normal force exerted by a surface on an object?

    <p>Perpendicular to the surface (C)</p> Signup and view all the answers

    What primarily causes the force of friction between two surfaces in contact?

    <p>Irregularities in the surfaces (D)</p> Signup and view all the answers

    What is the primary role of static friction?

    <p>To prevent objects from moving with respect to a contacting surface (D)</p> Signup and view all the answers

    An object is placed on a slope. As the angle of the slope increases, how does the magnitude of the normal force acting on the object change?

    <p>Decreases (C)</p> Signup and view all the answers

    Which statement accurately describes the difference between scalar and vector quantities?

    <p>Scalar quantities have magnitude only, while vector quantities have both magnitude and direction. (B)</p> Signup and view all the answers

    A force vector is represented by $\vec{F}$. Which of the following represents the magnitude of this vector?

    <p>$F$ (D)</p> Signup and view all the answers

    What does the negative of a vector represent?

    <p>A vector with the same magnitude but the opposite direction. (D)</p> Signup and view all the answers

    Two displacement vectors, one 5m and the other 3m, are acting along the same line. If they point in the same direction, what is the magnitude of the resultant vector?

    <p>8m (B)</p> Signup and view all the answers

    When resolving a vector into its components, what information do the components provide?

    <p>The magnitude and direction of the vector. (C)</p> Signup and view all the answers

    What is the significance of the algebraic sign ( + or − ) of a vector component?

    <p>It indicates the direction of the component along the axis. (B)</p> Signup and view all the answers

    Which of the following is a false statement about vector magnitudes?

    <p>Vector magnitudes can be negative. (B)</p> Signup and view all the answers

    If two vectors of magnitudes 3N and 4N are added, what is the minimum magnitude of the resultant vector?

    <p>1N (C)</p> Signup and view all the answers

    A car travels 5 km east, then 3 km south, and finally 2 km west. What is the magnitude and direction of the car's resultant displacement?

    <p>6.88 km at 26.9° south of east (A)</p> Signup and view all the answers

    A hiker travels 100 m north and then 50 m east. What is the magnitude and direction of the hiker's displacement?

    <p>112 m at 26.6° east of north (B)</p> Signup and view all the answers

    Which of the following is NOT a fundamental force?

    <p>Tension (D)</p> Signup and view all the answers

    What determines an object's motion when multiple forces act upon it?

    <p>The net force acting on the object (D)</p> Signup and view all the answers

    An object experiences two forces: 10N to the right and 4N to the left. What is the net force acting on the object?

    <p>6N to the right (A)</p> Signup and view all the answers

    According to Newton's First Law, what condition must be met for an object's velocity to remain constant?

    <p>The net force acting on the object must be zero. (A)</p> Signup and view all the answers

    Which of the following best exemplifies inertia?

    <p>A stationary book remains at rest on a table. (B)</p> Signup and view all the answers

    A force vector has a magnitude of 15 N and is directed 30° above the +x-axis. What is the magnitude of its y-component?

    <p>7.5 N (D)</p> Signup and view all the answers

    In a free-body diagram, which forces should be included?

    <p>All forces acting on the object of interest (C)</p> Signup and view all the answers

    A displacement vector has an x-component of -5.0 m and a y-component of +8.0 m. In which quadrant does this vector lie?

    <p>Quadrant II (C)</p> Signup and view all the answers

    Given a vector with a magnitude of 20 units and an angle of 60° with respect to the x-axis, what are the approximate magnitudes of its x and y components?

    <p>x = 10 units, y = 17.3 units (D)</p> Signup and view all the answers

    Vector A has components $A_x = -3$ and $A_y = 4$. What is the angle of this vector with respect to the positive x-axis?

    <p>126.9° (C)</p> Signup and view all the answers

    Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse in a right triangle?

    <p>Sine (B)</p> Signup and view all the answers

    A vector has a negative x-component and a negative y-component. In which quadrant does this vector lie?

    <p>Quadrant III (B)</p> Signup and view all the answers

    Vector A has a magnitude of 10 and makes an angle of 30 degrees with the positive x-axis. Vector B has a magnitude of 15 and makes an angle of 120 degrees with the positive x-axis. What is the x-component of the resultant vector A + B?

    <p>-5.4 (B)</p> Signup and view all the answers

    A projectile is launched with an initial velocity $v_0$ at an angle $\theta$ with respect to the horizontal. Assuming negligible air resistance, what is the y-component of the projectile's velocity at the highest point of its trajectory?

    <p>0 (D)</p> Signup and view all the answers

    When adding vectors $\vec{A}$ and $\vec{B}$ to obtain $\vec{C}$, which of the following statements is always true?

    <p>The x-component of $\vec{C}$ is the sum of the x-components of $\vec{A}$ and $\vec{B}$, and the y-component of $\vec{C}$ is the sum of the y-components of $\vec{A}$ and $\vec{B}$. (D)</p> Signup and view all the answers

    In a scenario where multiple forces are acting on an object, what is the purpose of creating a free-body diagram?

    <p>To illustrate all forces acting <em>on</em> the object from its surroundings, simplifying the analysis of their combined effect. (A)</p> Signup and view all the answers

    A force $\vec{F_1}$ of 30 N acts on an object at an angle of 30° above the +x axis, and a force $\vec{F_2}$ of 40 N acts on the same object along the +y axis. What is the approximate magnitude of the resultant force?

    <p>50 N (D)</p> Signup and view all the answers

    In the context of vector addition, what does 'resolving a force into components' mean?

    <p>Breaking down a force vector into its horizontal and vertical components. (A)</p> Signup and view all the answers

    Consider three forces acting on an object: $\vec{F_1} = 20\hat{i}$ N, $\vec{F_2} = -10\hat{j}$ N, and $\vec{F_3} = -5\hat{i} + 5\hat{j}$ N. What is the x-component of the resultant force?

    <p>15 N (B)</p> Signup and view all the answers

    An object has two forces acting on it: 50 N at 0 degrees and 30 N at 90 degrees. What is the approximate angle of the resultant force with respect to the x-axis?

    <p>31 degrees (B)</p> Signup and view all the answers

    A person is pulling a box with a force of 100 N at an angle of 60 degrees above the horizontal. What is the horizontal component of the force?

    <p>50 N (B)</p> Signup and view all the answers

    When should you exclude a force from a free-body diagram?

    <p>When the force is an internal force acting within the object. (D)</p> Signup and view all the answers

    Two spheres, each with a mass of 30 kg, are separated by a center-to-center distance of 0.05 m. Which of the following best approximates the gravitational force between them?

    <p>$2.4012 \times 10^{-6} N$ (C)</p> Signup and view all the answers

    A radio transmitter's power output is changed such that the new power, $P$, is four times the initial power, $P_0$. By what factor has the power increased?

    <p>4 (C)</p> Signup and view all the answers

    If the kinetic energy of an object increases by 25%, by what factor is the new kinetic energy, $E_f$, related to the original kinetic energy, $E_0$?

    <p>1.25 (B)</p> Signup and view all the answers

    The speed of a car decreases by 10% after the driver applies the brakes. If the initial speed was $v_0$, what is the final speed, $v_f$, in terms of $v_0$?

    <p>$v_f = 0.9v_0$ (B)</p> Signup and view all the answers

    An object's momentum increases by 300%. By what factor has its momentum increased?

    <p>4 (B)</p> Signup and view all the answers

    A scientist measures the length of a bacterium under a microscope and finds its length has decreased by 5%. If the original length was $L_0$, what is the new length, $L_f$?

    <p>$L_f = 0.95L_0$ (B)</p> Signup and view all the answers

    The population of a town increases by 8% in one year. If the initial population was $P_0$, what is the final population, $P_f$, at the end of the year?

    <p>$P_f = 1.08P_0$ (B)</p> Signup and view all the answers

    Coccal bacteria, with a mass of approximately $9.5 × 10^{-13}$ g each and a radius of approximately $0.5 \mu m$ each, form Diplococcal bacteria. Estimate the gravitational force between these two adjacent bacteria.

    <p>$2.53 \times 10^{-27} N$ (D)</p> Signup and view all the answers

    Flashcards

    Vector Addition

    The process of combining two or more vectors to determine their resultant vector.

    Components of a Vector

    The projections of a vector along the axes, typically x and y.

    Trigonometric Functions

    Functions like sine, cosine, and tangent used to relate angles and sides in right triangles.

    Finding x-component

    Calculated as the product of vector magnitude and cosine of the angle.

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    Finding y-component

    Calculated as the product of vector magnitude and sine of the angle.

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    Algebraic Sign of Components

    Indicates the direction of a vector's component along the axes.

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    Right Triangle in Vector Problems

    A geometric representation used to relate vectors to their components through angles.

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    Magnitude and Direction of a Vector

    Determined from the vector's x and y components using the Pythagorean theorem and trigonometry.

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    Resultant Vector

    The vector sum of two or more vectors, denoted as C = A + B.

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    Vector Component

    The projection of a vector along the x or y axis, expressed as Cx and Cy.

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    Magnitude of a Vector

    Calculated using the formula |C| = √(Cx² + Cy²).

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    Direction of a Vector

    Described by the angle θ, found using θ = tan⁻¹(Cy/Cx).

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    Free-Body Diagram

    A graphical representation showing all forces acting on an object.

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    Equations of Equilibrium

    Mathematical expressions that set the sum of forces to zero for an object at rest.

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    Resolving Forces

    Breaking down forces into their x and y components for easier analysis.

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    Force in a Direction

    The combined effect of multiple forces acting at specific angles on a point.

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    Fundamental Forces

    The four essential forces in physics: gravitational, electromagnetic, strong nuclear, and weak nuclear.

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    Contact Forces

    Forces that occur only when objects are in physical contact.

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    Net Force

    The vector sum of all forces acting on an object, determining its motion.

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    Newton's First Law

    An object remains at rest or in uniform motion unless acted upon by a net external force; also known as the law of inertia.

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    Free-Body Diagram (FBD)

    A visual representation showing all forces acting on a single object, excluding forces on other objects.

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    Vector Quantities

    Forces characterized by both magnitude and direction.

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    Inertia

    The tendency of an object to resist changes in its velocity.

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    SI Unit of Force

    The standard unit of force in the International System of Units is the Newton (N).

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    Scalar Quantity

    A quantity with magnitude, sign, but no direction.

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    Vector Quantity

    A quantity that has both magnitude and direction.

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    Vector Notation

    Arrows over symbols indicate vectors, italics show magnitude.

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    Graphical Vector Addition

    Adding vectors visually using arrows, direction matters.

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    Resolving Vectors

    Breaking a vector into components along axes (x, y, z).

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    Negative of a Vector

    Inversion of a vector's direction.

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    Gravitational Force Formula

    The equation for gravitational force between two masses, F = G(m1m2/r²).

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    Weight Formula

    Weight (w) is given by the equation w = mg, where m is mass and g is gravitational acceleration.

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    Gravitational Field Strength

    Gravitational field strength (g) is the force per unit mass experienced by a small test mass placed in the field, g = G(M/r²).

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    Inverse Square Law

    Gravitational force decreases with the square of the distance from the mass source, expressed as F ∝ 1/r².

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    Normal Force

    The force exerted by a surface, acting perpendicular to the contact surface supporting an object.

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    Static Friction

    The force that prevents two surfaces from sliding past each other until a limit is reached, keeping them at rest.

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    Force of Friction

    The force that opposes the motion of an object sliding on a surface, acting parallel to the contact surface.

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    Coccal Bacteria Mass

    A coccal bacteria has a mass of approximately 9.5 x 10⁻¹³ g and is spherical in shape.

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    Force of Gravity

    Attraction between two masses, calculated by Newton's law of gravitation.

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    Factor in Physics

    A number indicating how much a quantity has increased or decreased.

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    Percentage Increase

    The change in a quantity expressed as a percentage of the original value.

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    Percentage Decrease

    The reduction in a quantity expressed as a percentage of the original value.

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    Weight Change in Airplane

    Variation in weight when altitude changes compared to weight on ground.

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    Coccal Bacteria

    Spherical-shaped bacteria with mass and size relevant to gravity calculations.

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    Newton's Law of Gravitation

    Gravity is directly proportional to the product of two masses and inversely proportional to the square of the distance between them.

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    Force Calculation Example

    Use mass and distance to calculate force acting between two objects, like spheres.

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    Study Notes

    Unit 1, Chapter 2: Introductions to Vectors and Forces

    • This chapter introduces vectors and forces.
    • Scalars have magnitude and units, but no direction. Vector quantities have magnitude and direction.
    • Scalars are added/subtracted like regular numbers.
    • Adding vectors takes directions into account.
    • A vector is indicated by an arrow over a boldface symbol (e.g., $\vec{F}$).
    • The magnitude of a vector is represented by the symbol in italics (e.g., F). Magnitude can be positive or zero. It does not have a direction.
    • Vectors are represented by arrows.
    • The length of the vector arrow is proportional to its magnitude.
    • The negative of a vector points in the opposite direction.
    • The diagrams show graphical vector addition.
    • Vectors can be added graphically using the tail-to-head method.
    • Vectors can be added along the same straight line and the same direction.
    • Adding vectors that start at the same point involves drawing a diagram (see images).
    • Vectors can be added using components.
    • Any vector can be expressed as a sum of vectors parallel to the x, y, and optionally, z axes.
    • X, Y and Z components represent magnitude and direction along those axes.
    • Components have magnitude, units, and an algebraic sign. The sign of the component indicates the direction along the axis.
    • Finding components is called resolving the vector.
    • The trigonometric functions can be used to find vector components. The Pythagorean theorem can be used to find the magnitude of a vector from its components.
    • Problems can be solved using trigonometric functions, Pythagorean Theorem, and diagrams.

    Scalars and Vectors

    • A scalar quantity describes a physical quantity with only magnitude.
    • A vector quantity describes a physical quantity with both magnitude and direction.
    • Examples of scalars include mass, speed, distance, time, temperature, and energy.
    • Examples of vectors include force, velocity, displacement, and acceleration.

    Vector Representation

    • Vectors are represented by arrows.
    • The length of the arrow represents the magnitude of the vector.
    • The direction of the arrow represents the direction of the vector.

    Graphical Vector Addition

    • Vectors can be added graphically using the tail-to-head method.
    • Draw the first vector. Place the tail of the next vector at the head of the first vector.
    • The resultant vector starts at the tail of the first vector and ends at the head of the last vector.
    • Graphical methods are useful for visualizing vector addition, particularly in two dimensions.

    Vector Addition Using Components

    • Vectors can be added component-wise.
    • Add the x-components of the vectors together.
    • Add the y-components of the vectors together.
    • Use the results to find the magnitude and direction of the resultant vector.
    • In many cases, adding vectors using components is a more efficient method in determining the sum

    Problem-Solving Strategy: Finding Components of a Vector

    • Draw a right triangle.
    • Determine a relevant angle.
    • Use trigonometry functions to find magnitude of the components.
    • Determine the algebraic sign for the component from the diagram.

    Problem-Solving Strategy: Finding the Magnitude and Direction of a Vector

    • Sketch the vector; identify its components.
    • Draw a right triangle with the vector as the hypotenuse and its components as sides.
    • Determine the appropriate angle.
    • Use trigonometric functions to calculate the angle.
    • Use the Pythagorean theorem to determine the magnitude of the vector.

    Problem-Solving Strategy: Adding Vectors using Components

    • Find the x and y components of each vector to be added.
    • Add the x components with their algebraic signs.
    • Add the y components with their algebraic signs.
    • If necessary, use x and y components of the sum to find magnitude and direction of the sum.

    Net Force

    • The net force is the vector sum of all forces acting on an object.
    • Object motion is determined by the net force.

    Inertia and Equilibrium: Newton’s First Law of Motion

    • For an object in equilibrium, the net force = 0.
    • This means the sum of the forces in each direction (x, y, and z) is zero. (This implies zero acceleration.)
    • An object in equilibrium has a constant velocity (i.e., a zero acceleration).

    Forces

    • Forces are vector quantities that have both magnitude and direction.
    • Examples of forces include gravitational force, electromagnetic force, strong force, weak force, normal force, forces of friction (kinetic and static), and tension.

    Free-Body Diagrams (FBD)

    • An FBD is a simplified diagram showing all forces acting on a single object.
    • Draw the object as a point (or a simple shape).
    • Include all forces acting on the object in the diagram.
    • Label all force vectors.
    • Include relevant coordinate systems and angle measurements.
    • Label forces exerted on another object are not included.

    Definitions

    • Normal Force (N): The force exerted by a surface on an object. This force is always perpendicular to the surface
    • Force of Friction (f): The force exerted by a surface on an object that opposes the object's motion.
    • Static Friction (fs): The force required to start the object's motion. It has a maximum value
    • Kinetic Friction (fk): The force required to maintain the object's motion.
    • Weight (W): The force of gravity on an object.
    • Tension (T): The force exerted by a string, cord, or rope when it is pulled at its ends.

    Universal Gravitation

    • Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers (G=6.674 × 10⁻¹¹ N⋅m²/kg²).

    Important Notes from Self Study Chapter One

    • The word "factor" is often used in physics. It describes the ratio of new quantity to the old.

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