Physics Projectile Motion Quiz
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Questions and Answers

What force primarily influences a projectile's motion after it has been launched?

  • The force applied by external objects during the flight.
  • Air resistance acting against the projectile's movement.
  • The initial forward force imparted during launch.
  • The weight force due to gravity. (correct)
  • The horizontal velocity of a projectile changes consistently throughout its flight due to the constant force of gravity.

    False (B)

    At what point in the trajectory of an obliquely launched projectile is its vertical velocity equal to zero?

    At the highest point of its trajectory

    In projectile motion analysis, the acceleration in the horizontal direction ($a_x$) is typically considered to be ______, assuming negligible air resistance.

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

    Match the following steps with their corresponding descriptions in solving projectile motion problems:

    <p>Draw a diagram = Visually represent the problem to understand the trajectory and given variables. Separate vertical and horizontal components = Resolve initial velocity into its x and y components using trigonometry. Horizontal movement = Apply kinematic equations with constant horizontal velocity (ax = 0). Vertical movement = Apply kinematic equations with constant vertical acceleration due to gravity.</p> Signup and view all the answers

    A ball is thrown at an angle of 30 degrees above the horizontal with an initial velocity of 20 m/s. What is the initial vertical component of the velocity?

    <p>10 m/s (D)</p> Signup and view all the answers

    The time it takes for a projectile to reach its maximum height is independent of its initial vertical velocity.

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

    A projectile's flight path, assuming uniform gravity and negligible air resistance, follows a ______ trajectory.

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

    An object is moving in uniform circular motion. Which of the following statements is true?

    <p>The object's speed is constant, but its velocity is changing. (B)</p> Signup and view all the answers

    The period of an object in circular motion is the number of rotations completed each second.

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

    A particle is traveling with a constant speed of $5 m/s$ around a circle with a radius of $2m$. What is the magnitude of its centripetal acceleration?

    <p>12.5 m/s^2</p> Signup and view all the answers

    The formula that relates instantaneous velocity (v) to angular velocity ($ \omega $) and radius (r) is v = _______.

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

    Match the following terms related to circular motion with their correct descriptions:

    <p>Period (T) = Time taken for one complete revolution Frequency (f) = Number of rotations completed per second Angular Velocity ($ \omega $) = Rate of change of angular displacement Centripetal Acceleration ($a_c$) = Acceleration directed towards the center of the circle</p> Signup and view all the answers

    A car is moving around a circular track with a radius of 50 meters. If the car's angular velocity is 0.2 rad/s, what is its instantaneous velocity?

    <p>10 m/s (B)</p> Signup and view all the answers

    Centripetal force is a fundamental force of nature, like gravity or electromagnetism.

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

    An object is in uniform circular motion with a period of 2 seconds and a radius of 3 meters. Calculate its instantaneous velocity.

    <p>9.42 m/s</p> Signup and view all the answers

    In a conical pendulum, which of the following forces act upon the mass as it travels in a horizontal circle?

    <p>Tension, gravitational force, and centripetal force (D)</p> Signup and view all the answers

    The centripetal force in a conical pendulum is a fundamental force of nature, like gravity or electromagnetism.

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

    A conical pendulum is swinging, and the radius of the circle is decreased. What happens to the angle between the string and the vertical axis?

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

    Banked tracks are inclined at some ______ to the horizontal which allows cars to maintain greater speeds.

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

    Match the following variables with their corresponding formulas used in circular motion:

    <p>Centripetal Acceleration = $a_{c} = \frac{v^{2}}{r}$ Linear Velocity = $v = \frac{2\pi r}{T}$ Centripetal Force = $F_{c} = \frac{mv^{2}}{r}$ Angular Velocity = $\omega = \frac{\mathrm{\Delta}\theta}{t}$</p> Signup and view all the answers

    A car is driving around a banked track. What is the primary benefit of using a banked track compared to a flat track?

    <p>Greater possible speed without losing control (A)</p> Signup and view all the answers

    The angle of a banked track is independent of the speed a vehicle is traveling.

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

    A car traveling on a banked track hits the wall in front of it. Describe the direction in which the acceleration acts.

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

    What force provides the centripetal force required for an object to maintain a circular orbit around a central body?

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

    Torque is a force.

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

    State the equation to determine the banking angle of a curved road.

    <p>tan = v^2/rg</p> Signup and view all the answers

    According to Kepler's Law of Periods, the ratio of $r^{3}$ to $T^{2}$ is ______ for all satellites orbiting the same central body.

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

    Match the following orbital characteristics with the type of satellite:

    <p>Low Earth Orbit (LEO) = Short orbital period, lower altitude Geostationary Orbit (GEO) = Orbital period of 24 hours, high altitude Elliptical Orbit = Velocity is not constant</p> Signup and view all the answers

    What happens to gravitational potential energy as the distance, r, increases?

    <p>Gravitational potential energy increases (D)</p> Signup and view all the answers

    Gravity can repel objects.

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

    State the expression for escape velocity.

    <p>v = (2GM/r)</p> Signup and view all the answers

    A car is moving around a banked curve at its design speed. What is the primary benefit of banking the curve at the correct angle?

    <p>It eliminates the need for sideways friction (A)</p> Signup and view all the answers

    Torque () is calculated using the formula = r * F * sin(), where is the angle between the radius vector and the ______ vector.

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

    Flashcards

    Projectile

    Any object thrown or projected into the air, moving freely without a power source.

    Ballistic flight path

    The path a projectile follows, which is parabolic in shape.

    Forces acting on a projectile

    Only the weight force (gravity) acts on it during motion.

    Oblique projectile launch

    Launch at an angle, requiring trigonometry to analyze horizontal and vertical velocities.

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    Maximum height in projectile motion

    At the highest point, the vertical velocity is zero, only horizontal movement occurs.

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    Horizontal component of velocity

    In projectile motion, horizontal velocity remains constant without air resistance.

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    Vertical movement in projectiles

    Accelerated by gravity at -9.8 m/s²; initial velocity is often zero.

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    Projectile time of flight

    The time for both horizontal and vertical motions is the same, depending on height and angle.

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    Uniform Circular Motion

    An object traveling in a circular path at constant speed with changing direction and acceleration.

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    Period and Frequency Relationship

    T = 1/f or f = 1/T; T is the period, f is the frequency.

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    Average Speed in Circular Motion

    Average speed formula: v = 2πr/T, where r is radius and T is period.

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    Angular Velocity

    Angular velocity measures the angle of rotation per time: ω = Δθ/t.

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    Formula for Velocity

    The formula v = ωr merges angular and instantaneous velocities.

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    Polar Coordinates

    A system for representing points in the plane using (r, θ), where r is radius and θ is angle in radians.

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    Centripetal Acceleration

    Acceleration towards the center of the circle; formula ac = v²/r.

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    Centripetal Force

    A force that keeps an object moving in a circle, resulting from different forces acting in the system.

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    Angle of Bank

    Angle for optimal turning of a vehicle, eliminating friction.

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    Torque

    Turning movement of a force; product of distance and force.

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    Newton's Law of Universal Gravitation

    Every object attracts every other object; gravity is always attractive.

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    Gravitational Field Strength

    Acceleration due to gravity at a location; 9.8 m/s² on Earth.

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    Centripetal Force in Orbits

    For objects in circular orbits, the gravitational force provides centripetal force.

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    Kepler's Law of Periods

    Formula relating periods and radii of satellites orbiting the same body.

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    Satellite Definition

    An object in a stable orbit around a central mass.

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    Escape Velocity

    Speed needed to break free from a planet's gravitational pull.

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    Gravitational Potential Energy

    Energy of an object due to its position in a gravitational field.

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    Orbital Velocity

    Velocity required for a stable orbit around a central mass.

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    Centripetal Force (Fc)

    The force required to keep an object moving in a circle, balancing gravity and normal force.

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    Formula for Centripetal Force

    Fc = mv² / r, where m is mass, v is velocity, and r is radius.

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    Conical Pendulum Forces

    In a conical pendulum, the tension in the string counters gravity and provides centripetal force.

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    Finding the Angle of String (θ)

    tan(θ) = opposite / adjacent, used to find the angle of the string in a pendulum.

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    Banked Tracks

    Inclined tracks that help vehicles negotiate curves at higher speeds.

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    Effect of Speed on Banked Tracks

    Higher speed increases centripetal force, necessitating a banked angle for stability.

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    Centripetal Acceleration (a_c)

    The acceleration that keeps an object moving in a circle, calculated as a_c = v² / r.

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    Velocity on a Banked Track

    v = 2πr / T, where r is radius and T is the period of rotation.

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    Study Notes

    Projectile Motion

    • Projectile motion is analyzed and predicted using models
    • Projectiles launched horizontally
    • Projectiles launched obliquely
    • A projectile is any object thrown into the air with no power source
    • Projectiles follow a parabolic path
    • Force on a projectile in motion: Weight force (F=mg) only

    Projectile Motion (Oblique Launch)

    • Trigonometry is used to determine initial horizontal and vertical velocities
    • A projectile's vertical velocity is zero at its highest point
    • The horizontal component of the launch velocity determines the horizontal velocity
    • Initial conditions, like initial velocity and angle, are used in calculations

    How to solve projectile questions:

    • Create a diagram
    • Separate vertical and horizontal components
    • Horizontal movement: constant horizontal velocity (no horizontal acceleration, neglecting air resistance) and no initial horizontal velocity
    • Vertical movement: acceleration due to gravity, final velocity will be zero at maximum height
    • Time is the same for horizontal and vertical components and is influenced by angle and height

    Circular Motion

    • Objects move in circles due to circular motion caused by circular motion on banked tracks

    Uniform Circular Motion

    • Uniform circular motion involves an object travelling in a circular path at a constant speed with continual changing velocity
    • Velocity of an object is tangential to the path

    Period and Frequency Relationship

    • Period (T) is the time taken for one complete revolution
    • Frequency (f) is the number of rotations per second
    • T = 1/f or f = 1/T

    Instantaneous Velocity in Circular Motion

    • Average speed = distance traveled/time taken (speed divided by time)
    • Average speed = circumference / period

    Angular Velocity

    • Angular velocity (ω) measures the angle of rotation over time (ΔΘ/t)
    • Units are in radians/second
    • Formula: ω = ΔΘ/t

    Relationship between Angular and Instantaneous Velocity

    • v = ωr
    • This formula is not necessarily in the formula sheet

    Polar Coordinates

    • Polar coordinates are represented by (r, θ) where:
      • r is the distance from the centre (radius)
      • θ is the angle in radians

    Centripetal Acceleration

    • An acceleration that always points towards the centre of the circle.

    Centripetal Force

    • The force responsible for an object moving in a circle. This force is not a fundamental force.

    Conical Pendulum Forces

    • Tension in a string, gravity (mg), and centripetal force (Fc), acting on the mass
    • Formulas are used to solve problems

    Banked Tracks

    • Tracks inclined at an angle to the horizontal
    • Normal force and tangential components are important in analysis.

    Torque

    • Turning effect of a force (twisting)
    • Calculated by: T = r (force x perpendicular component), where r is the radius and force is perpendicular to the radius
    • Formula is T = rFsinθ, where θ = angle

    Motion in Gravitational Fields

    • Gravity determines the motion of planets and satellites.
    • Every object is attracted to every other object with an attractive force due to gravity (always +ve)
    • Formula for universal gravitation is F = GMm/r²
    • Gravitational field strength (acceleration due to gravity) is different across planets.

    Gravitational Potential Energy

    • Gravitational Potential Energy (U) = -GMm/r (negative when r is large)

    Orbits

    • Relationship between orbital radius and period is given as T²=4π²r³/GM
    • Centripetal Force = Gravitational Force
    • Circular orbital velocity is v = √(GM/r), given constant velocity in orbits.

    Satellites and Kepler's Laws

    • Satellites orbit large objects (e.g. planets and stars).
    • Kepler's Laws relate orbital periods and radii of satellites.
    • Formulas can be used to calculate values or relationships relating a satellite to various variables.

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    Physics Mod 5 Summary PDF

    Description

    Test your knowledge on projectile motion concepts, including both horizontal and oblique launches. This quiz covers the fundamentals of forces acting on projectiles, their trajectories, and techniques for solving projectile questions using trigonometry. Dive into the physics of motion and refine your understanding of how projectiles behave in different scenarios.

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