Physics Momentum and Kinetic Energy Quiz
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Questions and Answers

What is the relationship between momentum (p) and kinetic energy (EK)?

  • $EK = 2m / p$
  • $EK = p^2 / 2m$ (correct)
  • $EK = p / 2m$
  • $EK = 2p$
  • What is the SI unit of momentum?

  • kg*m/s (correct)
  • kg/s
  • N*m/s²
  • J/s
  • What happens to an object's momentum if the net force acting on it is zero?

  • The momentum decreases linearly
  • The momentum remains constant (correct)
  • The momentum oscillates
  • The momentum increases linearly
  • What is the relationship between the change in momentum and the net force acting on an object?

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

    Which of these scenarios would cause a change in momentum for an object?

    <p>A change in direction (A), A constant acceleration (C)</p> Signup and view all the answers

    What is the momentum of a 1 kg object traveling at 10 m/s?

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

    If the momentum of an object doubles, what happens to its kinetic energy?

    <p>It quadruples (A)</p> Signup and view all the answers

    Which of the following statements about momentum is true?

    <p>Momentum is a vector quantity. (B)</p> Signup and view all the answers

    What is the archer's velocity (v1f) after firing the first arrow?

    <p>-0.0250 m/s (B)</p> Signup and view all the answers

    What is the archer's velocity (v1f) after firing the second arrow?

    <p>-0.0467 m/s (A)</p> Signup and view all the answers

    What is the acceleration of the arrow?

    <p>1560 m/s^2 (D)</p> Signup and view all the answers

    What is the time for which the arrow is being accelerated by the bowstring?

    <p>0.0320 s (C)</p> Signup and view all the answers

    What is the x-component of the momentum equation for the first arrow firing?

    <p>m1 v1i = (m1 - m2) v1f + m2 v2f cos θ (D)</p> Signup and view all the answers

    What is the value of the archer's initial velocity, v1i?

    <p>0.0250 m/s (B)</p> Signup and view all the answers

    What is the final velocity of the second arrow?

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

    What is the angle at which the second arrow is fired?

    <p>30 degrees (C)</p> Signup and view all the answers

    What is the relationship between the average force exerted by m2 on m1 and the average force exerted by m1 on m2?

    <p>They are equal in magnitude and opposite in direction. (A)</p> Signup and view all the answers

    What is the significance of the equation 𝑚1 𝑣⃗1𝑓 + 𝑚2 𝑣⃗2𝑓 = 𝑚1 𝑣⃗1𝑖 + 𝑚2 𝑣⃗2𝑖?

    <p>It describes the conservation of momentum during a collision (A)</p> Signup and view all the answers

    Which of the following statements accurately describes the impulse-momentum theorem?

    <p>The change in momentum of an object is equal to the average force acting on it multiplied by the time interval over which the force acts. (C)</p> Signup and view all the answers

    What is the implication of the statement that the total momentum of an isolated system remains constant?

    <p>The system is not subject to any external forces. (B)</p> Signup and view all the answers

    In a head-on collision between two objects, what is the relationship between the change in velocity of the lighter object and the heavier object?

    <p>The change in velocity of the lighter object is greater than that of the heavier object. (A)</p> Signup and view all the answers

    In the equation 𝐹⃗21 ∆𝑡 = 𝑚1 𝑣⃗1𝑓 − 𝑚1 𝑣⃗1𝑖, what does 𝑣⃗1𝑖 represent?

    <p>The initial velocity of m1 (C)</p> Signup and view all the answers

    What is a key assumption made in the derivation of the equation 𝑚1 𝑣⃗1𝑓 + 𝑚2 𝑣⃗2𝑓 = 𝑚1 𝑣⃗1𝑖 + 𝑚2 𝑣⃗2𝑖?

    <p>The collision is a head-on collision (D)</p> Signup and view all the answers

    Why is it important to consider the concept of an isolated system when applying the law of conservation of momentum?

    <p>To ensure that the system is not subject to any external forces (C)</p> Signup and view all the answers

    What is the definition of impulse?

    <p>The product of force and time interval (D)</p> Signup and view all the answers

    When is the impulse-momentum theorem always true?

    <p>Always true, regardless of the force or time interval (B)</p> Signup and view all the answers

    What is the unit of impulse?

    <p>Kilogram-meter per second (kg·m/s) (A), Newton-second (N·s) (D)</p> Signup and view all the answers

    What is the average force?

    <p>The force that delivers the same impulse to the object in the time interval Δt as the actual time-varying force (D)</p> Signup and view all the answers

    What is the relationship between impulse and change in momentum?

    <p>Impulse is directly proportional to the change in momentum. (B)</p> Signup and view all the answers

    What happens to the momentum of an object if a constant force acts on it for a longer time?

    <p>The momentum will increase. (B)</p> Signup and view all the answers

    If the impulse acting on an object is zero, what can you conclude about its momentum?

    <p>The momentum is constant. (B)</p> Signup and view all the answers

    Which of the following is NOT a factor that affects the impulse experienced by an object?

    <p>The color of the object (C)</p> Signup and view all the answers

    What is the total mass of the car and truck after they collide?

    <p>4.00 × 10³ kg (C)</p> Signup and view all the answers

    Why is the final velocity of the wreckage determined by the x and y components?

    <p>All of the above. (D)</p> Signup and view all the answers

    What is the initial total momentum in the x-direction?

    <p>3.75 × 10⁴ kg m/s (D)</p> Signup and view all the answers

    What does the equation ∑𝒑𝒙𝒊 = 𝒎𝐜𝐚𝐫 𝒗𝐜𝐚𝐫 represent?

    <p>The initial momentum of the car in the x-direction. (B)</p> Signup and view all the answers

    Which of the following assumptions is NOT made in the provided example?

    <p>The collision occurs in a vacuum with no air resistance. (B)</p> Signup and view all the answers

    If the collision were elastic, what would be an additional conserved quantity?

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

    Which of the following correctly describes the final momentum of the wreckage?

    <p>The final momentum is equal to the vector sum of the initial momenta of the car and truck. (A)</p> Signup and view all the answers

    What happens to the total linear momentum of a system when no external forces act on it?

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

    In a glancing collision, what does 'glancing' refer to?

    <p>A collision where the objects collide at a non-zero angle. (A)</p> Signup and view all the answers

    In the equation for the conservation of momentum in the x-direction, m<sub>1</sub>v<sub>1ix</sub> + m<sub>2</sub>v<sub>2ix</sub> = m<sub>1</sub>v<sub>1fx</sub> + m<sub>2</sub>v<sub>2fx</sub>, what does the subscript 'i' refer to?

    <p>Initial velocity. (B)</p> Signup and view all the answers

    In the provided equations, how many unknowns are there for a glancing collision where the initial velocity, masses, and whether the collision is elastic are known?

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

    What does the equation 1/2 * m<sub>1</sub> * v<sub>1i</sub><sup>2</sup> = 1/2 * m<sub>1</sub> * v<sub>1f</sub><sup>2</sup> + 1/2 * m<sub>2</sub> * v<sub>2f</sub><sup>2</sup> represent?

    <p>Conservation of kinetic energy. (C)</p> Signup and view all the answers

    What is the significance of the y-component of momentum being zero in the equation 0 + 0 = m<sub>1</sub>v<sub>1f</sub> sin 𝜃 + m<sub>2</sub>v<sub>2f</sub> sin 𝜑?

    <p>It means the initial vertical component of momentum is zero. (B)</p> Signup and view all the answers

    If the collision is perfectly elastic, what is conserved?

    <p>Both momentum and kinetic energy. (C)</p> Signup and view all the answers

    Why are glancing collisions considered a special case of collisions?

    <p>The analysis of glancing collisions can be simplified by considering the motion only in two dimensions. (B)</p> Signup and view all the answers

    Signup and view all the answers

    Flashcards

    Components of momentum

    Momentum in Cartesian coordinates: px = mvx, py = mvy, pz = mvz

    Magnitude of momentum

    Magnitude of momentum is given by p = √(px² + py² + pz²)

    Kinetic energy and momentum relationship

    Kinetic energy EK relates to momentum as EK = p²/(2m)

    SI unit of momentum

    Momentum is measured in kg m/s in SI units.

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    Newton's Second Law Formulation

    Newton's second law gives net force as F_net = Δp/Δt.

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    Conservation of Momentum

    Momentum is conserved when net force F_net = 0.

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    Change in momentum

    The change in momentum Δp over time Δt equals the net force F_net.

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    Velocity terms in momentum expression

    Momentum in directions: px, py, pz relates to velocity components vx, vy, vz.

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    Impulse

    The product of force and the time interval during which it acts.

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    Impulse-Momentum Theorem

    States that the impulse on an object equals its change in momentum.

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    Momentum

    The product of an object's mass and its velocity.

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    Vector Quantity

    A quantity that has both magnitude and direction.

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    Constant Force

    A force that does not change in magnitude or direction during the time interval.

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    Average Force

    The constant force that delivers the same impulse as a variable force over a time interval.

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    Time Interval (Δt)

    The duration during which a force is applied.

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    Collision Impulse Calculation

    Finding the impulse by multiplying the average force by the duration of the collision.

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    Collision Forces

    F21 and F12 are forces during a collision, equal and opposite.

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    Total Momentum in Collisions

    Total momentum before and after a collision is constant.

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    Average Forces During Collision

    Average forces F21 and F12 account for changing forces over time.

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    Momentum Change in Collisions

    Change of velocity in lighter vs. heavier particles differs.

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    Newton’s Third Law

    For every action, there's an equal and opposite reaction force.

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    Isolated System Definition

    An isolated system does not exchange energy or matter.

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    Final momentum equation

    The equation 0 = m1v1f + m2v2f represents final momentum.

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    Substituted values for momentum

    Using m1 = 59.97 kg, m2 = 0.030 kg, v2f = 50.0 m/s in momentum calculations.

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    Archer's final velocity after firing

    The final velocity of archer after firing is v1f = v1i - (m2v2fcosθ)/(m1-m2).

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    Angle in momentum equation

    Angle θ is the direction the second arrow is fired, affecting momentum.

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    Acceleration of the arrow

    Acceleration a is calculated using a = (v2 - v20) / (2*Δx).

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    Estimating acceleration

    Acceleration can be estimated as a = (50 m/s)² / (2*0.800 m).

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    Time of arrow acceleration

    The time for acceleration calculated as t = (v - v0) / a.

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    Normal force on the archer

    Average normal force is related to acceleration of the arrow by the bowstring.

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    Two-dimensional collisions

    Collisions that occur in a plane, involving two objects.

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    X-component momentum equation

    m1 * v1i + 0 = m1 * v1f cos(θ) + m2 * v2f cos(φ)

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    Y-component momentum equation

    0 + 0 = m1 * v1f sin(θ) + m2 * v2f sin(φ)

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    Elastic collision

    A collision where both momentum and kinetic energy are conserved.

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    Unknowns in collision equations

    In collisions, variables such as v1f, v2f, θ, and φ are often unknowns.

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    Angle of deflection (θ)

    The angle at which the first object moves after a collision.

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    Angle of deflection (φ)

    The angle at which the second object moves after a collision.

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    Types of Collisions

    Collisions can be elastic or inelastic, affecting energy conservation.

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    Perfectly Inelastic Collision

    A collision where two objects stick together after impact.

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    Momentum Conservation

    Total momentum before collision equals total momentum after collision.

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    Kinetic Energy in Inelastic Collisions

    In inelastic collisions, kinetic energy is not conserved.

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    Initial Momentum Calculation

    Calculate initial momentum by summing object momenta before collision.

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    Final Velocity after Collision

    Final velocity after a perfectly inelastic collision is based on combined mass.

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    Friction Neglect in Collisions

    Assuming no friction simplifies momentum calculations during collisions.

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    Study Notes

    Linear Momentum

    • Linear momentum (momentum) of a body is defined as the product of its mass and velocity
    • p = mv, where p represents momentum, m is mass, and v is velocity
    • Momentum is a vector quantity, meaning it has both magnitude and direction

    Impulse

    • Impulse is a vector quantity with the same direction as the constant force acting on an object
    • Impulse, I, is equal to the change in momentum (Δp), and is calculated as:
      • I = FΔt = Δp = mv₁ – mv₀, where F is the force, Δt is the time interval, v₁ is the final velocity, and v₀is the initial velocity

    Conservation of Momentum

    • When a collision occurs within an isolated system, the total momentum of the system doesn't change
    • The total momentum before the collision equals the total momentum after the collision.
    • The principle of conservation of momentum is valid for both elastic and inelastic collisions, provided an isolated system is considered.

    Types of Collisions

    • Elastic collision: In an elastic collision, both momentum and kinetic energy are conserved
    • Inelastic collision: In an inelastic collision, momentum is conserved, but kinetic energy is not conserved
    • Perfectly inelastic collision: A perfectly inelastic collision is a specific type of inelastic collision in which the colliding objects stick together after the collision, moving with a common final velocity.

    Center of Mass

    • The center of mass (CM) of a system of particles is the average position of the system's mass. It's the point at which the system can be balanced if suspended from that point
    • In a system of multiple point masses, the coordinates of the CM are given by these expressions:
      • XCM = Σmixi/Σmi
      • YCM = Σmiyi/Σmi
      • ZCM = Σmizi/Σmi where mi represents the mass of the ith particle and xi, yi, zi represent the i-th particle's x, y, and z coordinates, respectively.

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    Test your understanding of the relationship between momentum and kinetic energy in this physics quiz. Answer questions about momentum calculations, SI units, and the effects of force on momentum. Perfect for students looking to strengthen their grasp of these fundamental concepts.

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