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

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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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