Physics Chapter: Impulse and Momentum
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Questions and Answers

What is the relationship between impulse and momentum according to the impulse-momentum theorem?

  • Impulse is inversely proportional to the change in momentum.
  • Impulse is independent of the change in momentum.
  • Impulse is equal to the change in momentum. (correct)
  • Impulse is directly proportional to the change in momentum.
  • Which of the following is a vector quantity?

  • Speed
  • Time
  • Impulse (correct)
  • Mass
  • In the context of the impulse-momentum theorem, what is the significance of the time of contact (∆t)?

  • It affects both the magnitude and direction of the force, and therefore influences the change in momentum. (correct)
  • It affects the direction of the force, but not the change in momentum.
  • It has no effect on the impulse or the change in momentum.
  • It affects the magnitude of the force, but not the change in momentum.
  • Why is it difficult to measure the net average force (σ 𝐹) during a collision directly?

    <p>The force is not constant during the collision. (A)</p> Signup and view all the answers

    In the example of the baseball and the bat, why is the weight of the ball neglected during the impulse calculation?

    <p>The weight of the ball is negligible compared to the force exerted by the bat. (A)</p> Signup and view all the answers

    What is the SI unit of impulse?

    <p>Newton-second (N  s) (A)</p> Signup and view all the answers

    How does the impulse-momentum theorem explain the launch of a space shuttle?

    <p>The impulse of the engines is equal to the change in momentum of the shuttle. (A)</p> Signup and view all the answers

    What is the correct formula for impulse?

    <p>$\Sigma F \Delta t = mv_f - mv_i$ (C)</p> Signup and view all the answers

    What is the formula for the gravitational potential energy PE of an object?

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

    Which of the following is NOT a correct unit for work?

    <p>watt-second (W-s) (A)</p> Signup and view all the answers

    If a gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down, what is the equation for the initial speed of the gymnast?

    <p>v = √(2gh) (B)</p> Signup and view all the answers

    What is the formula to calculate the center of mass (xcm) of a system of two particles?

    <p>xcm = (m1x1 + m2x2)/(m1 + m2) (D)</p> Signup and view all the answers

    What is the formula for work done against gravity?

    <p>Wgravity = mg(ho - hf) (B)</p> Signup and view all the answers

    What is the formula for work done by a constant force?

    <p>W = Fs (A)</p> Signup and view all the answers

    If m1 = m2 = m, what is the formula for the center of mass of a system of two particles?

    <p>xcm = (x1 + x2)/2 (A)</p> Signup and view all the answers

    What does 'Wgravity = mg (ho - hf)' represent?

    <p>Work done against Gravity (C)</p> Signup and view all the answers

    What is the calculated force exerted by the boy on the lever?

    <p>200 N (B)</p> Signup and view all the answers

    Using the given data, what is the weight of the boy if g is 10 m/s²?

    <p>20 kg (C)</p> Signup and view all the answers

    What is the force exerted by the fulcrum when the forces are balanced?

    <p>1000 N (C)</p> Signup and view all the answers

    Which of the following describes the conditions needed to find the magnitude of forces on the bridge?

    <p>Both B and C are correct. (D)</p> Signup and view all the answers

    How far along the bridge does the hiker stop relative to its total length?

    <p>One-fifth of the way (C)</p> Signup and view all the answers

    What is the net force acting on the diving board in the first example when it is in equilibrium?

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

    Why does the force F1 in the first example point downwards?

    <p>Because the bolt is pulling down on the board. (A)</p> Signup and view all the answers

    In the second example, why is the weight of the board ignored?

    <p>Because the problem specifically instructs to ignore the weight of the board. (B)</p> Signup and view all the answers

    What is the relationship between the torque produced by F2 and the torque produced by W in the first example?

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

    In the first example, what is the lever arm for the weight W?

    <p>2.50 m (A)</p> Signup and view all the answers

    If the woman in the first example moved closer to the fulcrum, what would happen to the force F2?

    <p>F2 would increase. (A)</p> Signup and view all the answers

    What is the concept used in the solution of the examples for determining the forces on the board?

    <p>Static equilibrium. (A)</p> Signup and view all the answers

    In the second example, if the boy moved closer to the fulcrum, what would happen to the mass of the boy required to balance the teeter-totter?

    <p>The required mass would increase. (A)</p> Signup and view all the answers

    A car with a mass of 1000 kg is traveling at a speed of 20 m/s. What is the car's momentum?

    <p>20,000 kg*m/s (B)</p> Signup and view all the answers

    A 0.5 kg ball is thrown vertically upward with an initial velocity of 10 m/s. What is the ball's momentum at its highest point?

    <p>0 kg*m/s (C)</p> Signup and view all the answers

    A 2 kg object is moving at a constant velocity of 5 m/s. What is the net force acting on the object?

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

    A 1.5 kg object has a momentum of 6 kg*m/s. What is the object's velocity?

    <p>4 m/s (D)</p> Signup and view all the answers

    A 2 kg object moving at 4 m/s collides head-on with a stationary 1 kg object. After the perfectly elastic collision, what is the velocity of the 1 kg object?

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

    If the momentum of a car is doubled while its mass remains constant, what happens to its velocity?

    <p>It is doubled (D)</p> Signup and view all the answers

    A 1000 kg car is traveling at 20 m/s when the brakes are applied. The car comes to a stop in 5 seconds. What is the average force exerted by the brakes on the car?

    <p>4000 N (D)</p> Signup and view all the answers

    Which of these statements about momentum is TRUE?

    <p>Momentum is always conserved in a closed system (B)</p> Signup and view all the answers

    What is the formula for the position vector of the center of mass of a system of particles?

    <p>$\frac{\sum_{v=1}^{N} m_v r_v}{M}$ (C)</p> Signup and view all the answers

    If the position vector of the center of mass is given by $\frac{\sum_{v=1}^{N} m_v r_v}{M}$, what is the formula for the velocity of the center of mass?

    <p>$\frac{\sum_{v=1}^{N} m_v \dot{r}_v}{M}$ (C)</p> Signup and view all the answers

    What is the formula for the x-coordinate of the center of mass in a system of particles?

    <p>$\frac{\sum_{v=1}^{N} m_v x_v}{M}$ (C)</p> Signup and view all the answers

    A system consists of three particles with masses 2kg, 3kg, and 5kg. Their position vectors are (1,2,3), (4,5,6), and (7,8,9) respectively. What is the y-coordinate of the center of mass of the system?

    <p>6.5 (C)</p> Signup and view all the answers

    The center of mass of a system of particles is a point that:

    <p>Represents the average location of the system's mass. (D)</p> Signup and view all the answers

    If the net external force acting on a system of particles is zero, what can be said about the acceleration of the center of mass?

    <p>The acceleration of the center of mass must be zero. (D)</p> Signup and view all the answers

    The torque on a rigid object is:

    <p>The force applied to the object multiplied by the lever arm. (B)</p> Signup and view all the answers

    Which of the following factors does NOT influence the magnitude of the torque on an object?

    <p>The mass of the object. (A)</p> Signup and view all the answers

    Flashcards

    Linear Momentum

    The product of mass and velocity (p = mv) of an object.

    Impulse-Momentum Theorem

    The impulse of a net force equals the change in momentum of an object.

    Impulse

    The product of average force and time (ΣF ∆t) during a collision.

    SI Unit of Linear Momentum

    Kilogram meter per second (kg.m/s) is the unit measure for momentum.

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    Equation for Net Force

    The net force equals mass times acceleration (ΣF = ma).

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    Change in Momentum

    Difference between final and initial momentum (mvf - mvo).

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    Average Force during Collision

    Force exerted by the bat that affects the ball's momentum.

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    Application of Impulse

    Applied forces during events like the shuttle launch increase momentum.

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    Momentum

    The quantity of motion of a moving body, measured as a product of its mass and velocity.

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    Average Force

    The change in momentum per unit time; calculated as F = Δp/Δt.

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    Kinetic Energy

    The energy an object has due to its motion, calculated as KE = 1/2 mv².

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    Elastic Collision

    A collision in which both momentum and kinetic energy are conserved.

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    Mass from Kinetic Energy

    Using kinetic energy and momentum to solve for mass; m = P/v.

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    Velocity of a Moving Object

    The speed of an object in a specific direction.

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    Rain's Impact Force

    The force exerted by rain when it strikes a surface, calculated as F = -m * vo.

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    Gravitational Potential Energy (PE)

    Energy an object has due to its height above ground, calculated as PE = mgh.

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    Work (W)

    The energy transferred when a force moves an object, defined as W = (F cosθ)s.

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    Initial Speed (vo)

    The speed of an object at the start of its motion, calculated using vo = - √(2g(ho - hf)).

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    Final Speed (vf)

    The speed of an object at the end of its motion, calculated from initial speed and work done.

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    Center of Mass (xcm)

    The average location of a system's mass, calculated as xcm = (m1x1 + m2x2) / (m1 + m2).

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    System of Particles

    A collection of particles whose motion is analyzed together, often using center of mass coordinates.

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    Height (h)

    The vertical distance an object is from a reference point, often ground level in physics.

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    Force (F)

    An interaction that changes the motion of an object, often calculated in Newtons (N).

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    Center of Mass

    The average position of all particles' mass in a system.

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    Position Vector

    A vector representing an object's position from a reference point.

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    Mass Sum

    The total mass of all particles in the system.

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    Velocity of Center of Mass

    The speed and direction of the center of mass over time.

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    Torque Definition

    A measure of how much a force causes an object to rotate.

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    Magnitude of Torque

    The product of force and lever arm distance, τ = Fℓ.

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    Lever Arm

    Distance from the axis of rotation to the line of action of the force.

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    Differentiation of Center of Mass

    Calculating changes in the position to find velocity and acceleration.

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    Equilibrium Condition

    In equilibrium, sum of forces and torques is zero.

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    Sum of Forces

    The total of all external forces acting on an object, must equal zero in equilibrium (ΣF = 0).

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    Sum of Torques

    The total of all torques about a point must be zero (Στ = 0) in equilibrium.

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    Force at Fulcrum

    The support force exerted upward by the fulcrum on a board in equilibrium.

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    Torque Calculation

    Torque is calculated as force times distance from pivot (τ = F × d).

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    Downward Force (F1)

    The downward force (F1) acting to prevent counterclockwise rotation on a board.

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    Weight's Effect

    Weight of an object creates a clockwise torque about the fulcrum.

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    Board Length in Torque

    The length of the board affects torque calculation by changing lever arms.

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    Torque Equation

    The sum of torques equals zero when in equilibrium: ∑τ = F λ1 - W λW = 0.

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    Net Force Condition

    The total vertical forces must balance: ΣFy = -F1 + F2 - W = 0.

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    Weight Calculation

    Weight (W) is calculated as W = mg, where g = 10 m/s².

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    Mass from Force

    To find mass, use F = mg and rearrange: m = F/g.

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    Bridge Support Force

    For a bridge, support forces depend on weight distribution and position of loads.

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    Study Notes

    Mechanics and Properties of Matter

    • This module covers conservative forces, conservation of linear momentum, kinetic energy and work, potential energy, systems of particles, center of mass, torque, vector product, and moment.

    Definition of a Conservative Force

    • Version 1: A force is conservative if the work it does on a moving object is independent of the path between the initial and final positions.
    • Version 2: A conservative force does no work on an object moving around a closed path, starting and ending at the same point.
    • Example of conservative forces: Gravitational force, elastic force of a spring, electrical force of electrically charged particles.
    • Gravity Work: Work done by gravity is calculated as Wgravity = mg(ho - h1).

    Linear Momentum and Collision

    • Forces on objects are not always constant.
    • Figure 1a illustrates a baseball being hit and Figure 1b shows the force applied to the baseball by the bat during contact.
    • Time of contact affects the force exerted over that time.

    Definition of Impulse

    • Impulse (J) is the product of the average force (F) and the time interval (Δt) during which the force acts. J = FΔt.
    • Impulse is a vector quantity, meaning it has both magnitude and direction. The direction of impulse is the same as the direction of the average force.

    Definition of Linear Momentum

    • Linear momentum (p) of an object is the product of its mass (m) and velocity (v). p = mv
    • Linear momentum is a vector quantity and points in the same direction as velocity.

    Impulse-Momentum Theorem

    • A net force acting on an object changes the object's momentum.
    • The impulse of this net force is equal to the change in the object's momentum.
    • This is expressed as ΣF(Δt) = mvf - mv0.

    Application of Impulse-Momentum Theorem

    • Engines apply an impulse during the launch of a space shuttle, increasing the momentum of the shuttle and launch vehicle.

    Example 1 (Baseball)

    • A baseball's initial velocity (v0) is -38 m/s.
    • Final velocity (vf) is +58 m/s
    • Mass (m) is 0.14 kg.
    • Time of contact (Δt) is 1.6 x 10-3 s.
    • Calculate impulse and average force.

    Example 2 (Rain on a Car)

    • Rain velocity (v0) is -15 m/s.
    • Mass of rain per second (m/Δt) is 0.060 kg/s.
    • Rain comes to rest upon striking the car.
    • Find average force exerted by rain.

    Class Activity 1 and 2

    • The momentum of a person walking.
    • Change in momentum for a bouncing ball.

    Class Activity 3 and Example

    • Momentum of and kinetic energy of a projectile are known. Given information find mass.

    Class Activity 4 and Example

    • Elastic collision between a van and a car stopped at a traffic light. Find the final car velocity

    Assignment- Question 1

    • Objects with equal momentum may have different velocities
    • Objects of equal magnitude can have different directions

    Assignment- Question 2

    • Impulse applied to change volleyball velocity.

    The Principle of Conservation of Linear Momentum

    • Momentum is conserved in collisions of isolated systems.
    • Internal forces in a collision are equal and opposite.

    Two Types of Forces Acting on a System

    • Internal forces are forces exerted between objects within a system.
    • External forces are forces exerted on objects by agents outside the system.

    Principle of Conservation of Linear Momentum (additional explanation)

    • Internal forces cancel out during a collision.
    • Total momentum of an isolated system is constant.

    Example (Freight Train)

    • Freight cars couple during a switching action.
    • Calculate common velocity when cars couple together.

    Class Activity (Skating)

    • Using conservation of momentum, calculate the recoil velocity of a skater.

    Elastic vs. Inelastic Collisions

    • Elastic: Kinetic energy is conserved.
    • Inelastic: Kinetic energy is not conserved in a perfectly inelastic collision, objects stick together.

    Example: Elastic Collision

    • Two balls collide.
    • Find the velocities of the balls after an elastic collision.

    ###Applying the Principle of Conservation of Linear Momentum

    • Four steps for applying Conservation of Momentum

    Work and Energy

    • Work (W) is a scalar quantity equal to the product of the force (F), displacement (s), and cosine of the angle (θ) between F and s : W = Fs.
    • The SI unit of work is the joule (J).
    • Work done by a constant force acting perpendicular to a displacement is zero.

    Example 1: Pulling a Suitcase-on-Wheels

    • Calculate work done.

    Positive vs Negative Work

    • Positive work when force and displacement are in the same direction.
    • Negative work when force and displacement are in opposite directions.

    Example (Accelerating a Crate)

    • Total work done on the crate.

    Definition of Kinetic Energy

    • Kinetic energy (KE) of an object with mass (m) and speed (v) is given by KE = ½ mv².
    • Kinetic energy is a scalar with the same units as work (joules).
    • Work done by a net force is equivalent to the change in kinetic energy

    Example: Work-Energy Theorem

    • When a net external force does work on an object, its kinetic energy changes.

    Deduction from the figure above

    • The work-energy theorem only applies to a net force.
    • Positive work increases kinetic energy.
    • Negative work decreases kinetic energy.
    • Zero work keeps kinetic energy constant.

    Example 1 (Space Probe)

    • Calculate the final speed of a space probe.

    Gravitational Potential Energy

    • Gravitational potential energy PE=mgh

    Example: Gymnast

    • Calculation of initial speed of a gymnast.

    Center of Mass

    • Center of mass, a single point representing the average location of a system's total mass, derived from the sum of positions weighted by mass.

    ###Example

    • The center of mass of a two-particle system is the midpoint if each has equal mass.
    • The center of mass moves closer to a heavier particle if masses are unequal.
    • Systems with more than two particles use generalized equations.

    System Of Particles

    • Center of mass coordinates are the best way to describe the motion of a system with many particles

    Examples and Definitions of Torque

    • Torque is a measure of the tendency of a force to produce rotation.
    • Torque is a vector quantity calculated as τ = r × F, where r is the position vector relative to the axis and F is the force acting on the object
    • Torques calculated around an axis are positive when they produce counterclockwise rotation.

    Examples of Torque

    • The torque produced when a force is applied to a door with different lever arms.

    Example (Ankle Joint)

    • Calculating the torque (magnitude and direction) exerted on an ankle joint.

    Cross Product and Torque

    • Torque can be mathematically calculated with the cross product of position vector r and force vector F: τ = r × F.

    Activity

    • Finding the torque when a force is applied at a point on an object that is pivoted around the z-axis.

    Moment

    • A rigid body is in equilibrium if its translational and angular accelerations are zero.

    Example (Diving Board)

    • Calculate the forces the bolt and the fulcrum exert on a diving board.

    Example (Teeter-Totter)

    • Calculating the mass of a boy using the concept of torque on a teeter-totter.

    Example (Bridge)

    • Calculating the force exerted on a bridge by supports when a hiker is on the bridge.

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    Description

    Test your understanding of the impulse-momentum theorem in this quiz. Explore key concepts such as the relationship between impulse and momentum, vector quantities, and the significance of contact time during collisions. Challenge yourself with practical examples and formulas related to these fundamental physics principles.

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