ch 8 Physics Chapter on Linear Momentum
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Questions and Answers

What is the SI unit for linear momentum?

  • kg.m/s (correct)
  • kg/s
  • kg.m
  • m/s

    • If an object's mass doubles while its velocity remains the same, what happens to its momentum?

  • It doubles. (correct)
  • It halves.
  • It remains the same.
  • It triples.

    • For a runaway train car of mass 15,000 kg traveling at 5.4 m/s, what is required to bring it to rest using a force of 1500 N?

  • 0.5 seconds
  • 10 seconds (correct)
  • 20 seconds
  • 15 seconds

    • What does the change in momentum (∆p) represent in the context of impulse?

    <p>The product of force and time.</p> Signup and view all the answers

    Which of the following statements about momentum is correct?

    <p>Momentum can be a negative value.</p> Signup and view all the answers

    In Newton's second law, how is the net external force related to the change in momentum?

    <p>It is proportional to the change in momentum and the change in time.</p> Signup and view all the answers

    What would happen if both the mass and the velocity of an object were reduced to half?

    <p>The momentum is halved.</p> Signup and view all the answers

    If a large ship has a momentum of $1.60 imes 10^9$ kg.m/s moving at a speed of 48.0 km/hr, what is its mass?

    <p>4,000 kg</p> Signup and view all the answers

    What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms?

    <p>900 N</p> Signup and view all the answers

    What impulse is imparted by a horizontal blow of 1000 N lasting 0.150 s?

    <p>100 N·s</p> Signup and view all the answers

    Which best defines an isolated system in momentum conservation?

    <p>A system with net external force equal to zero</p> Signup and view all the answers

    In an elastic collision, which type of energy is conserved?

    <p>Internal kinetic energy</p> Signup and view all the answers

    What happens to momentum in a two-car collision if car 1 loses momentum?

    <p>Total momentum remains constant</p> Signup and view all the answers

    During a crash, how does the force exerted by a seat belt relate to the passenger's mass and stopping time?

    <p>It is directly proportional to the mass and inversely proportional to the stopping time</p> Signup and view all the answers

    Which statement is true regarding the conservation of momentum at the subatomic level?

    <p>All subatomic particles, including massless photons, possess momentum</p> Signup and view all the answers

    What characterizes an elastic collision?

    <p>Internal kinetic energy is conserved.</p> Signup and view all the answers

    What is a characteristic of elastic collisions concerning kinetic energy?

    <p>All kinetic energy is conserved</p> Signup and view all the answers

    In a perfectly elastic collision, how does the total momentum of the system behave?

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

    What happens to internal kinetic energy in a perfectly inelastic collision?

    <p>It becomes zero.</p> Signup and view all the answers

    Which of the following statements is true regarding inelastic collisions?

    <p>They can involve objects sticking together.</p> Signup and view all the answers

    When calculating the velocities after an elastic collision, which formula is used?

    <p>Both momentum and kinetic energy conservation equations.</p> Signup and view all the answers

    What would be the result of an inelastic collision between two objects in terms of their motion?

    <p>They move together as a single object after colliding.</p> Signup and view all the answers

    During nearly elastic collisions on icy surfaces or air tracks, what type of energy transformation primarily occurs?

    <p>Kinetic energy is conserved as kinetic energy.</p> Signup and view all the answers

    If two steel blocks collide on ice, what aspect is most affected by the low friction conditions?

    <p>The ability to achieve nearly elastic collisions is enhanced.</p> Signup and view all the answers

    What is the final velocity of two clay models that stick together after a perfectly inelastic collision?

    <p>0.265 m/s</p> Signup and view all the answers

    During a perfectly inelastic collision, what happens to the internal kinetic energy of the system?

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

    If two train cars collide and stick together, how do you determine their final velocity?

    <p>Apply conservation of momentum</p> Signup and view all the answers

    What is a key characteristic of point masses in two-dimensional collisions?

    <p>They cannot rotate or spin</p> Signup and view all the answers

    What does a negative velocity indicate in the context of train car collisions?

    <p>The object is moving backward</p> Signup and view all the answers

    In the conservation of momentum equation for a two-dimensional collision, what must be true about the momentum components?

    <p>They are conserved separately</p> Signup and view all the answers

    What is the force exerted on a tennis ball if it reaches a final velocity of 45.0 m/s with a force applied for 5.00 ms?

    <p>540 N</p> Signup and view all the answers

    How do you calculate the mass of a tennis ball if it reaches a final velocity of 45.0 m/s due to a force of 540 N applied for 5.00 ms?

    <p>Use the impulse-momentum theorem</p> Signup and view all the answers

    Calculate the momentum of a 110-kg football player running at 8.00 m/s.

    <p>880 kg.m/s</p> Signup and view all the answers

    Calculate the momentum of a 2000-kg elephant charging a hunter at a speed of 7.50 m/s.

    <p>15000 kg.m/s</p> Signup and view all the answers

    What is the mass of a large ship that has a momentum of 1.60 x 10^9 kg.m/s, when the ship is moving at a speed of 48.0 km/hr?

    <p>mass = 80000 kg</p> Signup and view all the answers

    Compute the time required for a force of 1500 N to bring a runaway train car with mass 15,000 kg traveling at 5.4 m/s to rest.

    <p>time = 11.25 s</p> Signup and view all the answers

    What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms?

    <p>force = 900 N</p> Signup and view all the answers

    Calculate the force the seat belt exerts on a 70 kg passenger in a car moving at 10 m/s that crashes into a tree and stops in 0.26 s.

    <p>force = 2692.31 N</p> Signup and view all the answers

    Calculate the impulse imparted by a 1000-N horizontal blow that lasts for 0.150 s.

    <p>impulse = 150 N.s</p> Signup and view all the answers

    What is the principle of conservation of momentum?

    <p>The total momentum of an isolated system remains constant.</p> Signup and view all the answers

    What is the final velocity if a 0.200 kg clay model runs into 0.350 kg clay model at rest?

    <p>final velocity = 0.433 m/s</p> Signup and view all the answers

    What is the final velocity when two loaded train cars with masses of 150,000 kg and 110,000 kg and velocities of 0.300 m/s and -0.120 m/s collide?

    <p>final velocity = 0.188 m/s</p> Signup and view all the answers

    Using a force of 540 N exerted for 5.00 ms, find the mass of a tennis ball that achieves a final velocity of 45.0 m/s.

    <p>mass = 0.6 kg</p> Signup and view all the answers

    The equation representing the conservation of momentum for two objects in a one-dimensional collision is ___ + ___ = ___' + ___'.

    <p>p1, p2, p1', p2'</p> Signup and view all the answers

    In an elastic collision, what is conserved?

    <p>momentum and internal kinetic energy</p> Signup and view all the answers

    If the momentum of an object is increased while its mass remains constant, what must be true about its velocity?

    <p>It must increase.</p> Signup and view all the answers

    How does a change in momentum relate to an external force over time?

    <p>Net force is equal to change in momentum divided by time.</p> Signup and view all the answers

    Which of the following correctly reflects the relationship between impulse and momentum?

    <p>Impulse is the same as the change in momentum.</p> Signup and view all the answers

    What effect does a larger force acting over a short time have compared to a smaller force acting for a longer time?

    <p>The smaller force can match the change in momentum.</p> Signup and view all the answers

    What must occur if a stationary object experiences a net force applied for a certain duration?

    <p>The object's momentum will increase.</p> Signup and view all the answers

    In the context of momentum, what does the symbol Δp represent?

    <p>The change in momentum.</p> Signup and view all the answers

    When calculating momentum, if the velocity of an object is doubled while its mass remains constant, what happens to its momentum?

    <p>It doubles.</p> Signup and view all the answers

    What is the primary factor that influences the effect of a force on the momentum of an object?

    <p>The duration the force is applied.</p> Signup and view all the answers

    What is a key characteristic of an elastic collision?

    <p>Internal kinetic energy is conserved.</p> Signup and view all the answers

    What happens to the internal kinetic energy in a perfectly inelastic collision?

    <p>It reduces to the minimum possible.</p> Signup and view all the answers

    Which equation represents the conservation of momentum for two objects in a collision?

    <p>𝑝1 + 𝑝2 = 𝑝1′ + 𝑝2′</p> Signup and view all the answers

    In which scenario is kinetic energy conserved during a collision?

    <p>In a perfectly elastic collision.</p> Signup and view all the answers

    Which type of collision occurs when two vehicles collide and come to rest together?

    <p>Perfectly inelastic collision</p> Signup and view all the answers

    How would you describe the impulse experienced by an object when a constant force acts on it over a period of time?

    <p>It is the change in the object's momentum.</p> Signup and view all the answers

    What is the effect of an external unbalanced force on a two-car collision system with respect to momentum?

    <p>The total momentum of the system remains constant if no external force acts.</p> Signup and view all the answers

    What is the primary effect of choosing nearly frictionless surfaces for collisions?

    <p>It facilitates elastic collisions.</p> Signup and view all the answers

    In a perfectly elastic collision, which of the following statements is true?

    <p>Both momentum and kinetic energy are conserved.</p> Signup and view all the answers

    In the case of an inelastic collision, what best describes the fate of kinetic energy?

    <p>It is converted into other forms of energy.</p> Signup and view all the answers

    How is the simplification of kinetic energy relationship expressed for two colliding masses?

    <p>𝑣1 + 𝑣1′ = 𝑣2 + 𝑣2′</p> Signup and view all the answers

    During an elastic collision involving subatomic particles, which concept is primarily applicable?

    <p>Momentum conservation relates to wave properties and particle interactions.</p> Signup and view all the answers

    What happens to the internal kinetic energy during a perfectly inelastic collision?

    <p>Some internal kinetic energy is converted to other forms of energy.</p> Signup and view all the answers

    What determines the force exerted by a seat belt on a passenger during a car crash?

    <p>The collision's impact force and passenger's inertia.</p> Signup and view all the answers

    Which of the following best describes an isolated system in the context of momentum conservation?

    <p>A system with no net external forces acting upon it.</p> Signup and view all the answers

    What is the relationship between impulse and force when a force is applied over a short time period?

    <p>Impulse is the product of force and time duration.</p> Signup and view all the answers

    What is true about the final velocity of two objects that stick together after a perfectly inelastic collision?

    <p>It is zero if both had opposite equal velocities.</p> Signup and view all the answers

    What is the relationship between the internal kinetic energy of a system and inelastic collisions?

    <p>It reduces to zero after a perfectly inelastic collision.</p> Signup and view all the answers

    How do you determine the final velocity of two train cars that collide and stick together?

    <p>Apply conservation of momentum based on their masses and initial velocities.</p> Signup and view all the answers

    What is the momentum conservation equation along the x-axis for a two-dimensional collision involving two masses?

    <p>$m_1 v_1 = m_1 v_1' cos θ_1 + m_2 v_2' cos θ_2$</p> Signup and view all the answers

    What aspect distinguishes point masses in two-dimensional collisions?

    <p>They are considered structureless particles with no rotation.</p> Signup and view all the answers

    What initial condition allows for the conservation of momentum to be applied in a two-dimensional collision scenario?

    <p>The system must have no external forces acting on it.</p> Signup and view all the answers

    In the given scenario, if a tennis ball is accelerated to 45.0 m/s with a force of 540 N applied for 5.00 ms, how can you calculate its mass?

    <p>By using the formula $F = m imes a$ and rearranging.</p> Signup and view all the answers

    Which of the following statements about inelastic collisions is correct?

    <p>Kinetic energy is transformed into other forms of energy.</p> Signup and view all the answers

    Study Notes

    Linear Momentum

    • Linear momentum is the product of an object's mass and velocity.
    • Momentum is a vector quantity, with direction matching the object's velocity.
    • Momentum's SI unit is kg.m/s.

    Newton's Second Law in Terms of Momentum

    • Newton's second law describes the relationship between net force and change in momentum over time.
    • The net force acting on a system equals the change in its momentum divided by the time over which the change occurs.
    • For a constant mass, the change in momentum is equivalent to the product of mass and change in velocity.

    Impulse

    • Impulse is the change in momentum of an object.
    • It equals the product of the net force acting on the object and the time over which the force acts.
    • Impulse is also equivalent to the area under the force-time curve.

    Conservation of Momentum

    • The total momentum of an isolated system remains constant—the total momentum before a collision equals the total momentum after the collision.
    • This principle applies to macroscopic objects, subatomic particles, and even massless particles like photons.

    Elastic Collisions in One Dimension

    • Elastic collisions conserve both momentum and internal kinetic energy—the sum of kinetic energies before and after the collision remains constant.
    • Internal kinetic energy is the total kinetic energy of the objects within the system.
    • Macroscopic collisions can be nearly elastic, but some energy is usually lost to heat or sound.

    Inelastic Collisions in One Dimension

    • Inelastic collisions don't conserve internal kinetic energy—the sum of kinetic energies before and after the collision changes.
    • Internal forces can cause energy loss or gain in inelastic collisions.
    • Perfectly inelastic collisions involve objects sticking together after the collision, leading to the lowest possible internal kinetic energy.

    Collisions of Point Masses in Two Dimensions

    • Collisions where objects scatter to the side are two-dimensional.
    • Momentum conservation applies in both the x and y directions for two-dimensional collisions.
    • The laboratory coordinate system is often used, with a stationary target and incoming particles scattered to reveal information about the target's composition.

    Linear Momentum

    • Linear momentum is the product of an object's mass and velocity: p = mv
    • Momentum is a vector quantity with the same direction as velocity
    • SI unit for momentum: kg m/s

    Momentum and Newton's Second Law

    • Newton's second law can be expressed in terms of momentum: Fnet = Δp/Δt
    • Δp represents the change in momentum, and Δt is the time over which the change occurs
    • Change in momentum is Δp = Δ(mv)

    Impulse

    • Impulse is the change in momentum of an object: Δp = Fnet Δt
    • A large force applied for a short time can have the same impact on momentum as a smaller force applied for a longer time.
    • Impulse is a vector quantity with the same direction as the net force.

    Conservation of Momentum

    • The total momentum of an isolated system (a system with no external forces acting on it) remains constant.
    • ptotal = constant
    • Conservation of momentum applies to both macroscopic and subatomic objects, including massless particles like photons.

    Elastic Collisions

    • An elastic collision conserves both momentum and internal kinetic energy.
    • True elastic collisions are rare in everyday scenarios, but they can be approximated in specific situations like collisions between steel blocks on ice or carts with spring bumpers on an air track.
    • The conservation of momentum equation for two objects in an elastic collision is: m1v1 + m2v2 = m1v1' + m2v2'
    • Conservation of kinetic energy in an elastic collision is: 1/2 m1v1^2 + 1/2 m2v2^2 = 1/2 m1v1'^2 + 1/2 m2v2'^2

    Inelastic Collisions

    • An inelastic collision does not conserve internal kinetic energy.
    • Some kinetic energy is lost or gained due to internal forces within the system, which may involve changes in energy forms like heat or sound.
    • A perfectly inelastic collision is one where the objects stick together.
    • The conservation of momentum equation is still valid for inelastic collisions, but the kinetic energy equation does not hold true.

    Collisions in Two Dimensions

    • Collisions in two dimensions involve objects that scatter to the side.
    • To simplify analysis, we consider point masses which cannot rotate or spin.
    • Conservation of momentum applies in both the x and y directions for collisions in two dimensions.
    • The conservation of momentum equations for two-dimensional collisions are:
      • m1v1 = m1v1'cosθ1 + m2v2'cosθ2 (x-direction)
      • 0 = m1v1'sinθ1 + m2v2'sinθ2 (y-direction)

    Linear Momentum

    • Linear momentum is the product of mass and velocity: 𝑝 = 𝑚𝑣
    • Momentum is a vector quantity, having the same direction as the velocity.
    • The unit used for momentum is kg.m/s.

    Momentum and Newton's Second Law

    • Newton's Second Law can be expressed in terms of momentum: 𝐹𝑛𝑒𝑡 = ∆𝑝 / ∆𝑡
    • The net external force is equal to the change in momentum of a system divided by the time interval.
    • Change in momentum is given by: ∆𝑝 = ∆𝑚𝑣

    Impulse

    • Impulse is defined as the change in momentum of an object: ∆𝑝 = 𝐹𝑛𝑒𝑡 ∆𝑡
    • This concept highlights the effect of force duration, as a larger force over a shorter time can have the same impact as a smaller force over a longer time.
    • The force is often not constant, so an average effective force can be calculated to represent the impact.

    Conservation of Momentum

    • For an isolated system, where the net external force is zero, the total momentum remains constant: 𝑝𝑡𝑜𝑡 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
    • This principle applies to both macroscopic and microscopic systems, including subatomic particles and massless particles like photons.

    Subatomic Collisions and Momentum

    • The conservation of momentum principle is crucial for understanding subatomic particles.
    • It helps determine the masses and properties of previously unknown particles and components like quarks.

    Elastic Collisions in One Dimension

    • An elastic collision conserves both momentum and internal kinetic energy.
    • The total kinetic energy before and after the collision remains the same.
    • This is a theoretical ideal, and real-world collisions are often only near-elastic.

    Inelastic Collisions in One Dimension

    • In inelastic collisions, internal kinetic energy is not conserved.
    • Some kinetic energy is transformed into other forms, like heat or sound, during an inelastic collision.
    • Perfectly inelastic collisions are those in which the objects stick together, leading to zero internal kinetic energy.

    Collisions of Point Masses in Two Dimensions

    • Two-dimensional collisions involve scattering of objects, with velocities not confined to a single line.
    • The conservation of momentum principle applies to both the x and y axes independently in two dimensions.
    • Momentum is preserved along both axes even in two-dimensional collisions.

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