Podcast
Questions and Answers
Which of the following statements correctly describes the relationship between impulse and momentum?
Which of the following statements correctly describes the relationship between impulse and momentum?
- Impulse is the force that causes momentum.
- Impulse equals the change in momentum of an object. (correct)
- Impulse is the rate of change of momentum.
- Impulse is the mass of an object multiplied by its change in velocity.
In an isolated system, momentum is always conserved, regardless of whether the collisions within the system are elastic or inelastic.
In an isolated system, momentum is always conserved, regardless of whether the collisions within the system are elastic or inelastic.
True (A)
What condition must be met for the total momentum of a system to be conserved?
What condition must be met for the total momentum of a system to be conserved?
The vector sum of the external forces acting on the system must be zero.
In a perfectly elastic collision, both momentum and ______ are conserved.
In a perfectly elastic collision, both momentum and ______ are conserved.
Match the type of collision with the correct description.
Match the type of collision with the correct description.
What is a key characteristic of an isolated system concerning momentum?
What is a key characteristic of an isolated system concerning momentum?
The center of mass of an object must be located within the physical boundaries of the object.
The center of mass of an object must be located within the physical boundaries of the object.
If a cannon shell explodes in mid-air, what path does the center of mass of the fragments follow, assuming air resistance is negligible?
If a cannon shell explodes in mid-air, what path does the center of mass of the fragments follow, assuming air resistance is negligible?
The thrust of a rocket is proportional to the exhaust speed and the ______ of fuel ejected per unit time.
The thrust of a rocket is proportional to the exhaust speed and the ______ of fuel ejected per unit time.
Match each concept with its mathematical expression.
Match each concept with its mathematical expression.
What does the impulse-momentum theorem state?
What does the impulse-momentum theorem state?
During a collision, if the net external force acting on the system is negligible, the total momentum of the system is conserved.
During a collision, if the net external force acting on the system is negligible, the total momentum of the system is conserved.
Name three common types of collisions, categorized by whether kinetic energy is conserved.
Name three common types of collisions, categorized by whether kinetic energy is conserved.
In a rocket, the magnitude of the thrust is influenced by the relative speed and the ______ of the ejected material.
In a rocket, the magnitude of the thrust is influenced by the relative speed and the ______ of the ejected material.
Match the scenario to the collision type.
Match the scenario to the collision type.
In an elastic collision, which of the following is true?
In an elastic collision, which of the following is true?
The principle of conservation of momentum is only applicable in inertial frames of reference.
The principle of conservation of momentum is only applicable in inertial frames of reference.
Explain the difference between internal and external forces in the context of conservation of momentum.
Explain the difference between internal and external forces in the context of conservation of momentum.
For a system of particles, the total momentum is equal to the total mass multiplied by the velocity of the ______.
For a system of particles, the total momentum is equal to the total mass multiplied by the velocity of the ______.
Match the energy form to the appropriate location.
Match the energy form to the appropriate location.
What term is designated to the 'quantity of motion'?
What term is designated to the 'quantity of motion'?
For a completely inelastic collision between two objects, the final kinetic energy is always zero.
For a completely inelastic collision between two objects, the final kinetic energy is always zero.
How does an air bag in a car collision help reduce injury in terms of impulse and force?
How does an air bag in a car collision help reduce injury in terms of impulse and force?
In the absence of external forces, the center of mass of a system moves with ______ velocity.
In the absence of external forces, the center of mass of a system moves with ______ velocity.
Match the property with a description.
Match the property with a description.
A system is considered an isolated system when?
A system is considered an isolated system when?
Impulse is a scalar quantity.
Impulse is a scalar quantity.
What are two essential components of the thrust equation for a rocket?
What are two essential components of the thrust equation for a rocket?
The total momentum of a rifle will ______, if no outside forces are exerted on the system, after a bullet is fired.
The total momentum of a rifle will ______, if no outside forces are exerted on the system, after a bullet is fired.
Match the action with the correct type of Collision
Match the action with the correct type of Collision
Flashcards
Momentum (p)
Momentum (p)
Product of mass and velocity; a vector quantity. Symbol: p = mv.
Impulse (J)
Impulse (J)
Change in momentum due to a force acting over a time interval.
Newton's Second Law (momentum)
Newton's Second Law (momentum)
Net force equals the rate of change of momentum.
Impulse-Momentum Theorem
Impulse-Momentum Theorem
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Conservation of Momentum
Conservation of Momentum
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Elastic Collision
Elastic Collision
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Inelastic Collision
Inelastic Collision
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Completely Inelastic Collision
Completely Inelastic Collision
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Center of Mass
Center of Mass
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System's Total Momentum
System's Total Momentum
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Newton's Second Law (system)
Newton's Second Law (system)
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Rocket Thrust (F)
Rocket Thrust (F)
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Relative Velocity
Relative Velocity
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Potentional energy of a spring
Potentional energy of a spring
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Fission
Fission
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Study Notes
- This chapter focuses on momentum, collisions, and impulse
- It investigates phenomena unanswerable by direct application of Newton's second law
Learning Goals
- Define momentum of a particle and how impulse of the net force changes momentum
- Identify conditions where the total momentum of a system is constant
- Examine the solution of problems where two bodies collide
- Discern elastic, inelastic, and completely inelastic collisions
- Define the center of mass of a system, and its motion
- Analyze situations like rocket propulsion where a body's mass changes during movement
Momentum and Impulse
- Momentum is a vector quantity
- Momentum indicates a body's tendency to remain in motion
- Momentum (p) is the product of mass (m) and velocity (v): p = mv
- Net force acting on a particle equals the time rate of change of momentum
- ∑F = dp/dt
- Rapid momentum change requires a substantial net force
- Gradual momentum change needs less net force, and is applied in airbags
Impulse-Momentum Theorem
- Impulse (J) quantifies the effect of a force acting over time
- Impulse is key in collisions where forces are large but act for a short duration
- For a constant net force ∑F over a time interval Δt, impulse J = ∑F(t2 - t1)
- If force varies, impulse is the integral of net force over time: J = ∫∑F dt from t1 to t2
- Impulse-momentum theorem states change in momentum equals impulse of net force: J = p2 - p1
- Impulse is also the average net force multiplied by the time interval: J = Fav(t2-t1)
- Impulse and momentum are vector quantities
- Analyze by using components
Momentum and Kinetic Energy
- Momentum change depends on the time duration, impulse
- Kinetic energy change depends on the distance work
Conservation of Momentum
- Internal forces: Forces within a system
- External forces: Forces from outside a system
- Isolated system: No external forces acting on it
- Total momentum (P) of a system is the vector sum of individual momenta: P = pA + pB + ...
- Conservation of momentum says that in the absence of external forces, a system's total momentum is constant
Applying Conservation of Momentum
- Verify vector sum of external forces acting on the system is zero
- Treat each body as a paricle, and add both before & after sketches, include all components
- Define coordinate system with positive direction for each axis
- Identify variables with subscripts for before & after positions
- Write equations, plug all available data and compute the total momentum of a system
Elastic and Inelastic Collisions
- Elastic collision: Total kinetic energy conserved
- Examples include collisions between billiard balls or marbles
- Inelastic collision: Total kinetic energy is less after the collision
- Example is meatball landing on spaghetti
- Completely inelastic collision: Bodies stick together post-collision
- Momentum is conserved in all collisions where external forces are negligible
- In elastic collisions only, the total kinetic energy remains the same
Center of Mass
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Defined as the average position of all the mass in the system
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Total momentum P is the total mass M times the velocity of the center of mass vcm
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External forces determine center-of-mass motion
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Internal forces do not influence it
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If net external force is zero, center of mass moves with constant velocity
Rocket Propulsion
- Rockets propel themselves by ejecting exhaust, expelling mass
- Thrust is proportional to exhaust speed and rate of fuel ejection
- Exhaust speed is -Vex dm/dt
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