3B5 Linear Momentum and Impulse Flashcards
Describe the functions and conservation of linear momentum, and explain the concept of impulse.
Define:
Linear momentum
It is the quantity of motion of an object, defined as the product of its mass and velocity. It has both magnitude and direction.
Represented as p=mv, where p is momentum, m is mass, and v is velocity.
Fill in the blank:
Momentum is a _____ quantity.
Vector
Momentum’s direction aligns with the velocity of the object.
Fill in the blank:
Momentum depends on both _____ and _____.
mass; velocity
Since momentum is calculated as 𝑝=𝑚𝑣, increasing either mass or velocity results in greater momentum. This explains why heavier or faster-moving objects are harder to stop.
A cue ball with a mass of 0.50 kg is moving at 0.10 m/s. Calculate its linear momentum.
0.05kg m/s
The equation looks like p=0.50kg×0.10m/s. Linear momentum is the product of an object’s mass and velocity. It is a vector quantity.
True or False:
Momentum is always conserved, even when external forces act on a system.
False
Momentum is only conserved in isolated systems where no external forces act.
How are momentum (p) and kinetic energy (KE) mathematically related?
Momentum (p) and kinetic energy (KE) are related through the equation: KE= p²/2m
Momentum (𝑝=𝑚𝑣) depends linearly on velocity, meaning it increases proportionally with speed. In contrast, kinetic energy (𝐾𝐸 = ½𝑚𝑣2) depends on the square of velocity, meaning a small increase in speed results in a much larger increase in energy.
What does Newton’s second law state about momentum?
The net force on an object is the time rate of change of the momentum: F = Δp / Δt.
This can also be expressed as F = mΔv / Δt.
What is the SI unit of momentum?
kg m/s
This unit comes from p=mv, combining mass (kg) and velocity (m/s).
State the law of conservation of momentum.
The total momentum of an isolated system remains constant.
This applies when no external forces are acting on the system.
Fill in the blank:
Momentum conservation is valid only in the absence of ______ forces.
external
External forces disrupt the balance, changing the system’s total momentum.
How does a game of billiards represent the concept of momentum conservation in real life?
The momentum of the cue ball is transferred to other balls upon impact.
Friction and spin may slightly alter the outcome.
How does the law of conservation of momentum explain rocket propulsion?
Rockets eject mass backward to create forward momentum, conserving the system’s total momentum.
This principle underlies Newton’s third law.
How do internal forces influence the conservation of momentum?
Internal forces within a system cancel out in action-reaction pairs, meaning they do not change the system’s total momentum.
Only external forces can change the total momentum.
Under what conditions is momentum not conserved?
When external forces (e.g., friction, air resistance, or applied forces) act on a system, causing a net force that changes the total momentum.
Non-isolated systems do not preserve total momentum.
List the conditions that must be satisfied for momentum conservation.
- The system must be isolated (no external forces).
- The total momentum before the interaction must equal the total momentum after the interaction.
Momentum conservation is a fundamental principle of physics, particularly in collisions and explosions.
What does the equation m1v1=m2v2 represent?
The conservation of momentum in an isolated system involving two objects.
Specifically when an object at rest moves after an interaction (such as recoil) or when one object transfers all of its momentum to another in a special case of elastic collisions. It is commonly used in elastic collisions where no energy is lost.
Define:
Impulse
Change in momentum caused by a force acting over time.
J=Δp, where J is impulse and Δp is the change in momentum.
Explain why impulse is greater for objects with higher momentum.
Greater momentum requires a larger impulse for the same rate of deceleration.
This is evident in high-speed collisions.
What role does time play in impulse?
Longer time duration for a force decreases the force needed for the same change in momentum.
This principle is applied in airbags and cushioned surfaces for safety.
What is the SI unit for impulse?
newton-second (N⋅s)
It shares the same units as momentum (kg⋅m/s)
What is the Impulse Momentum Theorem?
A force applied to an object for some amount of time causes that object’s velocity to change, or an impulse causes a change in momentum.
This is represented mathematically as J = Δp.
How are force and impulse related?
Impulse (J) is the product of force (F) and the time interval (Δt) over which it acts: J=FΔt.
Impulse also equals the change in momentum of the object.
Why is increasing collision time beneficial in safety devices?
Increasing time reduces the force needed to achieve the same momentum change.
This principle is applied in airbags and helmets.
Fill in the blank:
In a collision, impulse is the area under the ______ vs. time graph.
Force
The graph provides a visual representation of impulse.
True or False:
A large impulse always means a large force.
False
Impulse can also result from a small force acting over a long time.
How does impulse apply in baseball?
A longer contact time between a bat and ball increases the ball’s final velocity.
The impulse-momentum relationship is critical in sports dynamics.
Fill in the blank:
For a uniform object, the center of mass is located at its _______ _____.
Geometric center
Irregular objects require integration or weighted averages to find the center of mass.
How can the center of mass be determined for a system of two particles?
r =(m1r1+m2r2)/(m1+m2)
In this equation, m1 and m2 are the masses, and r1 and r2 are their positions. The center of mass lies closer to the particle with greater mass.
Define:
Rigid body
Object that does not deform or change shape when forces are applied to it.
The distances between points within the object remain constant. Rigid bodies are idealized objects in physics used to simplify the analysis of motion.
What is the correct approach to find the center of mass for a rigid body?
Use an integral to account for continuous mass distribution.
For example, this applies to calculating the center of mass for a graduated cylinder filled with water.
True or False:
The center of mass always lies within the object.
False
For hollow or irregularly shaped objects, the center of mass can lie outside the object.
Where is the center of mass located in a donut?
Within the empty space in its donut hole.
This contrasts with a human’s center of mass, which lies within the body.
What happens to the center of mass when a system moves?
The center of mass follows the same trajectory as if the total external forces acted on it alone.
This simplifies motion analysis in systems like rockets.
What is the relation between the center of mass and linear momentum?
The total linear momentum of a system is the product of the system’s total mass and the velocity of its center of mass: p=Mv.
M is the total mass, and v is the velocity of the center of mass.
How is the center of mass related to impulse?
The impulse applied to a system equals the change in momentum of the center of mass:J=MΔv.
External forces change the motion of the center of mass via impulse.
