Define the principle of conservation of momentum .

The principle of conservation of momentum states that the total linear momentum of a system remains constant unless a net external force acts on it.

Two identical objects travel toward each other at the same speed. What is the total momentum of the system?

The total momentum is zero , because the two momenta are equal in magnitude and opposite in direction , so they cancel.

Since momentum is a .......... quantity, the momenta of the objects in a system must be added as vectors.

Since momentum is a vector quantity, the momenta of the objects in a system must be added as vectors.

Why is momentum conserved when two objects collide?

By Newton's third law , the two objects exert equal and opposite forces on each other for the same contact time, so the impulses are equal and opposite and the changes in momentum cancel.

Define an isolated system .

An isolated system is a system on which the net external force is zero .

What happens to the momentum of a system when the net external force on it is nonzero?

Momentum is transferred between the system and its surroundings , so the conservation of momentum principle is not valid for that system.

The velocity of the center of mass of an isolated system is .......... .

The velocity of the center of mass of an isolated system is constant .

True or False? In an isolated system, the momentum of each individual object stays constant.

False. Only the total momentum is constant. A change in one object's momentum is balanced by an equal and opposite change elsewhere in the system.

A collision is an event in which two or more objects come together and exert forces on each other.

What two assumptions are made in a collision?

The internal forces between objects are much larger than the net external force on the system The time interval during which the momentum changes is very short

State the steps for solving a one-dimensional collision .

Identify the objects in the system, making sure there are no net external forces Write the momentum of each object before and after the collision Write the total momentum of the system before and after the collision Apply the conservation of momentum principle Solve for the unknown quantity

In a one-dimensional collision, how is the direction of each velocity shown?

All velocities lie along the same axis , so direction is shown by a positive or negative sign and vector notation can be removed.

How is momentum conserved in a two-dimensional collision ?

Conservation of momentum is applied to the x -direction and y -direction separately , and the Pythagorean theorem is used to solve for the unknown.

If no external forces act on a system, the horizontal and vertical .......... of momentum are conserved.

If no external forces act on a system, the horizontal and vertical components of momentum are conserved.

True or False? A collision can only happen between two objects that are both moving.

False. Only one object needs to be moving. For example, a moving object can collide with a stationary object, and momentum is still conserved.

Define an explosion .

An explosion is an interaction in which forces internal to the system move objects within that system apart .

State two examples of an explosion .

Recoil of a gun after shooting a bullet Radioactive emission of a particle from an unstable nucleus

In a one-dimensional explosion of a stationary object, the ratio of the two masses equals the .......... ratio of their speeds.

In a one-dimensional explosion of a stationary object, the ratio of the two masses equals the inverse ratio of their speeds.

Why does the lighter object move faster in a one-dimensional explosion of a stationary object?

The total momentum stays zero , so the two momenta are equal in magnitude and opposite in direction. The object with the smaller mass therefore needs the greater speed .

How is conservation of momentum applied to an explosion in two dimensions?

It is applied to the x -direction and y -direction separately , using velocity components. The total momentum in each direction is zero before and after the explosion.

True or False? After a stationary object explodes, each resulting object has zero momentum.

False. Only the total momentum is zero. Each object has momentum, and the momenta add as vectors to zero.

Define an elastic collision .

An elastic collision is a collision in which the total kinetic energy of the system is conserved .

Define an inelastic collision .

An inelastic collision is a collision in which kinetic energy is not conserved , so the total kinetic energy of the system decreases .

Define a perfectly inelastic collision .

A perfectly inelastic collision is an inelastic collision in which the objects stick together and move with the same velocity afterward, losing the maximum amount of kinetic energy.

In an elastic collision, does the kinetic energy of each individual object stay the same?

No. Only the total kinetic energy of the system is conserved. The kinetic energy of individual objects can change.

State two examples of a perfectly inelastic collision .

Two lumps of clay sticking together after colliding A bullet becoming embedded in a wooden block (ballistic pendulum)

In an inelastic collision, some kinetic energy is transformed into other forms by .......... forces.

In an inelastic collision, some kinetic energy is transformed into other forms by nonconservative forces.

True or False? Momentum is not conserved in an inelastic collision.

False. Momentum is conserved in all collisions. Only the kinetic energy of the system decreases.

AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 4: Linear MomentumConservation of Linear Momentum

Conservation of Linear Momentum (College Board AP® Physics 1: Algebra-Based): Flashcards

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FrontThe Principle of Conservation of Momentum
Define the principle of conservation of momentum.
FrontThe Principle of Conservation of Momentum
State the equation for conservation of momentum.
BackThe Principle of Conservation of Momentum
$\sum {\vec{p}}_{i} = \sum {\vec{p}}_{f}$
${\vec{p}}_{i}$ = initial momentum, before the interaction (kg·m/s)
${\vec{p}}_{f}$ = final momentum, after the interaction (kg·m/s)

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Cards in this collection (35)

Define the principle of conservation of momentum.
The principle of conservation of momentum states that the total linear momentum of a system remains constant unless a net external force acts on it.
State the equation for conservation of momentum.
$\sum {\vec{p}}_{i} = \sum {\vec{p}}_{f}$
- ${\vec{p}}_{i}$ = initial momentum, before the interaction (kg·m/s)
- ${\vec{p}}_{f}$ = final momentum, after the interaction (kg·m/s)
Two identical objects travel toward each other at the same speed. What is the total momentum of the system?
The total momentum is zero, because the two momenta are equal in magnitude and opposite in direction, so they cancel.
Since momentum is a .......... quantity, the momenta of the objects in a system must be added as vectors.
Since momentum is a vector quantity, the momenta of the objects in a system must be added as vectors.
Why is momentum conserved when two objects collide?
By Newton's third law, the two objects exert equal and opposite forces on each other for the same contact time, so the impulses are equal and opposite and the changes in momentum cancel.
State the equation relating impulse to change in momentum.
$\vec{J} = ∆ \vec{p}$
- $\vec{J}$ = impulse exerted on the system (N·s)
- $∆ \vec{p}$ = change in momentum of the system (kg·m/s)
True or False?
In a collision between two objects, the change in momentum of object A equals the change in momentum of object B.
False.
The changes in momentum are equal in size but opposite in direction: $∆ {\vec{p}}_{A} = - ∆ {\vec{p}}_{B}$ .
State the equation for the velocity of the center of mass.
${\vec{v}}_{cm} = \frac{\sum m_{i} {\vec{v}}_{i}}{\sum m_{i}}$
- ${\vec{v}}_{cm}$ = velocity of the system's center of mass (m/s)
- $m_{i}$ = mass of each object (kg)
- ${\vec{v}}_{i}$ = velocity of each object (m/s)
State the equation for the total momentum of a system in terms of its center-of-mass velocity.
$\vec{p} = M {\vec{v}}_{cm}$
- $\vec{p}$ = total momentum of the system (kg·m/s)
- $M$ = total mass of the system (kg)
- ${\vec{v}}_{cm}$ = velocity of the center of mass (m/s)
How is the total momentum of a system found?
It is the vector sum of the momenta of the system's individual objects.
$\vec{p} = \sum m_{i} {\vec{v}}_{i}$
Define an isolated system.
An isolated system is a system on which the net external force is zero.
What can change the total momentum of a system?
Only a net external force.
What happens to the momentum of a system when the net external force on it is nonzero?
Momentum is transferred between the system and its surroundings, so the conservation of momentum principle is not valid for that system.
The velocity of the center of mass of an isolated system is ...........
The velocity of the center of mass of an isolated system is constant.
True or False?
In an isolated system, the momentum of each individual object stays constant.
False.
Only the total momentum is constant. A change in one object's momentum is balanced by an equal and opposite change elsewhere in the system.
Define a collision.
A collision is an event in which two or more objects come together and exert forces on each other.
What two assumptions are made in a collision?
- The internal forces between objects are much larger than the net external force on the system
- The time interval during which the momentum changes is very short
State the steps for solving a one-dimensional collision.
- Identify the objects in the system, making sure there are no net external forces
- Write the momentum of each object before and after the collision
- Write the total momentum of the system before and after the collision
- Apply the conservation of momentum principle
- Solve for the unknown quantity
In a one-dimensional collision, how is the direction of each velocity shown?
All velocities lie along the same axis, so direction is shown by a positive or negative sign and vector notation can be removed.
How is momentum conserved in a two-dimensional collision?
Conservation of momentum is applied to the x-direction and y-direction separately, and the Pythagorean theorem is used to solve for the unknown.
If no external forces act on a system, the horizontal and vertical .......... of momentum are conserved.
If no external forces act on a system, the horizontal and vertical components of momentum are conserved.
True or False?
A collision can only happen between two objects that are both moving.
False.
Only one object needs to be moving. For example, a moving object can collide with a stationary object, and momentum is still conserved.
Define an explosion.
An explosion is an interaction in which forces internal to the system move objects within that system apart.
State two examples of an explosion.
- Recoil of a gun after shooting a bullet
- Radioactive emission of a particle from an unstable nucleus
In a one-dimensional explosion of a stationary object, the ratio of the two masses equals the .......... ratio of their speeds.
In a one-dimensional explosion of a stationary object, the ratio of the two masses equals the inverse ratio of their speeds.
Why does the lighter object move faster in a one-dimensional explosion of a stationary object?
The total momentum stays zero, so the two momenta are equal in magnitude and opposite in direction. The object with the smaller mass therefore needs the greater speed.
How is conservation of momentum applied to an explosion in two dimensions?
It is applied to the x-direction and y-direction separately, using velocity components. The total momentum in each direction is zero before and after the explosion.
True or False?
After a stationary object explodes, each resulting object has zero momentum.
False.
Only the total momentum is zero. Each object has momentum, and the momenta add as vectors to zero.
Define an elastic collision.
An elastic collision is a collision in which the total kinetic energy of the system is conserved.
Define an inelastic collision.
An inelastic collision is a collision in which kinetic energy is not conserved, so the total kinetic energy of the system decreases.
Define a perfectly inelastic collision.
A perfectly inelastic collision is an inelastic collision in which the objects stick together and move with the same velocity afterward, losing the maximum amount of kinetic energy.
In an elastic collision, does the kinetic energy of each individual object stay the same?
No. Only the total kinetic energy of the system is conserved. The kinetic energy of individual objects can change.
State two examples of a perfectly inelastic collision.
- Two lumps of clay sticking together after colliding
- A bullet becoming embedded in a wooden block (ballistic pendulum)
In an inelastic collision, some kinetic energy is transformed into other forms by .......... forces.
In an inelastic collision, some kinetic energy is transformed into other forms by nonconservative forces.
True or False?
Momentum is not conserved in an inelastic collision.
False.
Momentum is conserved in all collisions. Only the kinetic energy of the system decreases.

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